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Summary

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SOVIET PHYSICS JETP A translation of the Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki Editor in Chief-P. L. Kapitza; Associate Editors-M. A. Leontovich, E. M. Lifshitz, S. Yu. Luk’yanov; Editorial Board E. L. Andronikashvili, K. P. Belov, A. S. Borovik-Romanov (Editor, JETP Letters), V. P. Dzhelepov, N. V. Fedorenko, E. L. Feinberg, V. A. Fock, V. N. Gribov, R. V. Khokhlov, l. K. Kikoin, I. M. Lifshitz, S. Yu. Luk’yanov, A.M. Prokhorov, D. V. Shirkov, G. F. Zharkov(Secretary). Vol. 30, No.6, pp. 973-1224 (Russ. Orig. Vol. 57, No. 6, pp. 1801-2253) June 1970 FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE* P. L. KAPITZA Physics Laboratory, U.S.S.R. Academy of Sciences Submitted August 8, 1969 Zh. Eksp. Teor. Fiz. 57, 1801-1866 (December, 1969) The main experimental results obtained in the course of an investigation of plasma in a filamentary high frequency discharge floating in the middle of a resonator are presented. An experimental ar rangement for obtaining a stable discharge is described; stabilization is obtained by rotation of the gas. The investigations are carried out primarily in an atmosphere of deuterium at a pressure of sev eral atmospheres. For an input power up to 20 kW the length of the discharge attains a value of 10 em. Spectrometric investigations and their theoretical interpretation lead to the conclusion that the dis charge consists of an internal cylindrical region filled with hot plasma at an electron temperature of the order of 106°K and of a cloud of partially ionized plasma (T = (7-6) x 103 °K) surrounding it. It is shown that the existence of such a high temperature is possible due to a temperature discontinuity at the plasma boundary; an explanation is proposed that this discontinuity arises as a result of a double layer at the boundary. The effective heating of the filament by HF current takes place due to the anom alous skin effect. Such an interpretation of plasma processes is experimentally confirmed by experiments on the ef fect on the discharge of a constant magnetic field (up to 25 kOe). A study is made of the ion tempera ture. The observed emission of neutrons is insufficient for the determination in terms of them of this temperature and cannot even be sufficiently reliably investigated in order to establish its thermonu clear nature. Other methods so far also do not give a reliable result for determining the ion tempera ture. The problem is considered as to how one could by means of magnetoacoustic oscillations and magnetic thermal insulation raise the ion temperature up to the level required for the production of a reliable thermonuclear reaction. Some preliminary experiments in this direction are described. The investigations reported here have been carried on for over ten years by the staff of the Physics Laboratory of the Academy of Sciences of the U.S.S.R.

INTRODUCTION heated and melted at one spot. This observation led to the thought that spherical lightning is a discharge which IN the course of development of high frequency (HF) is produced by HF radiation arising in storm clouds generators of high and continuous power we have con after ordinary lightning. Thus, a source of energy is structed in 1950 a planotron [[lJ, p. 115], which emit provided which is required to support luminosity of ted power of several kilowatts at a wavelength in the long duration accompanying ball lightning. This hypoth neighborhood of 10 em. When we passed this radiation esis was published in 1955.l2J Several years later after through a quartz sphere of 10 em diameter filled with we had constructed a more powerful generator of con helium at a pressure of 10 em of Hg a discharge was tinuous radiation which we have called a “nigotron [ [3, \ ignited in it which had a well defined boundary. The p. 7], we returned to the possibility of producing a free whole phenomenon was observed for several seconds HF discharge in helium. Indeed, in March of 1958 we since the walls of the quartz sphere became rapidly succeeded in obtaining in a spherical resonator, in which intense continuous oscillations of the H type oc 01 *Published by resolution of the Presidium of the U.S.S.R. Academy curred with a wavelength in the neighborhood of 19 em of Sciences, dated August 8, 1969. and which was filled with helium, a freely floating gas- 973 Copyright © by American Institute of Physics 1970

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974 P. L. KAPITZA eous discharge visually of oval shape. This discharge was produced in the region of a maximum of the elec tric field and moved slowly along a circle coincident with a line of force. Sometimes the discharge stopped along this line. Discharges of this type in helium could be observed up to a pressure of 9 atm. A further in crease in pressure was limited by the strength of the resonator walls. We have also obtained such floating discharges in argon, in carbon dioxide, and in air. It was most convenient to carry out the experiments FIG. 1.1. Diffuse discharges in helium stabilized by gas circula in helium and the discharge had a good brightness, was tion: a-p = 1.8 atm, Pa = 1.3 kW, b—p = 3.5 atm, Pa = 1.2 kW. Oscil easily “ignited” and, what is most important, no chem lations of E tye ( 1963). 01 ical reaction occurred in inert gases, while in air nitric oxide was produced in the discharge which reacted with the resonator walls. A photograph of the discharge in helium is given in Fig. 1.1. In the course of a further study of the discharge it was fOlmd that in actual fact the discharge does not always have a shape close to spherical, but can also occur in the form of a thin fila ment several millimeters in diameter and of length up to 4-6 em surrounded by a luminous cloud. It turned out that the spherical shape of the luminosity of the cloud, which we observed initially, owes its origin to a large extent to impurities in the gas. But if we take purer he lium, then the spherical luminosity almost disappears and one obtains a filament of ellipsoidal shape similar FIG. 1.2. Filamentary discharges in deuterium without stabiliza to the discharge in deuterium as can be seen in the pho tion by gas circulation, a-Pa = 2.9 kW; b-Pa = 4.5 kW; c-Pa= 6.4 tograph of Fig. 1.2. All the impurities which we tried kW, oscillations of H type (1961). 01 increased the luminosity of the eloud with the exception of hydrogen and deuterium. These gases, on the con trary, aided the production of the filamentary form of the discharge. The strongest influence on the luminos ity of the cloud was observed when 1-2 cm3 of acetone was mixed in with the helium. Then the discharge as sumed the shape of a sphere having a bright blinding white luminosity similar to ball lightning (photograph in Fig. 1.3). After such experiments the walls of the reso nator turned out to be covered with soot. In subsequent investigations it was established that even in a pure gas there exist two forms of the discharge. At low power input the discharge was of oval shape with poorly de fined boundaries, and glowed not very brightly emitting diffuse light (Fig. 1.1). Then as the power input was raised the discharge rapidly went over into the filamen tary form (Fig. 1.2). This phenomenon was observed most clearly in hydrogen and in deuterium at high pressures. As the level of the HF power was raised (it was sup plied to the resonator from below through a round quartz window) the length of the discharge increased, it began to float upwards in the helium into the upper FIG. 1.3. Diffuse discharge with an admixture of acetone without stabilization by gas circulation. p = 200 mm Hg, Pa = 0.6 kW, H part of the resonator sphere, and here a closed ring 01 ( 1960). could be formed of 8-10 em diameter, which floated in a stable manner in the upper portion of the resonator. A photograph of such a discharge is given in Fig. 1.4. teresting results. First of all, it turned out that the But more frequently, as is shown in Fig. 1.5, it stuck spectral lines were narrow and not smeared out, and, to the wall of the resonator. secondly, an intense continuous spectrum was observed. From the very beginning of the investigations a high As is well known, in a plasma the ratio of the bright degree of stability to the filamentary discharge was ob ness of the line spectrum to the brightness of the con served. For example, if an intense circulation of the tinuous spectrum of bremsstrahlung depends on the gas was produced, the discharge underwent fanciful electron temperature Te, and by measuring this ratio convolutions but did not go out, and the filamentary na it is possible to make an estimate of this temperature. ture of the discharge was not altered. A simple visual The higher is this temperature the more intense is the study of the spectrum of the filament already gave in- continuous spectrum compared to the line spectrum. [S; 61

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 975 difference in counts was reproducibly observed which indicated the presence of neutrons. The effect over a day of observation amounted to ~5%. This was insuf ficient in order to study in a reliable manner the regu larities in the radiation, but the existence of the effect was established with statistical reliability. It is evident that if the neutrons were of thermonuclear origin then their number should increase very rapidly with the tem perature of the ions in the plasma. It is natural to as sume that the plasma temperature would increase with the power supplied. In order to increase the neutron flux we began to increase the power supplied to the fil ament. Experiments showed that as the power was in creased the electromagnetic forces stabilizing the po sition of the filament in the resonator in its freely float FIG. 1.4. Ring discharge in helium without stabilization by gas cir ing condition turned out to be no longer sufficient. They culation. The reflection of the ring in the resonator wall can be seen. could not balance the force of buoyancy and the filament p= I atm,Pa= 1.8kW,H (1960). 01 began to float upwards and to stick to the resonator walls. Then we replaced the spherical resonators by horizontal cylindrical ones in which the oscillations were also of the form HOl’ With the aid of small air blowers (taken from a vacuum cleaner) a rotary motion of the gas was set up in the cylinder. Owing to the cir culation that was set up the filamentary discharge ceased sticking to the resonator walls, increased in size and the power supplied could be raised up to 20 kW. Experiments showed that in the course of this the filament underwent strong convolutions and began to break up into two parts. But the intensity of neutron emission did not increase significantly. Thus, it turned out that the neutron emission is not affected by the FIG. 1.5. Filamentary discharge in deuterium whose legs have stuck amount of power supplied, and we concluded that the to the resonator wall where its reflection can be seen. p = 1.8 atm, H 01 processes occurring in the plasma of the filament could (1961). be understood only by a study of the structure of the filament. A quantitative study of this ratio gave interesting re In experiments on increasing the power input great sults. At first we began to measure this ratio by exam stability of the discharge itself was observed and, just ining photometrically the photographs of the spectrum, as in the rotating gas, the filament underwent convolu then we began to do this in a simpler and more accurate tions and coiled in a most fanciful manner, but did not manner by projecting the spectral line on the screen of break up and was not extinguished. Of course, it was not a vidicon and by measuring the brightness in terms of possible to study the structure of the filament in view of the spread out image on a cathode ray oscillograph. its chaotic motion, and, therefore, the apparatus for the These measurements have shown that in accordance production of the filamentary discharge was altered in a with the theoretical calculations the electron tempera radical manner. In a cylindrical resonator the oscilla ture in the helium could not be less than 5 x 105- tions produced were not of the Ho1 but of the E01 type. 3 x 105 o K. We then went on to the study of a gas which This led to the fact that the stable position of the fila is simpler for theoretical calculations-hydrogen. Ex ment coincided with the axis of the resonator cylinder; periments on the measurement of the ratio of the inten in this case the stabilizing rotation of the gas did not sity of the bremsstrahlung and of the lines of the Bal lead to large chaotic displacements of the filament, it mer series continued to show that the electron temper almost did not undergo convolutions and preserved well ature must be greater than half a million degrees. The a shape close to that of an ellipsoid of revolution. possibility of the existence of such a high temperature In order to realize such an arrangement it became led us to replace hydrogen by deuterium in order to see necessary to develop a transformer of the oscillations whether neutrons might not be observed. of the Ho1 type generated by the nitrogen, into oscilla The method of measurement consisted of having two tions of Eo1 type which were fed into the resonator. counters constructed of a number of tubes filled with Since the impedance of the filament changed as its di enriched BF3. Each of the counters was in turn placed mensions were increased it was necessary to develop for 20 min near the resonator containing the filamentary variable coupling between the transformer and the reso discharge. Both counters were mounted on a common nator in order to achieve efficiency in supplying large frame in such a way that by rotating the frame one could amounts of power to the filament. The transformer was either raise them or move them sideways by about a of the spider type. The theory and the construction of meter and a half. For each counter separately the dif such a transformer have already been described by us ference was taken between the number of counts in the [l 7l, p. 7]. The “spiders” utilized here differed from near and the far positions. Experiments showed that a those previously de scribed only by the fact that they had

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976 P. L. KAPITZA rotatable legs and this enabled variable coupling to be of the skin-layer is considerably smaller than the elec achieved. The development of this whole experimental tron mean free path. Applying the theory of this process arrangement (it is described in the second part of Sec. 2) to plasma we obtain a value for the skin-resistance required more than two years, and after this it became which is in agreement with that experimentally meas possible not only to supply to the discharge a high level ured. These calculations are given in Sec. 6. Thus, we of power, but also to carry out more reliably and accu arrive at the conclusion that the existence of a free fil rately measurements of the dimensions of the plasma amentary discharge of the type observed by us is possi filament (of its length 2l and of its diameter 2a). A ble only due to the existence of the anomalous skin further significant improvement in our investigations resistance. Calculations have shown that in a cold plas was the development of an apparatus by means of which ma at the observed values of the current both for a con the image of the filament could be stabilized on the slit stant current and at lower frequencies such a high ab of the spectrograph, which was achieved by rotating a sorption of power cannot take place. mirror controlled by photocells. This enabled us to Another essential difficulty in explaining the exist make a detailed study of the emission spectrum of the ence of a hot plasma consists in the presence at the filament. In this manner we succeeded to measure in boundary of the plasma filament of a large temperature a more accurate manner the wi.dth of the spectral lines discontinuity. It is not difficult to calculate that elec in the different portions of the filament. They were trons striking the boundary with an energy correspond narrow (not greater than 3-4 A) and this according to ing to a temperature of 106-107 °K on penetrating dif the Stark effect corresponded te> a plasma density of fusely into the surrounding gas would give rise to a 1014-1015 cm-3• If we assume tllat the plasma is com thermal power flux of the order of 103 kW per cm2• pletely ionized, then at normal pressure such a density Therefore, in order to explain the absence of such a corresponds to an electron temperature of the order of powerful heat transfer one must assume that elastic 106 o K, and this agrees with the already described pre reflection of electrons occurs in the boundary plasma liminary observations on the relative intensity of the layer. The existence of such elastic reflection of elec continuous and the line spectra. trons in nature is already well known, it occurs in gas It is known from theory that the value of the electron discharge tubes and has a simple explanation. Elec density which we observe in the plasma can be explained trons hitting the tube walls from the inside penetrate in two ways. The first-and it would appear the more into the glass to a greater depth than ions, and as a re natural explanation-is that the plasma in the filament sult of this a double layer is formed on the surface the is cold, and its equilibrium temperature lies in the electric field of which reflects electrons from the walls range from 6000 to 7000° K. This in accordance with the without losses. We assume the existence of such a dou Saha expression gives a degree of ionization of 10-3- ble layer at the boundary of our plasma filament. In our 10-\ and this corresponds to the observed electron experiments the gas which surrounds the filament has a density. Another possible explanation consists of the density three orders of magnitude higher than the plas fact that the plasma is not and i.s therefore completely ma itself and can be regarded in comparison with it as a ionized, its temperature corresponds to its density and medium which exists as if in a different state. A de lies in the range from 106 to 107 °K. This explanation scription of the structure of such a layer and a quantita at first appeared to be very improbable, since it led to tive study of the possibility of existence of such bound a number of theoretical difficulties. A further experi ary conditions are given in Sec. 4. mental study of the filamentary discharge confirmed A further study of the filamentary discharge con ever more strongly the presence in the filament of hot firms that the discharge consists of an interior region plasma. It also turned out that the contradictions with of hot plasma at a temperature of the order of 106 °K the theory could be resolved. and of a relatively cold region surrounding it which we As is described below in Sec. 5, by measuring the shall refer to as a “cloud.” Such a structure of the fil coupling between the nigotron and the discharge it is ament can be seen in its photograph in Fig. 3.6 (cf., be possible to determine the absolute value of the field in low) taken at high values of the power and of the pres the resonator and, by assuming that the filament is a sure. conducting ellipsoid, it is possible to determine the cur Experiment shows that in such powerful discharges rent in it. Measurements have shown that the value of it is not possible to make a determination of the tem the current lies in the range 20-50 A. Here a signifi perature of the hot plasma in terms of the Stark broad cant difficulty arises in explaining the mechanism of the ening of the Balmer lines. It is well known that as the skin-resistance in the usual manner. According to the temperature of the hot plasma is raised the intensity of measurements on the filament the power absorbed the radiation from it diminishes. The cloud of cold plas amounts to several kilowatts; then, according to the ma surrounding the hot plasma inside the filament is at measured value of the current, the skin-resistance of a constant temperature and glow equally brightly, and the filament should be equal to a few ohms, but it turns this makes it impossible to study spectrographically the out that this value of the resistance is considerably interior less bright region of the discharge in the visi greater than the value which is calculated theoretically ble domain. It turned out to be possible to overcome for an electron gas on the basis of Coulomb collisions. this difficulty by measuring the temperature of the elec We explained this contradiction by the fact that a so trons inside the plasma in terms of its radiation in the called anomalous skin-resistance occurs in plasma. A microwave domain (100 fJ.). It is well known that in this similar mechanism for the absorption of the surface part of the spectrum it is possible to determine the current is well known in metals at low temperatures, it proper plasma frequency in terms of the threshold fre is possible only at high frequencies, when the thickness quency for emission, and in terms of it the density and,

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 977 since the plasma is hot, to determine its temperature. up a gas circulation sufficiently well ordered to produce A confirmation of the fact that the plasma is indeed a discharge which did not undergo great convolutions. hot is also given by the intensity of its radiation in the We give a summary of the results for the toroidal reso A). extreme ultraviolet region ( >c ::::J 1000 Measurements nator. During the whole time of counting of 500 hours show that bremsstrahlung (cf., Sec. 3) is particularly they were as follows: the first counter recorded 143 698 intense in this domain, and is higher by a factor of at pulses, the excess in the close position was 4380; in the least 108 than it would be if the plasma were cold. case of the second counter there were 160 442 pulses There exists a number of other factors which estab with an excess of 4842. Thus, the excess in the number lish the high temperature of the plasma. The most sig of counts lies outside the limits of statistical error, but nificant of them is the effect of a magnetic field on the we were unable to correlate it with the processes in the shape of and on the radiation from a filamentary dis filament. Not a single change in the conditions for the charge. When the filamentary discharge was placed in existence of the discharge affected the difference in the a magnetic field of intensity up to 25 kOe, it remained counts in a sufficiently noticeable manner. If the ob stable but a change occurred in its structure: it became served emission of neutrons were of thermonuclear ori longer and the diameter of its cross section reduced to gin, then calculations have shown that it would have as low as 30%, while the intensity of the radiation from corresponded to a temperature from 6 x 105 to 8 x 105 o K. it increased. These experiments are described in This temperature is not higher than the electron tem Sec. 7. The basic theoretical concepts of plasma proc perature and is therefore quite possible. But, based on esses show that such phenomena can take place only in the scale of the phenomenon and on the impossibility of a hot plasma. There exists also another set of obser relating it quantitatively to conditions under which the vations which cannot be explained by phenomena occur discharge occurs, it is not yet possible to regard that ring in a low temperature plasma. For example, the the thermonuclear origin of this emission has been homogeneity of the temperature, the stability of the proven, and one should for the time being regard its na shape of the filament, the less intense radiation from ture as not having been established. We have so far the interior region of the plasma as can be seen from been able to determine the lower possible limit for the the photograph of Fig. 3.6 (cf. below). ion temperature only by means of theoretical calcula It turned out to be possible to investigate by the tions (cf., Sec. 4). It is estimated as 105 °K, methods which we have employed, in a sufficiently com At the present stage in our investigations we assume plete manner, the electron structure of the filament and that the plasma obtained by us is hot and that the elec its density, and to determine the electron temperature, tron temperature in it is of the order of a million de but until now we have not succeeded in determining ex grees, while the temperature of the ions is probably perimentally with a sufficiently high degree of accuracy considerably lower. It is natural to pose the question of the temperature of the ions. In order to determine this the possibility of raising the ion temperature in a fila temperature one could utilize two methods. The first, mentary discharge to a level required for the reliable and the most reliable one, is based on the partial pres realization of a controlled thermonuclear reaction. sure of the ions. This partial pressure is the difference It is well known that the principal difficulty in ob between the total gas pressure in the resonator and the taining a high temperature in a plasma is the heat loss partial pressure due to the electrons, which is deter the main part of which is due to electrons since their mined in terms of the density of the electrons and their mass is small and they have a greater mobility than the temperature. Therefore, if one knows how to determine ions. In a plasma under the conditions of our filamen sufficiently accurately the temperature of the electrons tary discharge the heat loss due to electrons is small and their density, then it is possible to determine the ion because of the existence of a double layer, and, there ion temperature. Since this quantity is determined as a fore, one of the principal difficulties of obtaining a high difference, one requires good accuracy in determining temperature plasma disappears. Two other difficulties the density and the temperature of the electrons, which remain: overcoming the heat losses from the ions and we have not yet attained. We expect to attain it in ex the supply to them of the energy required in order to periments involving increased dimensions of the fila raise their temperature. Apparently both these difficul mentary discharge. Another method of determining the ties can be resolved by placing the filament in a longi ion temperature is in terms of the neutron radiation. tudinal magnetic field. From theoretical investigations The count of neutrons carried out by us could have given it is well known that for a sufficiently intense field when us, if they were of thermonuclear origin, reliable in the radii of the cyclotron orbits of the ions are less than formation on the ion temperature. the radius of the filament and when the time between In going over to resonators with oscillations of the collisions of the ions is great the heat losses in the Eot type and to the resultant increase in the power input plasma can become so small that the ion temperature to the filamentary discharge we continued our neutron can attain high values. count, but, as before, it did not increase significantly. Energy can be supplied to the ions in two ways: either We later constructed an apparatus involving a toroidal by means of a collective interaction with the electrons, resonator in which stabilization of the filament, as be or by the generation of magnetoacoustic oscillations. fore, was produced by rotation of the gas, and with its These oscillations arise in a plasma in the presence of aid we obtained an increase in the power supplied to the a magnetic field when a high frequency component is filament. In this apparatus we had considerably length superimposed on it. Both these processes have received ened the filamentary discharge and raised the power in little study theoretically and experimentally. The theory put to 40 kW. Because of the small dimensions of the of magnetoacoustic oscillations and the experiments that toroidal apparatus it turned out to be impossible to set have already been carried out are described in Sec, 8

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978 P. L. KAPITZA and give us a basis for assuming that it is possible to in the microwave domain were carried out together with achieve in the hot plasma of the filamentary discharge E. A. Tishchenko, and also with the creative aid of a conditions for obtaining ions of a temperature required number of comrades; the work involving counters was for the production of a thermonuclear reaction, but for carried out by D. B. Diatroptov, the investigation of os this it is necessary to increase in a significant manner cillations by L.A. Prozorova. V. I. Chekin, N. I. Kon the dimensions of the filamentary discharge. A priori it drat’ev, A. G. Nedelyaev, N. I. Milyukov and A. V. Leb may be seen that since the heat losses are proportional edev participated in carrying out the experiments. Con to the surface of the filament while the power supplied structors A. I. Degal’tsev, Yu. E. Saprykin, V. I. Tsvet by magnetoacoustic oscillations is absorbed in a volume, kov and A. D. Nikulin participated in the construction of then as the dimensions are increased the ion tempera experimental apparatus. A. N. Vetchinkin and K. A. ture will be increased. In this case it is necessary to Zhdanov participated in constructing electronic appara adjust the intensity of the magnetic field to the dimen tus. AU the apparatus was made in the machine shop of sions of the filament since for a given magnetic field the Institute. Master mechanics V. V. Aref’ev, A. M. the ion orbits attain a value which is close to the cross Goncharov, V. V. Khristyuk and S. A. Smirnov partici section of the filament and the input of energy by acous pated creatively. tic waves will not produce any further increase in the I am grateful for aid in theoretical developments to temperature. In determining the magnetic field this lim Comrades L. P. Pitaevskii, L. A. Vainshtein, and in the iting ion temperature is proportional to the square of initial stages to A. A. Abrikosov and L. P. Gor’kov. A the diameter of the filament. In order to obtain a re number of calculations and estimates were carried out liably measured thermonuclear effect the ion tempera by B. E. Meierovich and G. P. Prudkovskii. ture should be greater than 106 “K. In order to obtain this temperature it is necessary to increase the lin- 2. EXPERIMENTAL SETUP ear dimensions of our apparatus by a factor of 3-4. The possibility of utilizing a plasma filament for the The most laborious part of the investigations of the realization of a thermonuclear reactor will be investi properties of a freely floating plasma filament was the gated in another paper. design and construction of the apparatus itself for ob The aim of our further investigations is to increase taining a stable filamentary discharge of large size. the dimensions of the apparatus in order to raise the For this a high level of HF power was required. There ion temperature to that required for the production of fore, the first problem was the construction of a contin thermonuclear neutrons and thus to carry out a further uous HF generator. We developed such a generator of check of the correctness of the interpretation adopted the magnetron type to which we have given the name of by us for the phenomena observed in a filamentary dis nigotron. The theory and the design of this type of gen charge. erator have been described by us in detail [[3, 41, p. 7]. Until now in our investigations we have not increased The nigotron which we are now using to obtain a plasma the dimensions of the apparatus since the main difficulty filament has a continuous power reaching 175 kW. It was development of the apparatus itself for obtaining a generates oscillations of H01 type at frequencies corre stable easily observable filamentary discharge and de sponding to a wavelength of 19.3 em. velopment of methods for measuring its parameters. As we have already indicated in the Introduction, we Such development consisted of finding the correct con began our investigations with a study of discharges in struction of resonators, an efficient supply of HF power, resonators in which oscillations of the Ho1 type were etc. excited. These resonators were either spherical or Work of such an exploratory nature is associated cylindrical; in them the filamentary discharge at high with construction of a large number of experimental ar power “floated” in a sufficiently stable manner and not rangements and with their modification. In a small very fast along a circle in that region of the electric research institute such as ours work of this nature pro field where it had its maximum value. As the power in ceeds faster if it is carried out on a small scale. Now, put was increased the dimensions of the filamentary when the methods of observation have been found and discharge increased until it lost its stable position in the construction of the resonators in which the dis the resonator. In this case the filament simply floated charge takes place has been developed, one can under upward and assumed the shape of an arc which stuck to take experiments on a larger scale with a sufficient de the wall and at the point of contact heated the surface gree of reliability. until it melted. A photograph of such a filament stuck to The investigations described here have been carried the wall is given in Fig. 1.5. In order to ensure stabil out over several years and a group of scientific work ity of the position of the filament we utilized circular ers, constructors and mechanics has participated in circulation of the gas since under these conditions the them. lighter heated gas in the filament had a tendency to po A number of investigations the results of which we sition itself along the axis of rotation. In order to re shall mention here only briefly will be published in the alize effectively such systems of stabilization we had to near future with a more detailed description of the ex go over to resonators in which oscillations of the Eo1 perimental methods in the form of separate papers by type were excited. In order to achieve this we developed individual members of our group. a wave transformer of the spider type. The theory and The creation of all the apparatus and the experimen the calculations for such transformers have been de tation was carried out together with S. I. Filimonov; the scribed in [ 71• A further increase in the power of the optical investigations were carried out together with filamentary discharge was made difficult by the nature E. A. Narusbek, assisted by Yu. F. Igonin; investigations of the load of the filamentary discharge, since the power

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 979 absorbed in it was proportional to the intensity of the heated both from the high frequency of the field, and electric field E, and this does not correspond to the also from contact with the hot gas circulating within most advantageous load characteristic for a nigotron. the load. Circulation of the gas for cooling the quartz If the nigotrom is used over a wide range of power, then window is brought about by a centrifugal air blower 9 the power absorbed must be proportional to E2• There into which gas is admitted that had been previously fore, we had to develop an apparatus which enabled us cooled in the heat exchanger 10. to establish variable coupling between the generator and The load resonator 6 is tuned to the frequency gen the resonator. This was realized by the same spider erated by the nigotron by moving the piston 11. A reli transformer which was so constructed that the legs of able contact between the piston and the walls of the reso the “spider” could be simultaneously rotated. In this nator is guaranteed by a device which we have devel case the greater was the angle between the directions oped and to which we have given the name of a hydro of the legs and the radius, the greater became the cou seal. This is a thin walled copper tube which is placed pling. in a somewhat collapsed state into a channel machined A study of the plasma structure of the discharge in the piston. The tube is filled with oil. When subse showed that a study of the effect on the discharge of a quently additional oil is pumped into it pressure is gen constant magnetic field was of considerable interest. erated, the tube straightens out and presses tightly With this aim in mind we constructed a solenoid with a against the walls of the resonator; in this way a good diameter of the opening sufficiently large to accommo contact is formed between them. date a resonator which had an inner diameter of 20 em. The magnitude of the coupling between the resonator A description of and the construction of such a solenoid and the generator is determined by the identical rota but of somewhat smaller dimensions are given in l 81• tion of the legs 12 of the “spider” transformer. Special With a power input of 500 kW we could obtain in it fields channels are provided in the walls of the resonator, the up to 25 kOe. piston and the waveguide; in them for cooling purposes, We shall give a detailed description of our apparatus there is continuous circulation of distilled water which, in a number of subsequent papers together with a de in turn, is cooled in a heat exchanger by tap water. By scription of the experimental investigations. Here we measuring the consumption and the temperature shall restrict ourselves to giving only the schematic di changes of the circulating water we determine that part agram of the apparatus which is shown in Fig. 2.1. of the power which goes from the discharge to the walls The power input at a voltage of 18 kV is delivered to of the resonator. Another part of the HF power input is the nigotron 1. It is situated in the solenoid 2 which absorbed in the heat exchanger 17 which cools the gas produces a homogeneous field required for the genera circulating in the resonator. As we have already pointed tion of HF oscillations. In the resonator 3 in which the out, circulation of the gas in the resonator serves by nigotron is situated oscillations of Hot type are produced means of rotary motion to stabilize the position of the with a wavelength .\ = 19.3 em. These oscillations are filament. The gas is set in rotation in the following transformed by the spider 4 into ones of Eot type and manner: by means of the air blower 13 the gas is di they enter the wave guide 5 which cuts off oscillations rected along the two tubes 14 and 15 into both ends of of the Hot type. In the load-resonator 6 in which the the resonator 6. At the ends of the cylinder along its plasma discharge 7 is formed a number of standing circumference there is situated a number of inclined waves of wavelength A is produced. The coupling be nozzles, and, therefore, the gas entering through them tween the resonator 6 and the feeder waveguide is re acquires a rotational motion. Near the central section alized through the window 8 made of two concave discs of the resonator a number of openings 16 is situated of optical quartz. One of them is sealed into the wave through which the gas leaves the resonator and then guide 5 in such a manner as to guarantee a vacuum in returns back to the air blower through the heat ex it. The second quartz disc closes the entrance aperture changer 17. Naturally, in streaming through the reso into the resonator 6. Such an arrangement of two discs nator the gas in addition to the rotational motion around is associated with the necessity of cooling them by a the longitudinal axis also acquires a certain vortex mo stream of gas; otherwise they can become strongly tion with a radial component as is shown in Fig. 2.1 by thin lines with arrows. In practice it has turned out ‘f::2:s:Jt that a more stable position of the filamentary dis l0:-.6JS’(,~ charge is achieved when the circulation of the gas in ,J ,, .. these vortices in the region where the filament is situ 11 r , ·J6;;‘jclc,;c.;::;~~-.,;.L.”’!J_oc r IT\ ~~lfljl - ated has a direction from the periphery towards the center as is shown in the diagram. At first we utilized )lr~~t~~Ik af1~~ in our apparatus air blowers from ordinary vacuum cleaners, but later it turned out that the carbon brushes of the motors introduce undesirable carbon dust which on penetrating into the discharge burns up and contami ,; i7 ‘t] nates the gas in the resonator. For example, if the gas is hydrogen then methane is formed. We now use air FIG. 2.1. Schematic diagram of the apparatus for the study of a fil blowers of a special type with alternating current mo amentary discharge. l~~nigotron, 2~~solenoid, 3~~resonator, 4~~spider tors which have no brushes. In Fig. 2.1 we have also transformer, S~~waveguide, 6~~load resonator, ?~~filamentary discharge, 8, 19, 20~~windows, 9, 13~~centrifugal air blowers, 10, !?~~heat ex shown the outline of the solenoid mentioned by us. changer, ll~~piston, 12~~legsofthe”spider,” 14, IS~~tubes, 16~~anum Observation of the spectrum and of the shape of the ber of apertures for the passage of gas, 18~solenoid. discharge was made through a number of windows 19

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980 P. L. KAPITZA made in the wall of the resonator 6. These windows discharge could “burn” for a long time continuously have a diameter of 2-2.5 em and are usually made of and the experiments could last for hours. optical quartz discs of 5 mm thickness. Several such We have adopted the power Pa absorbed in the dis windows are situated in the central cross section of the charge as the principal characteristic of a filamentary resonator. For longitudinal observation of the dis discharge. This power was measured by the heating of charge window 20 has been provided. In order to be the water which served to cool the resonator 6 and the able to look through this window the rod for moving the circulating gas in the heat exchangers 10 and 17. The piston is made hollow. If necessary an endoscope can quantity of the circulating water was measured by con be inserted in it. sumption meters, and the temperature change was The configuration of the HF field in the resonator is measured by thermocouples. After each measurement shown below in Fig. 5.1. The axial component Ez of a check was made of the consistency in the balance be the electric field along the axis varies sinusoidally. The tween the supplied and the measured power; usually maxima of the field are separated from one another by this was realized within limits of 5%. The power Pa distances of the waveguide half-wavelengths A/2 (cf., was determined with approximately the same accuracy. Sec. 5). If the load resonator is tuned by moving the pis We determined the structure and the temperature of the ton 11, then for a sufficiently intense generation in the discharge by observing the radiation from it. The meth nigotron a breakdown occurs in the gas and at one of ods of measurement and the results obtained will be these maxima of the field a filamentary discharge lights described below. up. In order to guarantee that the discharge would oc In order to carry out these investigations success cur at the center of the resonator opposite the windows fully it was necessary that the discharge should be sta we constructed a special device which we have called a tionary as far as possible. For a number of investiga lighter. It consists of a thin quartz rod at the end of tions the circular circulation of the gas could not guar which a thin tungsten wire of length 2-2.5 em is at antee the required lack of mobility in the position of the tached to form aT. With relatively small oscillations, discharge. Therefore we have developed a special de but close to resonance, the quartz rod of the lighter is vice which could stabilize the image of the filament. A introduced through one of the windows 19 in such a way detailed description of this stabilizer will be given in that the tungsten wire is at the center of the resonator the course of describing our optical experiments, while and is situated perpendicular to the electric field. Then here we shall give only the principle according to which the rod is rapidly turned through 90° in such a way that it operates. Schematically the stabilizer is shown in the wire becomes parallel to the field, and then oscilla Fig. 2.2. The optical system of the stabilizer consists tions appear in it. If the HF field is sufficiently intense, of two lenses and two mirrors. A ray from the fila then corona discharge appears at its ends and the fila mentary discharge 1 passes through the lens 2, then un ment lights up. After this the rod is again rapidly ro dergoes two reflections from mirrors 3 and 4 set at an tated into its initial position and is taken away. Such angle of 45° to the direction of the ray and gives an im precautions are necessary so as not to melt the tung age of the filament 8 on the slit of the spectrograph. sten wire. The lighter is moved inside the sealed en One of the mirrors 4 can be rotated about a horizontal closure by means of a permanent magnet. axis. The purpose of this device consists of ensuring The resonator, the whole gas conducting system at the automatic rotation of this mirror in such a manner tached to it and the heat exchangers were so constructed that as the filament moves within the resonator its im- that the gas pressure could be raised up to 5 atm. Ex periment shows that at this pressure the filamentary discharge can exist freely and so far no indications have been observed that a further increase in pressure could limit the existence of filamentary discharges. We have carried out our investigations usually with deu terium since it has the advantage over hydrogen that it has a lower heat conductivity and, therefore, the dis charge requires less power. Experiment shows that both in hydrogen and in deuterium the filamentary type of discharge arises more easily and shows greater sta bility than in other gases. In Sec. 9 a brief description is given of experiments on obtaining discharges in gas mixtures. It was found that a small admixture of hydro gen to a number of gases facilitates the existence of a filamentary discharge. The gas which fills the resona tor is purified. If it is deuterium, hydrogen, or helium, this purification is carried out by means of passing it through a trap of activated charcoal cooled by liquid nitrogen. When in the case of some spectrographic in vestigations it was required to have in the resonator exceptionally pure deuterium and hydrogen, the gas fill FIG. 2.2. Schematic diagram showing the principle of the stabi ing the apparatus was subjected to continuous circula lizer of the image of the discharge on the slit of the spectrograph. ! tion through a cooled trap. This device is not shown in discharge, 2, 7-lenses, 3, 4-mirrors, 5, 6-photoresistors, 8-image of Fig. 2.1. In the apparatus described above a filamentary the filament, 9-frame, 10-magnet, 11-control unit.

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 981 age should remain motionless both on the aperture be tween the photoresistors 5 and 6, and on the spectro graph slit. It is evident that as the image moves in the plane of the photoresistors one of them will be illumi nated more strongly. As can be seen from the circuit shown in Fig. 2.2 usual for this kind of devices, this will result in a current appearing in the winding of the frame 9 situated on the axis of the mirror 4. Since the frame is situated in the field of the magnet 10 it begins to turn together with the mirror in such a direction that the image of the filament returns to a position symmet ric with respect to the photoresistors 5 and 6. If the image of the filament moves over to the other photore sistor then, evidently, a reverse motion of the frame will occur and, as a result, the image of the filament will tend to remain motionless on the spectrograph slit. FIG. 2.3. A sample record of the intensity of emission of the Dll By means of such a stabilizer it is possible to hold the line for a filamentary discharge across a diameter. Deuterium, p = 1.4 filament sufficiently motionless on the spectrograph atm. Curve 1-Pa = 8.0 kW, H = 1.6 kOe; curve 2-Pa = 8.7 kW, H = 21.7 slit that the filament diameter of 2-2.5 mm can be kOe. measured with an accuracy of 5-10%. The spectrograph used for our investigations was ISP-51 with a camera UF-90; at a wavelength of 4861 A it had a linear disper 2a,mm 10 sion of approximately 4 A/mm. The collimator slit can be slowly moved vertically and horizontally in the plane of the image of the spec trum by means of a micrometer. Its motion is trans mitted by means of potentiometer to a two-coordinate recorder and causes the motion of the recorder pen along the abscissa. The vertical deflection of the re corder was determined by the intensity of the light z passing through the slit and falling on the cathode of a photomultiplier. The horizontal motion of the vertical collimator slit determined the distribution of intensity o L-------~5--------,~o-------,~5------~u of the spectral lines. The slit could be replaced by a Pa, kW small aperture. Then one could measure the profile of FIG. 2.4. Curves of the dependence of the diameter of a filamentary the spectral line at different sections of the filament. discharge in deuterium on the power input. The collimator could also be provided with a horizontal slit which had a vertical motion; in this manner one could measure the distribution of intensity of monochro Zt,cm matic radiation across the filament. A sample of such a IZ 0 p•Zati4 I record is given in Fig. 2.3. Both curves represent the 10.0 .x• / > x t---- 4 p•J ~ at · m __.J: intensity of emission of the n 13 line for a filamentary />( ~ oyy discharge of power P a ~ 8-8.7 kW in deuterium at a 8.0 v ip= latm/ pressure of p = 1.4 atm. Curve 1 was obtained for a magnetic field of 1.6 kOe, curve 2 for a field of 21.7 kOe. We determine the width of the filament from 5.0 J 10 15 zof such a curve by the half-height denoted by 2a and FIG. 2.5. Variation in the length of a filamentary discharge in deu adopted as the external diameter of the filament. If the terium as a function of the power input. filament is regarded as a cylinder of homogeneous in tensity then the true diameter 2ao would be equal to produced on the screen of a television set where its (2.1) length was measured. The latter method has the advan The dependence of the measured diameter along the tage that it enables one to trace the oscillations in the middle of the filament on the power Pa is shown by the position of the filament which are due to the fluctuations curves of Fig. 2.4. The measurements were carried of the circulating gas, and this gives us the possibility out at different pressures p. As can be seen, it has a of observing and choosing such a gas circulation that relatively small effect on the value of the diameter of the filament in the resonator should be in its most quite the filament. The accuracy of these measurements is state. The dependence of the length of the filament on to a large extent determined by the degree of perfec the pressure and on the power input is given in Fig. 2.5. tion of the ope-.:-ation of the stabilizer. As can be seen, the length of the filament reaches a lim The length of the filamentary discharge was deter iting value as the power is increased, while the pres mined by different methods: either the filament was sure has little effect on the length of the filament. simply photographed, or it was projected through pin The most difficult problem was to ensure the axial hole apertures onto the screen of a vidicon and was re- stability of the filament, in particular when it attained

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982 P. L. KAPITZA limiting dimensions close to hall a wavelength. From put to the filament is increased its length and diameter Earnshaw’s theorem it is well known that the electric grow. When the length of the filament begins to ap forces acting on a dipole cannot hold it in a state of proach half a wavelength then the magnetic field will stable equilibrium. This theorem has been proven for also begin to influence the stability of its position as static fields, but if the length of the filament is small well as the electric field. When the electric field compared to a wavelength then it is applicable to its po reaches a value for which the length of the filament is sition of equilibrium in the resonator. It can be easily close to half a wavelength of the oscillation (in our case seen that in our case for oscillations of Eo1 type the fila this is approximately 10 em) resonance occurs and the ment will not be stable with respect to radial motion, energy of the magnetic field surrounding the filament but will have stability in the axial direction tending to becomes equal to the electrical energy. Then the value become situated in the region of maximum electric of the current in the filament will be determined only field. Therefore, in order to guarantee radial stability by its active impedance. In this case the angle between in our case it was necessary to introduce stabilization the phase of the oscillation of the electric and the mag by means of rotation of the gas. As has been noted al netic field surrounding the discharge and the phase of ready, the rotational motion of the gas is also needed in its own field will change to 90° and the force of interac order to prevent the floating of the filament upwards tion between the filament and the field in the resonator which occurs due to the fact that the heated gas in the will be absent. But if the filament could continue to in filament is of lower density than the gas surrounding it. crease in length and to pass through resonance, then the If one produces a rotational motion of the gas with an forces of interaction would change sign and the position angular velocity ng, then in the case of an inhomogenei of the filament would lose its longitudinal stability and ty in its density centripetal forces appear in the radial would acquire radial stability. direction which per unit volume of the gas are equal to A gradual development and improvement of the sys tem of gas circulation enabled us recently to raise con dFp-g—r.l2g D Cr r lp- d 1 · , (2.2) siderably the power input to the filament, to practically double it and to increase the length of the filament to where p is the gas density. 10 em, which corresponds to a dipole with oscillations Since the plasma in the filament has a higher tem equal to hall a high frequency wavelength. Experiment perature and a lower density than the surrounding gas, has shown that on reaching this length the filament then under the influence of the force Fn the gas will ceases to increase in length as the power input is in g move towards the axis of the cylinder. Owing to radial creased. Its diameter continues to grow but up to a electric forces, the filament itsell will be attracted to definite limit after which the filament begins to break up into two parts. Under these conditions it is observed wards the walls and will move somewhat in that direc that its longitudinal stability becomes less, and it more tion radially, but, on the other hand, owing to the rota easily jumps over along the axis of the resonator from tion of the gas, it will be returned towards the center by the stream of gas “blowing” on the filament in such a one maximum to another, but still there was enough direction as to return the discharge to the center of the stability that the filament could remain for a long time at the middle cross section of the resonator. The re cylinder. Such will be the mechanism of radial stability tention of the stability of the filament in the resonator of the filament created by the rotary motion of the gas cannot be ascribed due to the electromagnetic forces. surrounding it. The buoyant force arising in this case will be equal to: It also cannot be explained by the vortices formed in the eire ulation of the gas, since in Fig. 2.1 it can be (2.3) seen that the axial flow of gas produced by the vortex is directed from the middle of the filament towards the ends of the resonator, and could much more easily give where g is the acceleration of gravity. rise to instability in its position. We consider the fol In order not to have the filament floating upwards it lowing explanation to be the most natural one: the place is necessary that this force should be balanced by the centripetal force. Equating the last two expressions we at which the energy is supplied to the filament is situ obtain the following: ated in that region of the filament where the greatest current flows, and this region coincides with the one r = g (Q,~:.!· (2.4) where the electric field has a maximum along the reso This expression gives the value of the displacement of nator axis. If the filament moves along the axis then one of its ends moves into a region of low electric field the filament due to the force of gravity. The displace ment occurs in the horizontal direction and the stability and therefore less heat is supplied to it and it behaves of the position of the filament arises due to the “blow as if it were being extinguished. The other end of the ing” on it from above downwards. Experiment shows filament arrives at a region of strong fields and, con that there is no difficulty in creating a rotation of the versely, grows. In this manner the filament is retained gas which would guarantee the radial stability of the within the regions of maximum electric field. filament. Supporting the validity of this mechanism is the fact The experimentally observed stable position of the that in those resonators where the waveguide wavelength filament along the axis of the resonator can be explained A is much greater than the free wavelength A and, only to a certain extent by the stable position of a dipole therefore, a high degree of homogeneity of the field is in the electric field, since in our case the forces acting produced along the filament, the longitudinal stability of on a dipole will hold it in those regions of the actual the filament decreases. Experiment confirms that it is field where it has its maximum value. If the power in- not possible to obtain stable long filamentary discharges

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 983 when the diameter of the resonator is small. Converse the power input to the filament. From these curves it ly, by increasing the diameter of the resonator and de can be seen that the value of the broadening ~A is not creasing the waveguide wavelength A, we achieved great and does not exceed 4 A. The observed broadening greater longitudinal stability of the discharge and thus is somewhat greater than the Stark broadening, since a obtained a filament with a diameter of its cross section part of it should be ascribed to the apparatus effect, much greater than at the beginning of these experi which for our spectrograph was estimated to be equal ments. to ~Ap"" 0.3-0.4 A. Further, line broadening can occur due to the Doppler effect [[6l, p. 221], which for the Df3 3. SPECTRAL INVESTIGATIONS OF THE PLASMA lines is equal at half height to IN THE FILAMENT (3.6) The principal problem in the study of the plasma in The temperature of the deuterium plasma in the fila the filament is the determination of the electron density ment cannot be less than 7000-6000° since according to Ne, the ion density Ni and the neutral atom density N 0, this expression the Doppler broadening will always be and also of their temperatures Te, Ti, T 0• In view of greater than 0.2 A. Therefore, in order to obtain Stark the fact that in our case the plasma is not an equilib broadening we must subtract from the observed broad rium one these temperatures can be different. Since ening ~A the quantity AAp + ~AD, which is equal to 0. 5- our plasma is neutral and of high density we have the 0.6 A. equality As long as the power input to the filament in our ex (3.1) periments did not exceed 9-10 kW the observed Stark broadening was not less than 2 A., which according to For such a plasma the usual relationship exists be (3. 5) corresponds to an electron density of Ne ~ 1015• tween the temperature, density and pressure. If the Then, considering that the plasma is hot, the electron partial pressure of the electrons Pe, of the ions Pi and temperature is estimated by us in accordance with ex- of the neutral atoms p is expressed in atmospheres, 0 then we have p, ,~~c 1.:1:; .J0-20 .\‘eTc atm, p; = 1.35 ·10-22 .V;T; atm, + Po = L):J.jl\}·” .VoT~~ atm, p = Pe p; +Po, (3.2) where p is the gas pressure in the resonator.1> When FIG. 3.1. A sample record of the the plasma is hot, i.e., when it is fully ionized, we have DJ3 line in deuterium (curve I); ~AJ3 = 1.53 A, Pa = 12 kW, p = 1.6 atm. Also T,+T;=7.4·10”p/Ne, No=O. (3.3) reproduced is the record of the He line of the hydrogen gasotron (curve 2); If the temperature of the ions Ti is much lower than 6X13 = 0.4A. the electron temperature Te, then expression (3.3) as sumes the form 1’, = 7.4·10” pIN,, Tc ~ T;. (3.4) The first fundamental problem of spectral investi gations is to determine the value of the electron density z Ne. In the visible part of the spectrum this is accom plished most simply by means of the Stark effect by measuring the broadening of the spectral line. In the emission spectrum of the filament we selected for this purpose the hydrogen line Hf3 and the deuterium line /J zo D13. If we determine the broadening ~A and separate P0 , kW out that part ~AS which is due to the Stark effect [ [S l, FIG. 3.2. The width of the D13line as a function of the power input p. 22 5] , then we have to the discharge in deuterium. (3. 5) A. where ~As is expressed in As has been already described in the preceding sec tion the determination of the broadening of spectral lines is carried out by means of an automatic recorder which records the intensity of emission as a function of the wavelength. A sample of such a record of the D13 line is given in Fig. 3.1. For comparison we have also recorded there the H13 lines from a gasotron. On the curves of Fig. 3.2 we have given the broadenings ~A for D13 taken at different gas pressures as a function of r,mm FIG. 3.3. Distribution of the Intensity I and of the width L’l’A of the 1lEverywhere, unless stated otherwise, the temperature is expressed D13 line as a function of the radius of a discharge in deuterium. Pa = 6.5 in degrees Kelvin, and the pressure in absolute atmospheres. kW, p = 1 atm.

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984 P. L. KAPITZA the deep ultraviolet, the weaker emission from the in terior region of the filament and a number of other phe nomena. The second possible explanation of this phe nomenon, which, as will be shown, is completely satis factorily confirmed also by other observations, con sists of the fact that in reality the filament consists of two regions: in addition to the external region of diam eter 2a, there exists an internal region of diameter 2b. The plasma confined in this region is hot. It is com FIG. 3.4. Widths of the Dll and Hlllines as a function of the power pletely ionized, and therefore, n = 0, and the electron input to the discharge. 0 density is homogeneous and equal to ne. The cloud of diameter 2a surrounding the filament forms a cold pressions (3.4) and (3. 5) to be in the neighborhood of sheath of electrons which by the brightness of its radi 107 °K, In doing so it is assumed that the high frequency ation appears to mask the radiation from the internal current flows at a small depth along the exterior sur region of the filament. Therefore the density Ne which face of the filament and, consequently, the temperature we determine in accordance with the Stark effect refers over the whole cross section of the filament will be the to the electrons of the cloud and the density N of neu 0 same and the intensity of emission over the whole vol tral atoms corresponds to the temperature of the cold ume of the plasma must also be the same. plasma lying in the range 6000-7000°. The electron If this is so, then the curves recorded by the auto density in the cloud is low, the resistance is great, and matic recorder of the distribution of intensity across therefore there is practically no HF absorption in it, the diameter must coincide with half of an ellipse. In the oscillations penetrate inside and the current flows Fig. 2.3 we have already given a sample of the record along the surface of the interior region of the filament of the distribution of intensity of emission across a di of diameter 2b. The fact that inside the plasma filament ameter of the filament for the Df3 line. In Fig. 3.3 we the charge density was higher than on the periphery was have also given the distribution of the total intensity for observed from measurements of the broadening of the the line Df3, measured across a diameter of the filament. spectral line Df3 inwards along the filament radius. In From these two curves it can be seen that the distribu order to do this, as we have described in the preceding tion of intensity along the diameter differs from an el section, the slit of the collimator of the spectrograph lipse. We ascribe this discrepancy as bein£” due to in was replaced by a small aperture which was moved sufficient stabilization of the image of the filament on along the spectral line in different regions of the cross the spectrograph slit. In the initial stages of our inves section of the filament. The results of these measure tigations we considered this agreement to be sufficiently ments are shown in Fig. 3.3. From these curves it can good. be seen that the Stark broadening ~“-S is greater by a The insufficiency of such a method for the determi factor of several fold at the center compared to that on nation of electron temperature became apparent when, the periphery. as we have already stated, during the last half a year The most accurate measurement of the electron den we have succeeded in considerably increasing the power sity inside the filament turned out to be possible in input to the filament having raised it up to 15-17 kW. terms of the emission in the far infrared region of the The high power domain both in the case of deuterium spectrum in the range of wavelengths from 100 to 500 11· and in the case of hydrogen has been studied by us more We have utilized an already well-known method of plas closely. The results are shown in Fig. 3.4. As can be ma diagnostics [[6J, p. 329]. This method is based on seen from the curves, the broadening of the Hf3 and Df3 the fact that plasma cannot emit oscillations whose fre lines diminishes to 0.8 A. This left for the Stark broad quency is lower than the proper plasma frequency (the ening only 0.2-0.3 A, and this corresponds to an elec Langmuir frequency). The latter in our case lies in a tron density of Ne = 3 x 1013 and to an electron temper region corresponding to wavelengths in the range from ature T e = 3 x 108 °K. It can be easily understood that 100 to 500 11· The relationship between the electron such values are not real since, as simple calculations density ne and the proper plasma frequency v is de 0 show, such a plasma could not be realized by a high termined by the well-known expression: frequency current in view of the fact that at such a low electron density the corresponding skin-resistance (3. 7) would make it impossible to feed in large amounts of where the frequency is given in reciprocal centimeters. power. The investigations are made difficult by the fact that In order to resolve this contradiction two possible the intensity of emission by the plasma in this region of explanations were proposed. The first is that this is a the spectrum is low and one requires a spectrograph cold equilibrium plasma with a low degree of ioniza with a sensitive detector. There is no standard equip tion. In order to have the observed electron density in ment for this, and a special Fabry-Perot spectrometer accordance with the Saha expression their temperature using reflectors constructed from metal grids was de Te must be in the neighborhood of 6 x 103 °K and veloped. As filters we have utilized pressed polyethyl N 0 = 1018• As will be shown below, such a cold plasma ene gratings. A carbon bolometer maintained at liquid cannot explain a number of the observed properties of helium temperature served as the detector. The curves the plasma filament, for example, such as its electrical of Fig. 3.5 give in arbitrary units the reduced data of conductivity, the effect of a magnetic field on the struc the measurements of the intensity of emission by the ture of the filament, the high intensity of emission in filamentary discharge at different frequencies v. The

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 985 v curves shown there refe.r to a plasma filament at pres r ) •;, . L\ /. he kT, sures of p = 1 atm and p = 2 atm. From these curves q = 2.G·I0-·11n,.2 ( - k . l - , c e-”··.ti<T,S~l- I. . , - l.k . T - ,. ~ — f , it can be seen that as the frequency is reduced beyond 11 a certain frequency v 0, to which we shall refer as the q=1.1-10-”n .. 21 ’ — ” ;;- \ l ’! , gS.\1 ,\ - _; . _ - , -. h - e . -<’; - /,1 - ’, , (3.8) limiting frequency, the intensity of emission begins to \ J.-7 ,. I. 1./.‘f, E fall off sharply. We consider this limiting frequency v 0 where g is Gaunt’s logarithmic factor, E is the ioni to be equal to the proper plasma frequency and in ac zation energy, q determines the number of photons cordance with (3. 7) we determine the electron density emitted by a filament of cross section S along a length ne in the filament. If the filament were of homogeneous ~~ of the filament. density [[61, p. 331], the falling off of intensity at the A study of the intensity of emission in the short wave limiting frequency would be somewhat sharper than ob region confirms that inside the filament the plasma is served by us. This shows that in our case, as should be hot. expected in accordance with the model of the filament We adopt the already described model of our dis adopted by us, the plasma density is not homogeneous charge, but in further calculations for the sake of sim it increases from the periphery towards the center, and plicity we shall regard it as a cylinder which inside the measured electron density is situated in the hot re consists of a volume of radius b filled completely by gion of the filament. The reliability of the results ob ionized plasma of electron temperature Te and ion tained by our equipment was checked by replacing the temperature Ti, and of density ne which we determine filament in the resonator by its “model” in the form of from emission in the microwave region. a heated carbon rod which radiated as a black body. In We shall assume that the filament is surrounded by this case the measured intensity of radiation must be a cloud with an electron ion density Ne and a neutral proportional to the quantity Tv3 multiplied by the mag atom density N (the values of these densities are esti 0 nitudes of the external surface of the rod and by the mated in terms of the Stark broadening, expression figure of merit v /v of our spectrograph. Experiment (3.5)), with a cloud temperature which varies but little has confirmed that in the frequency region investigated and lies in the range 6000-7000°. Since this plasma is by us the intensity measured by our spectrometer fol partially ionized, the density Ne in the cloud, as can be lows this law. seen from Fig. 3.5, can fall off appreciably as we pro The data obtained on the temperatures and densities ceed from the center towards the periphery. of plasma filaments are shown in the Table. We have The intensity of emission ~ per unit surface of the also presented there data of other measurements ob internal region can be determined with an accuracy up tained for the same filaments. From the assembled to a logarithmic term by means of (3.8). This quantity data, for example, it can be seen that in the filament will be proportional to: for p = 1 atm and for a power input of Pa = 12.4 kW the electron density inside the plasma filament is ne (3. 9) = 7.3 x 1015 cm-3 and is greater by a factor of about 50 If we take into account expression (3.4), then we have than Ne = 1.4 x 1014 em -3 determined by means of the (3 .10) Stark effect. Knowing the density ne inside the filament one can estimate the electron temperature in accord The current flows over the surface of this region, the ance with expression (3.3). In order to do this accu skin-layer is thin and the electron heat conductivity is rately one must also know the ion temperature Tb and great, and, therefore, we can assume that the tempera this, as will be seen from subsequent discussion, until ture T e within the cylinder of radius b is homogeneous now has been achieved only by means of calculations of and the emission per unit volume is also homogeneous. low reliability. But since the ion temperature is in any The intensity of bremsstrahlung from the surface of case lower than the electron temperature, we can from the cloud surrounding the internal region will be pro expression (3.3) determine within a factor of two the portional to limits within which Te lies. From subsequent discus sion it will be seen that the ion temperature is consid Q. =(a—b)N.,‘,p2, To= COBSL (3.11) erably lower than the electron temperature and, there Experiment shows that for small diameters of the fila fore, the upper limit on the temperature T e should be ment and a low power input Pa the surface emission regarded as being closer to reality. from the core of the filament ~ is somewhat greater

J - •, . - - k - W - - I I - J’ - , · a - tm - - I ! I ~ · - ,, - ~ e - m - -~ I - ~ ·. · _: m _ _ __ ’ _ I _ t ”, : ’ ~ I - ” - """ P IT 6 -iI= ’ ( ‘K i) I …‘ll-., _.\ I 11) N t4 e c , m -~ s.s (1,~ :.n .s I I f ’-’-) I (i. ~ I 1.2 I ! l.fi 4.6 L I - ’ !.. ’ ’ i ’ ! i 1 l’ , 0 ,,- ) I ’ T ~~; 2 I, ,1 ,- 1 ) I J 7 1 . .5 ~ I 5 7 . .3 ~ I J 1 .~~ I 1 J. . D 35 ‘l 6 1. . ! 6 1 Some information about the plasma can be obtained than Qa -the emission from the external cloud, and by studying the intensity of the emission over the spec this, as we suppose, is the reason for the fact that at trum. The intensity in the range ~A/A of the continuous low power we observe a distribution of intensity which bremsstrahlung is determined by the following well differs from an ellipsoid, with an increased value in the known expressions [ [ 91, p. 330]: middle, as we have indicated at the outset, and as can

Page 14

986 P. L. KAPITZA ure 3.6. Similar reduced intensity in the volume emis sion of the middle portion of the filamentary discharge can be seen in the curve of Fig. 3. 7; it is calculated from a record of the intensity of emission made along the diameter for a filamentary discharge of high power. A copy of the original of this record is reproduced in Fig. 3.8. From the photograph reproduced here one can esti mate the ratio of the thickness of the cloud to the radius of the filament: FIG. 3.5. Intensity of emission from a filamentary discharge in deu terium in the far infrared region of the spectrum. Curve 1-p = I atm, y == (a- b) I a. (3.12) Pa = 8.8 kW; curve 2-p = I atm, Pa = 12 kW; curve 3-p = 2 atm, Pa = From the photograph of Fig. 3.6 and the curve of 14.7 kW. Fig. 3. 7 this quantity can be determined only very ap proximately: we take it to be equal to y = 0.6. One of the checks on the correctness of the model of the filament adopted by us can be a determination of the absolute value of the intensity of emission of the fila ment in the microwave region (expression (3.4)), since it can be obtained from a comparison with the emission of a black body of the same shape as the filament placed in the resonator. The surface emission of the plasma in this frequency range is the sum of the emission from FIG. 3.6. Photograph of a filamentary discharge in deuterium with the cloud and from the filament. According to the calcu an admixture of 5% argon at high power Pa = 14.7 kW and high pressure lations using (3. 8) it is by approximately a factor of 10 p = 3.32 atm. Length of the discharge 10 em. The left edge of the dis greater than the emission of a black body at a tempera charge is blocked by the window. Oscillations of E type ( 1969). 01 ture of 880° K. Within the limits of experimental error this is confirmed by experiment. Of great interest is the study of the intensity of emis sion in the far ultraviolet region, since in accordance with the model adopted in this region the intensity of emission from the cloud compared to the intensity of emission from the hot plasma in the filament must be come lower. The possibility of studying the plasma in this region is greatly limited by the fact that in the res onator the filament is surrounded by hydrogen or by deuterium at high pressure which very strongly absorb r,mm the ultraviolet radiation. This absorption, starting with FIG. 3.7. Distribution of the volume intensity of emission(,\ ,\ = 860 A, attains exceedingly high values. Thus, in our 5800 A) along the radius of a high power discharge in deuterium calcu apparatus over the distance from the filament to the lated from the curve of Fig. 3.8. Pa = 14.3 kW, p =I atm. counter this absorption can attain values of 10-400 of emission from the plasma [[91, p. 359]. Experiment shows that the intensity of emission from the plasma can be reliably measured by counters with lithium flu oride windows only for wavelengths not less than 1040 A. For a hot plasma of temperature T e = 106 °K FIG. 3.8. Sample record of the intensity of monochromatic radiation we obtain in accordance with (3.8) for these wavelengths along the diameter of a high power discharge in deuterium. Pa = 14.3 kW, that the emitted number of photons is equal to: p = 1.0 atm, 2a = 9.9 mm, ,\ = 5800 A. .‘11 q ::::= ;),.J·1017c-cJ· .. ;..hri’P’\},:cU2.\l-.-”, I.~ 5Ct-\ I. be seen in Fig. 3.3. But the same experiment also shows that as the power input is increased the tempera (3.13) ture T e also increases. The intensity of the surface emission of the filament, since it is inversely propor It is of interest to carry out a study of this radiation tional to T~·5, falls off rapidly. In this case the surface over a narrow range of wavelengths, and, therefore, we intensity of the exterior emission is of a more constant began by utilizing special counters which transmitted nature, since NeN varies but little. It turns out that at radiation selectively from 1050 to 117 5 A, which corre 0 high values of power and pressure conditions are cre sponds to ~A./A. = 0.1. These counters had a counting ated under which the surface emission from the core efficiency of 1%. The first experiments showed a high of the filament may become less than that from the ex intensity of emission in this region. The counter was ternal cloud; then when the distribution of intensity is situated at a distance of 15 em from the filament, but measured along a filament diameter one can observe a its window had to be stopped down by a diaphragm to an minimum at the center. This minimum can be seen in aperture of 2.3 x 10-6 cm2, otherwise it was saturated. the photographs of the filament, for example, in Fig- Under these conditions the counter gave more than 1000

Page 15

FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 987 counts per second, and this corresponds to a number of served value. Such a discrepancy both in terms of sign photons emitted by the filament in the range of 1015-1016 and in terms of magnitude is quite acceptable consider per second. Such high emission from the plasma in this ing the approximate nature of the quantities utilized in extreme ultraviolet region enabled us to go over to this quantitative comparison. If the plasma were cold, measuring it by a selectively sensitive ionization cham then at a temperature of T = 6.5 x 103 °K in accord 0 ber. We used an ionization chamber filled with nitric ance with (3.13) it would emit in this spectral region a oxide, with a lithium fluoride window with a quantum number of photons which would be less by a factor of at yield of 0.3 [[ 91, p. 221]. Such an ionization chamber least 108• Thus, this experiment practically excludes was sensitive only within the wavelength range from the possibility of explaining the observed radiation as 1050 to 1350 A. The window of the ionization chamber bremsstrahlung from a cold plasma. has a diameter of 0.8 em and is situated at a distance It would be of interest to extend these investigations of 15.4 em from the filamentary discharge. The window further into the domain of still shorter wavelengths, but in the resonator restricted entry of radiation from the this turns out to be impossible due to the absorption of filament over a length of D.l = 3 em. Into the path of ra the short wavelength radiation in its passage through diation on its way to the chamber one could insert a the gas surrounding the filament. At wavelengths short fluoride filter which limited the radiation up to 1240 A er than A = 860 A the absorption of the radiation by the or a q,uartz filter which limited the radiation up to deuterium at a distance of 15 em between the counters 1400 A. The photocurrent from the ionization chamber and the filament attains a value of exp ( -3000 p), where attained values of 10-7 A and could be measured well. p is the gas pressure. For still shorter wavelengths On the insertion of the quartz filter the current eased. the absorption diminishes rapidly and at a wavelength of This indicated that the photocurrent comes from radia A= 50 A becomes equal to 10-2•61>. At an electron tem tion in a region 300 A in extent in the wavelength range perature in the plasma of T e = 106 emission from the from 1050 to 1350 A. The observed radiation increased plasma in the filament could be observed from the greatly as the deuterium was purified. As was indicated “Maxwellian tail” if it were not restricted by the trans in Sec. 2, purification of deuterium was achieved by its parency of the window through which the radiation enters continuous circulation through a trap at liquid nitrogen the counter. temperature. Without such purification the measured In order to transmit the radiation this window must radiation in this region of the spectrum was less by a be thin, but at the same time it must be sufficiently factor of several tens of times and attained its greatest strong to withstand a pressure of several atmospheres. value only after an hour and a half or two hours of puri The only material suitable for this purpose so far is a fication by circulation. We explain such a great influ lavsan polyester film of thickness from 5 to 7 ll· The ence of impurities in deuterium by their great absorp main disadvantage of such a window consists of the fact tive power, which is well observed in the case of an that the elements N, 0, C which enter into the compo oxygen impurity. This is experimentally demonstrated sition of lavsan have a stron$ selective absorption in the when only 1 cm3 of heavy water is introduced into the region starting with A = 45 .A and shorter. This nar deuterium in the apparatus which has a volume of 60 li rows the range of transmission down to !l.A = 5-8 A. ters. In this case the current through the ionization The absorption in our lavsan films is estimated as chamber is reduced by a factor of several tens of 10-2.s. times. In order to shield the counter from very intense ra We further observe that the introduction of the fluo diation in the longer wavelength region A > 860 A (the ride filter reduces the current through the ionization absorption edge for hydrogen itself), the lavsan has to chamber to approximately one-third of its initial value. be coated with a layer of aluminum of thickness not less This shows that the average intensity of emission in the than 0.41J.. We estimate the absorption of such an alumi wavelength range from 1050 to 1250 A differs but little num layer as being equal to 10-2”5• Nevertheless, we from the intensity of emission in the range from 1250 still carried out an experiment with such a counter. In to 1350 A. Since in this range deuterium has no lines in this case we had a high background-several counts per its atomic spectrum, the observed radiation must be second, which, apparently, was due to the fact that the ascribed to bremsstrahlung. This assumption was con aluminum layer had very small pinholes and, therefore, firmed when a spectrum was taken with a vacuum spec could not completely shield the counter from radiation trograph. The spectrogram showed the existence of a in the longer wavelength region. The counting rate was continuous spectrum and at the position of the Lyman very uneven and insufficient for quantitative conclu a line (1215.7 A) an absorption band was seen. sions. It is of interest to note that in the hot part of the The calculations we have made have shown that un plasma we so far have been unable to observe any line der the conditions under which the experiments have spectrum, even when an admixture of oxygen, argon or been carried out, i.e., with an absorption on the way to helium is present in the deuterium. The emission from the counter of 10-12 of the emitted photons, the experi our filament in the range 1050-1250 A under the condi ments cannot be reliable. tions shown in the Table was approximately 5 x 1015 pho A more detailed analysis shows that a quantitative tons. We calculate the number of photons q by means of investigation of the filamentary discharge surrounded of (3.13) in accordance with the data in the Table. We by hydrogen or deuterium at a pressure of several at take 2a = 0.9 em, and then according to (3.12) we have mospheres by means of studying soft X-ray emission 2b = 0.36, D.l = 3 em, and for D.A./A. = 0.2 Te = 106 °K by the method of counters or photomultipliers can be and p = 1 atm we obtain the value 2 x 101~ which is ap carried out reliably only when the electron temperature proximately by a factor of four greater than the ob- is not less than 107 deg.

Page 16

988 P. L. KAPITZA the temperature of the hot electrons Te is proportional to a power of the diameter somewhat smaller than unity, I, rel. un. and also does not increase strongly with pressure. We roo expect to develop a method for the measurement of ra diation with the aid of which it will be possible to deter mine with a greater degree of accuracy the relationship between the temperature T e and the pressure p, the diameter 2a and the power Pa. We have also carried out experiments using mixtures of gases. From the outset a curious phenomenon was observed here. The argon lines are completely absent o,mm in our photographs, while the deuterium Balmer lines FIG. 3.9 FIG. 3.10 can be seen perfectly although with a reduced bright ness. In the same gas mixture, but in a Geissler tube, FIG. 3.9. Intensity of monochromatic emission per unit volume of a the spectral lines of Ar are quite pronounced. In exper discharge in deuterium as a function of the radius. A,., 4 730 A, p = I ments with an admixture of He, Ne, Ar and Kr gases we atm, 3.7 kW < Pa < 12 kW. have also observed a similar complete absence of the FIG. 3.1 0. Intensity of monochromatic emission per unit volume of a lines of their spectra in the filamentary discharge. Only discharge in deuterium as a function of the square of the gas pressure. when Xe was admixed a trace of its lines appeared. Pa,., 13kW. The most natural explanation of this phenomenon con sists of the fact that in a hot plasma the atoms are mul Measurement of the intensity of emission opens up a tiply ionized and neutron atoms are practically absent. number of possibilities for the study of the properties of Thus, the emission spectrum must be displaced into the the filamentary discharge. region of shorter wavelengths. The absence of line In Fig. 3.9 we have shown in arbitrary units the value spectra of admixed atoms in the glow of the cold cloud of the intensity I, measured on the basis of the current can be explained by their higher ionization potential from a photomultiplier in a small spectral interval situ than that for deuterium. In this case only Xe glows for ated at a sufficient distance from the emission lines which the ionization potential is lower. H13 and DtJ, as a function of the radius of the discharge. Finally, the reduced intensity of glow can be ascribed The curve of Fig. 3.10 represents the same quantity I to the fact that in a hot plasma the number of ions de as a function of the square of the pressure p2• Only creases. Since they carry a larger number of positive limited possibilities exist for the interpretation of these charges a smaller number of ions is required to neu results since the observed emission is the sum of the tralize the electron gas. emission from the interior region containing the hot A study of the spectra of impurities in the extreme plasma and the emission from the cloud. From the ultraviolet (i\ = 1050-1350 A) which has now been curve of Fig. 3.9 obtained at a constant pressure of started also shows a complete absence of line spectra p = 1 atm it can be seen that the value of I shows only of the impurities in the hot portion of the plasma. The a small decrease as the radius increases and for a gen absence of lines from multiply ionized atoms precludes eral discussion of the properties of the filament it can the possibility of using them for plasma diagnostics in be taken as constant. This shows that the intensity of terms of the Stark or Doppler effect, and therefore the emission per unit volume of the filament diminishes spectral radiation of the plasma in the extreme ultra as its diameter increases. From this it follows that the violet until now has opened up no new possibilities for temperature of the hot plasma increases with increas determining the temperatures of the ions and of the ing dimensions of the filament. From the curve of electrons in the plasma. Fig. 3.10 it follows that the value of I is proportional to the square of the pressure. Since from the curves of 4. HEAT LOSSES FROM THE FILAMENTARY Fig. 2.4 one can assume that the diameter of the fila DISCHARGE ment 2a for a given power level Pa is independent of the pressure, then the intensity of emission per unit As has been pointed out in the Introduction, the most volume is proportional to the square of the pressure. noteworthy feature of the filamentary discharge is the This indicates that the electron temperature T e does fact that although in the interior region of the filament not depend strongly on the pressure. More reliable in the electron temperature exceeds a million degrees, formation should be given by a measurement of the in nevertheless, the heat flux in this case into the sur tensity of bremsstrahlung in the ultraviolet, since it is rounding gas is small-one or two kilowatts per centi completely due to the hot portion of the plasma. We meter of the filament. It is not difficult to calculate carried out measurements of the intensity of the spec that if the electrons striking the boundary of the fila trum in the ionization chamber that has already been ment at these temperatures simply diffused into the described which is filled with nitric oxide. The difficul surrounding gas they would have carried away with them ty in interpreting these results is associated with the hundreds of kilowatts of power. We explain such ther fact that in this region we cannot stabilize the image of mal insulation by the fact that at the boundary of the hot the filament as we did in the visual domain by means of plasma a double layer is formed from which the elec the stabilizer shown in Fig. 2.2. If we assume that the trons are reflected without significant losses. The ex diameter of the filament of hot plasma 2b is propor istence of an analogous phenomenon has been known for tional to diameter of the cloud 2a, then we obtain that a long time. It occurs in cases when the plasma is

Page 17

FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 989 boooded by walls of a dielectric substance, for example, like glass or porcelain. It is well known that ooder such conditions even at appreciable pressures the elec trons in the plasma can have a high temperature without heating the walls strongly. This phenomenon has been FIG. 4.1. Diagram showing the distri explained long ago by the creation on the surface of the bution of the temperatures and the den dielectric of a double layer. The mechanism for the sities of ions and of electrons across a production of the double layer is simple. It consists of section of the discharge. the fact that because of their great mobility the elec trons on striking the surface penetrate into the dielec tric deeper than the less mobile ions. The volume charge of the electrons is formed in the dielectric electron density in the double layer by Ne· This layer deeper than the volume charge of the ions, and this cre also consists of neutral atoms of density No and of tem ates an electric field directed in such a way that elec perature To and of ions of density Ni at the same tem trons are elastically reflected from it. The poor heat perature. The electrons in the double layer will pri conductivity between the plasma and the walls is uti marily undergo elastic collisions with ions and with lized in gas discharge type of light sources at high neutral atoms which alter their direction of motion, but pressure. due to the large difference in the masses the transfer We assume that a similar phenomenon of thermal of kinetic energy will be small, and we neglect it in our insulation also occurs at the boundary of the hot plas ma in the filament, but with the difference that in place calculations. For example for Te = 100 V the cross of the dielectric wall the double layer is formed at the section q < 10-17 cm2 [[101, p. 150, Fig. 4.1.9]. There fore, we assume that the electrons in the double layer boundary between the plasma and the gas. In such a retain a temperature T e close to the one which they case a discontinuity is created between the temperature have inside the filament. Thus, the electrons moving in T of the surrounding gas and the electron temperature 0 the electric field E of the double layer will only change T e in the plasma. their density Ne, but not their temperature. We treat Calculation of the structure of the double layer and the processes in the double layer as a plane problem. of the processes occurring in it represents a complex We denote the distance from the booodary of the hot problem. Moreover, a number of quantities required plasma by x. Also in order to simplify the problem we for this which determine the collision processes be assume the filament to be in the shape of a cylinder. tween atoms, ions and electrons is, as yet, poorly de As can be seen from the Stark broadening (Fig. 3.3) the termined. Therefore, we limit ourselves to an approxi distribution of the electron density in the cloud has the mate consideration which has for its aim only to dem nature of an exponential function. We therefore assume onstrate the reality of the possibility of the existence of such double layers at the boundary between the gas and (4.1) the hot plasma. A model for the structure of the central cross sec wher~ ne is the density of the electrons in the hot plas ma, E is the average value of the field E in the double tion of the filament is shown in Fig. 4.1. Inside the cyl layer. Since the field E is created by volume charges inder of radius b is filled with hot plasma. Experimen one can assume that its value is proportional to Ne, tally we determine the density of its electrons ne (cf., and we assume Table). The radii b and a can be estimated from the darkened portion in the photograph of the filament in (4.2) Fig. 3. 6. Since the power in the filament is supplied to where Eo is the field at the boundary of the hot plasma the electrons at the surface of the hot plasma in the skin-layer, while the electron thermal conductivity in at x = 0. The difference in the density of the electrons Ne and of the ions Ni creates the electric field E of the hot plasma is great, the electron temperature T e the double layer. In accordance with the Poisson equa is higher than the ion temperature Ti. Therefore, the tion we obtain electron temperature can be determined in accordance with (3.4) in terms of the density ne. (4.3) The heat losses suffered by the power input to the filament Pa occur in two ways. A considerable frac Since the quantity eNid is large, while the field E is tion of the electrons is reflected without losses from small, we can practically take the double layer, but still a portion of their energy will (4.4) be utilized to make up the losses occurring in the bound ary layer as a result of the diffusion and the recombina The partial pressure created by the electrons at the tion of the ions. We denote the power spent in maintain boundary will be transmitted through the electric field ing the double layer by Pa rp. The other part of the pow to the ions, and, therefore, in accordance with (4.1) and er Pa(l - rp) is transmitted to the hot plasma by the (4.2) we have heat exchange between the electrons and the ions, raises r the ion temperature up to Ti and then by means of the Pe = e .l 1V,Edx = ’ E 2 ~ /J ~ : n, ~ . kl’e. (4.5) ordinary heat conductivity is transferred to the sur 0 rounding gas. Since we also have p e = nekT e• then We assume that the double layer begins at the bound ary of the plasma filament of radius b. We denote the Fo = 2£. (4.6)

Page 18

990 P. L. KAPITZA We determine the average thickness of the double layer: MiNi i!Ni -,;:;-=fit· (4.12) (4.7) Treating a as a constant quantity and utilizing expres sions (4.8), (4.9) and (4.12), we obtain The electric field E pushes the electrons from the double layer back into the plasma, while the ions move in the gas in the opposite direction until they recom -ialeE;N;-i = - 2nqom;v;N ?-. (4.13) bine with the electrons. This process of the motion of Utilizing expressions (4.1), (4.2), (4.3) and (4. 7) and the ions in the gas is associated with liberation of heat, differentiating we find and this basically represents the expenditure of the power Pa<P which is utilized to maintain the double (4.14) layer. We evaluate this power. In moving through the gas an ion after a time interval Ti undergoes a colli From this expression, according to the experimental sion with neutral atoms. The average increase in the velocity which the ion has acquired during this period data quoted above we obtain a= 1.6 x 10-10-4 x 10-11• is given by These values are close to the calculated ones [[11 J, p. 667]; thus for a temperature of T0 = 6500° and Ne

l

~.i·= e

E T j, (4. 8) = 7.3 x 1015 we have a = 3 x 10-10• For a plasma subject 2mi to our conditions the value of a is poorly known both experimentally and theoretically. In accordance with where mi is the mass of the ion. The value of T i is the theoretical paper by Gurevich and Pitaevskii, at equal to [UJ high gas pressure a depends on the gas density and on 1; = 1 I l]o.\‘oc;, (4.9) its temperature: where q0 is the cross section of the neutral atom. The n <:r.>No!T”•. (4.15) energy required to maintain the double layer is equal to the work done as the ions move in the electric field E. If such relations actually hold, then from (4.10) and (4.14) one can see that the power which is expended in Then the power expended after taking into account the maintaining the double layer does not depend strongly preceding expressions is equal to on the temperature, but increases with the pressure. The double layer has a surface tension S which is (4.10) equal to the energy of the electric field: In this expression one can estimate all the quantities. ‘r Let us take the example which we have already consid t S’ = 8 1- rr • \ J n !. o - d X. (4 .16) ered (cf., Table). For deuterium we have b = 0.18, 0 Te = 106, ne = 7.3 X 101\ No= 1018, To= 6.5 x 103, vi Utilizing expressions (4.2), (4.6), and (4.7) we obtain = 7.4 x 105. According to the photograph of Fig. 3.6 one can take the average thickness d of the double layer to (4.17) be equal to d = 0.2 em. The least well determined quan tity is q0-the value of the cross section for the colli This quantity is not large and, apparently, should not sion of neutral atoms with ions. This cross section is exert any appreciable influence on the structure of the the sum of two quantities: qp-the cross section for a filament. collisions in which charge exchange between the ion and The investigations which we have carried out show the atom occurs, and qn-the cross section for a colli that as yet there is no possibility of carrying out a com sion in which the energy is equalized. Both these quan plete numerical estimate of the processes in the double tities (cf., [101, pp. 150, 285) increase rapidly with de layer, but the adopted model for the structure of the creasing temperature. No measurements are available filament agrees with the experimental data obtained in for such low temperatures as exist in a cloud with T 0 the course of our study of the plasma in a filamentary = 6500 deg. discharge. Extrapolating known data one can estimate that q0 We consider the process for the removal from the lies within the limits q0 = (1-3) x 10-14• We then obtain hot plasma of the other part of the power Pa(l- <P). Pa<P /l = 2-0.7 kW /em, which does not contradict the For this it is first necessary to calculate the heat trans experimental values of Pa/2l referred to the middle of fer between the ions and the electrons. This heat ex the filament which lie within the limits 2.5-1.5 kW. change can occur in two ways: the first is the well It is of interest to determine the value of d-the av known mechanism of Coulomb collisions; the second is erage thickness of the double layer-in terms of a the heat transfer involving a collective interaction, but the recombination coefficient for the ions and the elec no method of calculating it has yet been found. But the trons. The recombination coefficient is defined by the transfer of energy between charged particles in virtue following relation: of their Coulomb interaction can be reliably calculated. At the basis of this calculation lies the quantity T eq iJ - J. = Yi -a;\..-r’.’ (4.11) which defines the average time for the redistribution of ilt energy in a collision of two types of charged particles If we consider the element dx in the double layer and of masses m1 and rna characterized by different tem determine the material balance, then we have peratures T1 and Ta. The time T eq required for equa-

Page 19

FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 991 lizing the temperature of the mixture is given by the == (4.27) ’ following expression, l121, p. 13 5: ‘tj A ne From this we obtain T,·” = 8JI 3 Z :tn m ,e1 1 Z m 1 ” Z k z ‘l , , \ ( ~ Tt -t , - T m 2 2 )”’ ’ (4•18) c ·= 6.2 A ’ - ’ 1 / Q m — ; 1 9 ’ % = 2,5. (4.28) where Z 1 and Z2 are the charges of the ions, while A If we set r = b and assume that the temperature of is a logarithmic term. In the hot plasma of the filament the ions at the center Tio is considerably greater than interaction occurs between electrons and ions. The Tib at the boundary of the hot plasma which we assume mass of electrons is small compared to the mass of to be equal to the gas temperature, we then have deuterium ions, while the electron temperature is usu l””’ • ally much higher than the ion temperature, and, there . -[ %+1 Pn(l-<P) (4.29) fore, expression (4.18) can be simplified in the follow T,o- 4:tC 21 ing manner: For the example under consideration we obtain under 1 mi(kTe)‘f, the condition (4.22) Teq =- __ _ , Zt = Z2 = 1, m; ~ m •• (4.19) G.7 e’l’me.\ne T;o = 9·10’ •K. (4.30) The power Pa(l- cp) which is transferred from the The temperature of the ions in the plasma obtained electrons to the ions in the central section of the cylin in this manner is considerably lower than the electron drical filament is equal to temperature and increases slowly with increasing pow Pa n.(T,-T;)k[ er input. -(1-<P)=nb2- kWJ1. (4.20) An experimental determination of the ion tempera 2/ T,.,1 ·1010 ture in the hot region of the plasma in the filament is of << Under the condition Ti T e we have considerable interest. The most reliable determination P” 6.7n,.0e~ym.A l of the temperature Ti could be realized by determining

2 ( 1 1-’!’) = ItiJL lO - ” - ‘m — c - ( ~ kT — ,. - ) - ’, , [kW. (4.21) the partial pressure Pi due to the ions. From expres sion (3.3) it may be seen that for this it is necessary As an example we consider the same experimental data only to determine with sufficient degree of accuracy the from the Table for the filament p = 1 atm, Pa = 12.4kW, temperature Te and the density Ne. Until now we can b = 0.18 em, Te = 106 °K, ne = 7.3 x 1015• (We have not measure these quantities in the plasma of the fila used these data also in considering the processes in the ment with an accuracy required for this purpose, al boundary layer.) We find that the power which can be though with an increase in the scale of the experiment transferred from the electrons to the ions is equal to this will apparently become possible. Pa(l-lj)) /:‘.1=2 kW/cm. (4.22) A second experimental method for determining the ion temperature is in terms of the emission of neutrons Since in the central portion of the filament we have by the filament. As has been pointed out in the Intro Pa/2l approximately equal to 3 kW /em, then a sig duction such emission is observed and it corresponds niicant portion of the power can be transferred to the to a te~perature of the ions in the plasma of (6-8) ions. x 105 °K, This temperature is lower than the electron We evaluate the temperature Tio of the ions at the temperature, and, therefore, it is possible to attain it, center of the cross section of the filament. We consider but since in our experiments the number of neutrons first the general problem of radial heat transfer in a emitted is small compared with the background (from cylinder. We assume that over the whole cylindrical 3 to 5%), the accuracy of the experiment does not per volume the power transferred from the electrons to the mit us to associate this emission quantitatively with ions is the same; then the equation for the heat transfer the state of the plasma. Therefore it does not appear is given by to us to be possible to treat the available data as a basis for determining the ion temperature. (4.23) There exists still another interesting experimental possibility for estimating the ion temperature, even Since the heat conductivity depends on the temperature though it is of an indirect nature. We have experimen we assume: tally studied the thermal diffusion of ions in the fila :J\{ = CJ’z. (4.24) ment. In order to do this we have compared the inten sities of the H13 and D13 lines in the spectra of hydro Then, integrating (4.23), we obtain gen and deuterium. For high power input to the fila . [· -(,!\}__)z+t] __ ment these lines are sufficiently narrow and well sepa %+1 Pa(1-·<e) (4.2 5) :Jl’T” 1 J’. - ;, ”l rated so that from their relative intensity we could de w l:t .:.. termlne sufficiently accurately the composition of an H where Tio is the temperature at the center, while Ti is and D mixture. The most detailed study we have made the temperature at a distance r from the center. The was of a mixture of 50’-0 deuterium and 50% hydrogen. heat conductivity for the ions is equal to (cf., l 131 The recorded curve for these lines is given in Fig. 4.2. p. 192): As can be seen, no difference (larger than ± 3%) was ob served in the intensity and width between the H13 and (4.2 6) D13 lines. Experiments were carried out at different where values of the power and for other concentrations of hy-

Page 20

992 P. L. KAPITZA temperature. Another possibility to remove this contra diction is to assume, conversely, that in this region the ion temperature is close to the electron temperature, Ti ~ Te. In this case in the hot plasma there would again be no temperature gradient for the ions, and the ion temperature would be sufficiently high to be able to explain the observed neutron flux. Jlf (discharge) Such an explanation also encounters great difficulty, since for this one must assume that at the boundary of the hot plasma a temperature discontinuity exists for ions as well as for electrons. To justify the possibility of the existence of such a second discontinuity appears FIG. 4.2. Record of the Oil and Hillines in a mixture of 50%0 and to be difficult, and this explanation for the time being 50% H. Pa = 13 kW, p = I atm. The spectrum of the discharge has been appears to be of low probability. Thus, on the basis of recorded twice. available experimental data and theoretical concepts it does not appear to be possible for the time being to de termine the ion temperature and its distribution across the diameter of the filament. We expect that it will be possible to solve this problem as the scale of the ex periments is increased. 5. THE ELECTRIC CHARACTERISTIC OF A FILAMENTARY DISCHARGE In this section we describe the method for the ex perimental determination of the current, of the skin resistance and of the other parameters of the filamen tary discharge which determine the electrodynamic FIG. 4.3. Record of the distribution of intensities of the Oil (curve I) processes occurring in it. and Hil (curve 2) lines along the diameter of the filament for the same The resonator in which the discharge takes place is mixtureasinFig.4.2;Pa= 13kW,p= I atm. shown in Fig. 5.1. We denote the length of the cylinder 1 of the resonator by L and its radius by A. In the reso drogen and deuterium. In all these experiments the nator, n half-wavelengths A of E 01 type will be set up. We denote the wavelength of the eigenoscillations by Ao, relative intensity of the Hf3 and D(3 corresponded to the and the critical wavelength by A.c· There exists the well prepared mixture and did not vary with the power input known relationship to the discharge. We also measured the intensity of the Hf3 and D(3 lines across a diameter of the filament. The (5.1) record is reproduced in Fig. 4.3. As can be seen, in the mixture of 50% Hand 50% D the distributions of in For small changes t.L in the length of the resonator L tensity of H \{3 and D(3 coincide within the limits of ac the wavelength of its eigenoscillations A.0 will be altered curacy of the record. This shows that over the whole by t-A.o: cross section of the filament the ratio of the densities l!.i.o = y!J.L, of deuterium and hydrogen remains constant. Thus, we could discover no excess of hydrogen at the center of where the filament due to thermal diffusion in the plasma in spite of the fact that with the ratio of the masses of the y=2- ( -\}· 0- )3 , LHo<;;;f.o (5.2) n .1 hydrogen ions to the deuterium ions equal to two, and We denote the variable electric field at the center along for a temperature gradient determined from expres the axis of the resonator by E and its amplitude by li: sion (4.25), one might expect in the hot region of the 0, 0, and then the high frequency field in the resonator will plasma a well pronounced difference in the densities of be given by the following well known expressions: deuterium and of hydrogen. This contradiction appar

2n ently indicates that the mechanism adopted by us for Ez=Eolo(kcr)cos-z, Ilz=O, the heat exchange processes of the ions differs from the A actual one. It is possible to attain in two different ways E , ,.=-E .,_ o; A :- o !i(k,r)sm . -;; 2 ; n - z, 11,=0, the result that within that part of the filament where the t H e \{3 m a p n e d r a D tu \{3 r e l i g n r e a s d a ie r n e t . e m T i h t e te f d i r t s h t e w io ay n s o f s h a o c u h l i d e v h i a n v g e t a h is E~ = 0, !I~= iE - 0 li(k,r) cos 2 A - n z , is that the ion temperature should in general be much k, = 2n /i.e, Ac = 2.61 A. (5.3) lower than the one determined from the Coulomb inter The oscillations occur with a frequency w and a wave action (expression (4.29)). This explanation encounters length A. 0• W z, e denote the length of the filamentary dis great difficulties in the fact that the factors considered charge by 2 the total current in an arbitrary cross by us such as, for example, the collective interaction, section by I, and the density of the electric charge should increase the heat exchange between the electrons along the filament by o. From the law of conservation and the ions and, consequently, should increase their of the quantity of electricity we have the relation

Page 21

FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 993 n·4 charge is distributed along the length of the filament

•,t and is equal to

t - ’ 5t 1ll,q0 E 0 = t5E,z dz. (5.11) ” z -l When in our experiments the length of the filament is small compared to A/2, then one can take the electric field Ez to be constant along the filament, and we then FIG. 5 .I. Structure of the HF field in a resonator for E01 oscillations. have: l S lll,qo =’ 6~ dz A~ 21 E - E (5.12) ’ ’ z- O· .!!_ = !!:… = iroll. ( 5. 4) -I iJz dt We denote the eigenfrequency of the oscillations of the By denoting by q the quantity of electricity carried filament by np. We then have across a cross section we have (5.13) dq I= dt= i<uq. (5.5) Differentiating the Lagrangian we obtain two fundamen tal equations for the oscillations: We denote all the variable quantities referring to the central section of the filament z = 0 by the subscript [~~·-( 1~~ :”)+iwR]qo-J-MeEo=O, zero; then for the amplitude we have D.[( :J+ ]Eo-J-M,qo=BEfo, (5.14) I 1- lo=tjo=iroqo==iu> 0 ~ lfdz, l0 =loei“‘t. (5.6) where \{3 E 0 is the force giving rise to the forced oscil For the description of oscillatory processes in our lations, [If 0 is the field in the feeder waveguide. Here we have also added terms with an imaginary coefficient system we choose as independent variables the intensity which determine the dissipation of energy in the fila of the electric field at tqe center of the resonator E and its time derivative E 0, and also q 0 and <io = Io o 0 v er i m ty e n fa t c a t n o d r i f n o r th t e h e r e o s s o c n il a l t a o t r io . n T s h i e n q th u e a n r t e it s y o n Q a t i o s r , t h w e h q il u e a l R the central cross section of the filament. We write down is equivalent to the ohmic resistance of the filament. the Lagrangian: Equations (5.14) enable us to determine the funda Sf = —D,,t,2 - ])J.,;< +-~~flo”-~~-1-qo”-M,qoEo + Mmtjol;·o, mental value of interest to us of the current Io in the .• ~ ~ - Cp (5. 7) central cross section of the filament. For this one has where the first four terms represent the electric and to determine the absolute value of the quantity \{3 80• This is carried out in the following manner. The inten the magnetic energy of the resonator and of the filament, and the two last terms respectively their mutual en sity of the field 0 0 of the oscillations in the waveguide 2 from the supply generator is measured by the loop 3 ergy. The term DeE/2 represents the energy of the (Fig. 5.1) by means of a detector or a thermocouple electric field; it is equal to situated sufficiently far from the quartz window 4 A A/52 through which the coupling with the generator takes ~~DJ;o”·”…;_:…~~ (E,‘-l-E,‘)2nrdrdz. (5.8) place. The reading on the scale of the instrument is bit 0 c proportional to the intensity of the supply field (!)0, The Utilizing (5.3) we obtain after integration coefficient \{3 determines the degree of coupling between the resonator and the generator. We begin the determi nation of the quantity \{3 by exciting oscillations in the resonator without a discharge for the same value of 00 where twice: at first for a natural wavelength of the resonator A, and then after a small retuning of the resonator for (5.9) an eigen wavelength A. Then in accordance with ex At resonance the electric and the magnetic energy in pression (5.2) we have the resonator are equal, and, therefore, we have (5.15) (5.10) where AL is the change in the length of the resonator where 0 is the eigenfrequency of the resonator and Ao which is produced by moving the partition 5 (Fig. 5.1). is the wavelength corresponding to it. We assume that We then measure at the center of the resonator the ab the mutual energy between the field in the resonator and solute values of the corresponding magnitudes of the the filament is brought about only via the electric electric component of the field E and E. In carrying forces, and we neglect the magnetic coupling Mm. This out the measurements it is also necessary to measure is permissible when the length of the filament 2l is the frequencies of the generator itself. Let the corre small compared to half a wavelength .\.o/2, and the fila sponding wavelengths be A’ and A11• We denote their ment is situated along the axis of the resonator (r = 0, difference by Hc,o = 0). /). = )/-). . ”. (5.16) The mutual electric energy between the filament and the field is determined by the manner in which the For a high quality factor for the resonator and for

Page 22

994 P. L. KAPITZA small values of ~A and ~Ao by setting q 0 = 0 we can The quantity of electricity q 0 flowing across the cen obtain from expression (5.14) with a high degree of ac tral cross section will be given in accordance with the curacy the following values for (3 f!f 0: preceding expression by J ~&‘o = 2D, (_ E _ o ;_ ’ _— E ~ o” ) · -t ~1- 1 o . o

~\}., qo = l 6 rlz = - “4 iff b2• (5.23) i11. ~ f.o, L’li.o ~ ),0. (5.17) From the last two expressions we have In this expression De and ~A0 are evaluated from (5.10). The values of Ao and A are calculated ac 6=1 2q 2 o z. (5.24) cording to (5.2) and are determined directly from the oscillations of the resonator by measuring the wave On the other hand, in accordance with (5.12) and (5.22) lengths. We carried out aA determjnation of the intensi we have ties of the electric field E and E in absolute units by s m p e h a e s r u e r i s n u g s p th en e d d e e d f l n e e c a ti r o t n h s e o c f e a n t s e m r a o l f l t h h o e l l r o e w s o c n o a n t d o u r c . ti T n h g e llfeqo = • ~ l - if 2 f - j l 2 2 z2 dz = - 3 if f b’l. (5.2 5) -l method is described in detail in a previous paper [[71, From the last two expressions we obtain that for the p. 206]. In subsequent measurements the value of E 0 ellipsoid the coefficient Me of the mutual energy be was determined from the deflection of a galvanometer tween the filament and the field in the resonator is connected to the loop 3 (Fig. 5.1) with a coefficient equal to2> which determines its absolute value. The following experimental observation simplifies Me=4/al (5.26) further measurements in an essential manner. Experi From this expression and from (5.19) we obtain ment shows that when the discharge is struck for a con stant value of <! 0 in the waveguide the field intensity in l - o= 4 3 7 B(J) iffo (5.27) the resonator E is dimished by a factor of several 0 tens. Thus, at resonance one cAan assume with a suffi All the quantities on the right hand side can be meas cient degree of accuracy that E 0 is small and the qual ured. The absolute value of the quantity (3iff 0 is deter ity factor Q is large; then from expression (5.14) by mined by the method described above in terms of the setting A = “-o we obtain the simple relation deflection of a galvanometer connected to the loop 3 (Fig. 5.1). The frequency w is measured by means of a (5.18) wavemeter, the length of the discharge 2Z can be deter This relation gives a direct connection between the cur mined as described in Sec. 2. Thus, one can determine rent in the filament of the discharge and the supply the amplitude of the current Io in the middle of the dis field. In accordance with expression (5.5) the current in charge. Experimental results for determining the aver the central section of the filamentary discharge will be age current 1 as a function of the power Pa in a fila 0 given by mentary discharge in deuterium at a pressure in the range from 1.37 to 1.86 atm are given in Fig. 5.2. f - o = J1 ( -!) e Bo-o. (5.19) These results are obtained for a power Pa not exceed ing 4 kW. At these power levels the length of the fila It now remains only to determine the value of the cou ment is considerably smaller than half a wavelength pling coefficient. But in order to determine Me, as may Ao /2, and, therefore, it is permissible not to take into be seen from (5.12), one must know how the charge 6 is account the magnetic coupling between the filament and distributed over the length 2Z of the filament. For this the field in the resonator. As can be seen from Fig. 5.2 it is necessary to know the distribution of capacitance we obtain a linear relationship between the power and and self inductance over z. For an approximate calcu the current. In order to determine the value of the cur lation it is possible to assume with a sufficient degree rent at high values of the power we extrapolate this lin of reliability, as may be seen from the photograph of ear dependence in accordance with the expression Pa the filament in Fig. 3.6, that the boundaries of the plas = 1.4 + 0.28 lo· ma represent an elongated ellipsoid of revolution with The average power dissipated in the discharge is z. semi-axes b and In terms of cylindrical coordinates equal to r, z this ellipsoid is described by the equation Pa oo ‘Mllr\}. (5.28) r’ = b’(l-z2/ F). (5.20) This power is sufficiently high and could be determined calorimetrically in terms of the heating of the water We further assume that the ellipsoid is homogeneously which cools the resonator. For example, in the case electrified with a field 8 inside; then the charges do when deuterium was used at pressures from 1 to 10 atm not penetrate into the filament and only on its surface the power in the discharge Pa was in the range from 1 charge.3 appear whose linear density is equal to 15. We to 20 kW and could be, as indicated in Sec. 2, measured denote the cross section by S, and then have with an accuracy up to 3-8%. Having determined the power Pa and the value of the current 1 in accordance C:rlS = l,:,~rlz, b ~I. (5.21) 0 with (5.27) we can determine the resistance R. Since the cross section is given by S = 11T2, utilizing (5.20) we obtain approximately 2)This expression, which does not take into account coupling through the magnetic field, is an approximate one. More exactly we (5.22) have: Me= 4/31(1-4/2 /‘A2 r 1.

Page 23

FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 995 Pa, [kW_ t_ I , ficiency and not to overload the generator it becomes s HI i ’ ! necessary as the power level is raised to increase the ~~- magnitude of (3, i.e., to increase the coupling between 3 ---1- -1— I”’”’” the generator and the resonator as has been described X- I 2 I I in Sec. 2. From expression (5.14) it can be shown that in order I I to obtain for a given value of (3<5’ the greatest current 0 0 3 1 g in the filament one must satisfy the condition 10, A FIG. 5.2. Dependence of the current 10 in the filament on the power De( 1- VJ: )( 1- 2,)= Jf.”; (5.3 5) input Pa determined from the experimental data for short filamentary !Jo •·P discharges in deuterium. 0-p = 1.37 atm, X-p = 1.86 atm, Pa = 1.4 + in this case the current in the filament will be given by 0.28 10. (5.36) For studying properties of plasma in the discharge we are interested in the skin-resistance Ps of the dis Thus, for the optimum extraction of power from the charge. In order to determine it we assume that the generator into the resonator the latter must be some discharge has along its length a circular cross section what detuned. This is essential when the length of the of radius b which varies as in an elongated ellipsoid. filament 21 is great, while the resistance R is small. Then from (5.4) and (5.24) we obtain for the current in Therefore, in practice one needs to tune the resonator any cross section by means of a small movable piston 11 (Fig. 2.1). It I=-iw I’ 2’1’ z dz •= iwqo (1— z~ ), should be noted that for large lengths of the filament J l” i’ one can no longer neglect the magnetic coupling between 1=0, z~ l. (5.29) the filament and the resonator. All the calculations According to expression (5. 5) we have have been carried out on the assumption that the cur rent in the filament is entirely determined by the ca I~=lo(1—~“/l”). (5.30) pacitance, i.e., it is reactive. To check this hypothesis Experiments on the spectral investigation of the fila we determine the active and the reactive impedance of ment show that its temperature and density remain con the filament. stant over the whole volume of the hot plasma. There We calculate the value of the field E produced at 0 fore, we assume that the skin-resistance Ps remains the center of the ellipsoid by the charges 6: constant over the whole length of the filament; then, uti 1 zd: lizing (5.20), we find that the time average of the power Eo= 2 S 6 (r’ + ‘“J”o’ dissipated in the segment dz will be given by 0 In accordance with expression (5.20) we take (5.31) r’+=“~~b’+z’, b/!«!‘;1, After integration we obtain and, utilizing (5.24), we obtain 5 I\ = lG 3 -~~ l , -p,J - ,”, ]2= [,\}/2, (5.32) E ” =- 4 P G · o 1 o ( &” z + ’ d z z “r, ~- 4 f2 q l o ( n - 2 b 1 - 1 ) ’ T b ~~1 · ( 5 . 3 7 ) from where, after comparison with expression (5.28), Utilizing (5.5) we obtain the reactive impedance of the we find filament: Ps=g 1G - -z b R . (5.33) Z,=~~=..i(ln~-t). (5.38) In hu b If we substitute into (5.32) the value of 1 from (5.19) Correspondingly the active impedance is equal to R and 0 and take into account (5.26), we obtain in accordance with (5.33) is given by (5.34) (5.39) Since, as is shown by experiment, as the intensity rS 0 Experimental data show that Zr is by an order of mag supplied to the resonator is increased the length of the nitude greater than Za. The electrical field E acts on 0 filament 21 and b both increase and the skin-resistance the charge and stretches the filament. The stretching can also vary, the absorbed power will not be propor force in a homogeneous field is given by i: tional to the square of but, as is shown by experi 0, (5.40) ment, has a linear dependence. The experimental data given in Fig. 5.2 indicate a linear dependence of the Utilizing expressions (5.5) and (5.39) we obtain current Io on the power input Pa. On the other hand, in accordance with expression (5.27) f5’ is proportional to (5.41) 0 Io, and, therefore, between f5’ 0 and the power a linear relationship should also hold. This linear relationship The calculations carried out above are valid only in leads to the fact that in supplying the resonator from a the case when the length of the filament is considerably high frequency generator in order to maintain high ef- smaller than half a wavelength. When the length of the

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996 P. L. KAPITZA filament approaches half a wavelength resonance oc curs. In our type of resonator we could not obtain in a stable manner a filament length greater than half a wavelength. If this could be successfully accomplished, then the current would be determined not by the capac itance but by the inductance of the filament, and the phase of the current with respect to the field would be changed by an amount rr. 6, THE STRUCTURE AND THE SHAPE OF THE FILAMENTARY DISCHARGE In accordance with the structure of the filamentary discharge adopted by us the plasma is heated by the HF current when it flows in the layer at the boundary of the inner region of hot plasma. The skin-resistance of this layer is determined by the frequency of the current w and by the condition of the plasma. Between the mean depth of penetration 15 and the skin-resistance there FIG. 6.1. Total skin-resistance as a function of the temperature of exists the well-known relation: the electrons in the plasma calculated for a frequency w = 1010. c2 li=~—p,[cm]. (6.1) 2alo ther reduction in the usual skin-resistance which begins In future we shall denote the skin-resistance by Ps and at a plasma temperature in the neighborhood of 105 °K the specific resistance by Tis· The quantities Ps and and which occurs when the frequency v of the collisions Tis are related by the well-known expression of electrons becomes considerably lower than the fre quency of the HF current in the plasma. (6.2) From expression (6.6) it may be seen that at low de grees of ionization, when the ratio N /Ne is large, the 0 The specific resistance of the plasma is in the general resistance of the plasma is determined by collisions case determined by the following expression: l l2J with neutral atoms. In our case this occurs in a cloud surrounding the hot plasma, where the value of N /Ne 0 (6.3) is greater than 103• Here the resistance of the plasma is high and the depth of penetration 6 of the HF field is a where Ne is the density of the electrons, v is the fre correspondingly large. If the height of the cloud is quency of collisions between electrons and atoms, which less than o, then the HF field will penetrate to the sur is equal to v = 1/T, where T is the time during which face of the hot plasma without any appreciable absorp the electrons lose the directionality of the momentum tion. acquired in the electric field. If the gas is not com The specific resistance of the hottest plasma, since pletely ionized then v is the sum of frequencies of two there are no neutral atoms present in it (n 0 = 0), is de types of collisions: v 0 with a neutral atom and Vi with termined by Coulomb scattering. From the curve of an ion Fig. 6.1 it can be seen that also in a hot plasma at an

electron temperature of Te = 106 °K the skin-resist ,. = vo \‘i· (6.4) ance will turn out to be so small that for currents in the The frequency of collisions with neutral atoms is deter filament amounting to tens of amperes no heating of the mined from the expression filament will occur. We, therefore, assume that in a plasma there must exist also another more powerful (6. 5) mechanism for dissipating the ordered velocities of electrons arising due to the passage of a current. It is where q is the cross section for collisions of neutral associated with the fact that at a high frequency w and 0 atoms with electrons. This quantity is determined ex for large thermal velocities the electrons may leave perimentally. For deuterium it can be taken equal to the skin-layer and thereby destroy the ordered motion q 0 ""’ 2.5 x 10-16 cm2 (l 10J, p. 150]. Collisions between brought about by the current. This phenomenon was electrons and ions are determined by the Coulomb in discovered at low temperatures and for HF fields in the teraction. Then for the specific resistance of the plas investigation of metals. It was discovered by Pippard. ma we will obtain Such a skin-resistance turned out to be much greater 1 than the usual one, and was called anomalous. It can be lj ]’,;,.~~.,,r~~ . • T : .! N -(0 !.1’ )‘I,,,_L 1 - ( - : : t - - · ) ’·’• _ c · ’ _ \ ”- (6.6) easily seen that the mechanism giving rise to the anom ’ C.CC c’ L/ ’ N,. · e ’ 2 :! · ( kl’c) ’(, . alous skin-effect in metals is also applicable to plas The skin-resistance evaluated from this expression in ma. We need only replace the Fermi-velocity of the accordance with (6.2) as a function of the electron tem electrons by their mean thermal velocity in the plasma; perature is shown in Fig. 6.1 by the segment of the at the same time the expression itself determining the curve which is called the ordinary skin-resistance. On skin-resistance remains the same. the same curve we have also taken into account the fur- We give a simple derivation of the expression deter-

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 997 mining the anomalous skin-resistance in a plasma, plasma is due to collisions between electrons and ions since it shows in a graphic manner how this phenome and has the following dependence: non arises when the mean free path of the electrons is (6.15) large compared to the thickness of the skin-layer. At the boundary of the plasma (Fig. 6.2) in a layer Thus, the anomalous skin-resistance increases with the of thickness o a current I flows which is equal to temperature while the ordinary one diminishes. In Fig. 6.1 are given curves for the dependence on Te of (6.7) the total skin-resistance calculated in accordance with (6.2), (6.6), and (6.13) at a frequency of w= 1010• As where ne is the electron density while t::..v is the incre can be seen, up to a temperature of T = 105 °K the re ment in their velocity in the alternating electric field. sistance is determined by the ordinary skin-resistance, When the mean free path for an electron is greater than but above that temperature already by the anomalous o, the electron will freely leave this layer with a veloc one. ity Vx normal to the boundary, and will carry away the We determine the skin-resistance for hot plasma in kinetic energy me(t::..v)2/2 acquired in the electric field. the filament according to the data given in the Table If there is no specular reflection of electrons at the (Sec. 3). For Pa = 12.4 kW, p = 1 atm, a = 0.45 em outer surface of the plasma then the power lost over and Te = 106 °K we obtain from the curves of Fig. 6.1 both boundaries will be equal to Pa = 0. 59 ohm. From (5.32) we have the following expression for the (6.8) current in the central cross vsec tion of the filament: The power lost in this manner is equal to the ohmic losses, while the velocity vx normal to the layer is lo=i Pab. (6.16) ’\}‘3 lp, If we take the length of the filament to be 2l = 10 em and in accordance with (3.12) b = 0.18 em we then ob ;]L; , FIG. 6.2. Schematic diagram for tain for the current Io = 63 A. But if we determine the calculation of the anomalous skin same current by extrapolating experimental data, ob resistance. tained in the course of a direct measurement of the cur rent and shown in Fig. 5.2, we then obtain Io = 39 A. Taking into account the approximate nature of the com equal after averaging to one-half of the average thermal parison the agreement may be considered to be satis velocity. From the preceding expression we obtain factory. As can be seen from the experimental data quoted (6.9) above, the power Pa which is dissipated in the filament where Pa is the anomalous skin-resistance. Substitut attains values up to 18 kW. In the final analysis it is ing into this expression the value of the current from carried away by the heat flux through the gas from the (6. 7) we obtain filament towards the walls of the resonator. Let us con sider the process of heat transfer from the filament. Pu ~--- 4 1 1 e n ‘n 1:C e ’! . ~ Ve ’ (6.10) In photographs of the filament it can be seen that at a distance of two-three radii from the axis of the fila Taking into account in accordance with (6.1) the rela ment the gas no longer glows, and this shows that start tionship between the skin-resistance and the depth of ing with this value practically no ionization is present, penetration we introduce the plasma frequency for the and one can assume that from this point the gas has the electrons: ordinary heat conductivity. We denote the temperature in this region by Tn. For deuterium this is 6000- (6.11) 70000. We denote by an the radius of the region start Then from (6.10) we obtain the skin-resistance ex ing with which normal heat transfer begins. We consid pressed in ohms: er the heat taken away from the ellipsoid of rotation of radius an and of the same length 2Z as the filament. (6.12) We denote the temperature in the gas surrounding this ellipsoid by T, and its heat conductivity by .rt [W / deg] • The expression for the skin-resistance of the plasma We assume that .rt depends on the temperature in the derived rigorously in a manner analogous to l 14l is following manner: given by .rt = .Yto(T I To)”-, (6.17) flo= 30)’ - 3:t”, [( ( - tj ) - 0 __ v : ’ ]” IJ . (6.13) where :Jt 0 is the heat conductivity at the normal tem Qt: c perature of 273°K. It is well known that for a gas As may be seen, this expression gives a skin-resist where the molecules can be regarded as hard spheres ance which is only 20% lower than the approximate one. the index is K = %. In actual fact, due to the dependence The dependence on the pressure, the frequency and the of the distance of closest approach of molecules in a temperature of both expressions is the same: collision on the value of the kinetic energy, the quantity (6.14) K is somewhat greater than %. If in the surrounding medium there are no sources of absorption or libera According to (6.6) the usual skin-resistance in the hot tion of heat except for the filament itself, then according

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998 P. L. KAPITZA to the classical theory of heat transfer the temperature well known, is often the main component of heat trans satisfies the equation fer in a gas. The main temperature drop is near the filament, and div :Jt grad T = 0. (6.18) therefore, to increase the heat flux in this region one Substituting the value for :Jt, we obtain must increase the heat conductivity in that neighbor hood. Due to the fact that near the filament the gas tem (6.19) perature is high its density is less than the normal den The heat flux P .g” created by the heat conductivity will sity by a factor of approximately 20, and, consequently, be given by its volume heat capacity is small. Therefore, convec tion at ordinary velocities is not effective. Estimates P:x = ·.7r dS, (6.20) show that both convective and turbulent methods of heat transfer are insufficient to explain the observed dis where the integral is taken over the surface of the ellip crepancies between Pa and Px. The absence of any ap soid. From this expression on introducing the value of preciable effect due to turbulence and convection is :Jt from (6.17) we obtain confirmed by experiment. If for a constant regime of the power input to the filament from a high frequency \\DT” PJ(’= + :I C n —d1 S. (6.21) source one alters the velocity of rotation of the gas by (>< 1) To’” Dn a factor of several fold, it turns out that this has little Since it follows from (6.20) that T ~ + 1 is a harmonic effect both on the shape of the filament and on the value function, we can write by analogy with the electrostatic of the power input. problem The increased heat conductivity of deuterium and of hydrogen in the high temperature domain which occurs (6.22) in our experiments should possibly be explained by a heat transfer mechanism which was first pointed out by where Tn is the temperature of the surface of the fila Nernst.[ 151 At the temperature of the surrounding gas ment, T is the temperature of the resonator walls, the molecules become dissociated and molecular vibra 0 while C is numerically equal to the capacitance of the tions occur in them. This gives rise to an additional en filament with respect to the resonator. In our case ergy of the molecules the magnitude of which depends when the filament is small compared to the resonator on the temperature. The diffusion transfer of this en and is situated far from its walls C may be taken equal ergy along the temperature gradient is what is respon to the capacitance of a free ellipsoid of revolution with sible for the additional thermal conductivity. Theoreti axes equal to an and l. We then have the well-known cally it has been studied for hydrogen [ 161 and it was expression for the capacitance of an ellipsoid: shown that by this method in the temperature range which happens to be close to the one possessed by the (6.23) gas surrounding the plasma filament, this “portable” heat transfer may exceed the ordinary one by a factor where E is the eccentricity. Since our ellipsoid is of several fold. Numerical calculations of heat removal elongated we have from the filament taking this “portable” heat transfer into account turn out to be a complicated computational problem, but estimates show that it can explain the in creased heat removal from the filament which is ob Thus, for a filament of radius an and long axis we fi served in our experiments. nally have At the present stage of our investigation of the plas ma filament we can assume that under all conditions the power taken away will be determined by the shape of the filament and will have a form analogous to the one We calculate, as an example, the thermal flux for a fila given by expression (6.25): ment in deuterium with parameters given in the Table (Sec. 3): Pa = 8.8 kW, 2Z = 9.4 em, a 0 = 0.4 em. The f(1’n, P) (6.27) radius an from the normal heat transfer begins we will ln(l/a) ’ take to be equal to three times the value of a 0: an where f(Tn, p) is a function of the temperature T n at = 1.2 em. For dissociated molecules at a temperature the surface of the filament, while p is the gas pres of T 0 = 273°K we assume the heat conductivity to be sure. From this expression we obtain . i 7 o C0 n i

ze 2 d .1 g 6 a x s w 10 e

c 3 a W n / t d a e k g e . T F n o r

t 7 h e x t 1 e 0 m 3 p ° e K r . a t T u h re en o f o n t h s e e u t n V ~~ l/a = exp (/1/Pa), (6.28) ting K = %, we obtain from where it can be seen that a small change in the in dices strongly affects the ratio Z/a. From this expres Px= 4.5kW, Pa/Px= 2. (6.26) sion it follows that the ratio of the radius of the filament Thus, only one half of the total power is removed to its length is to a large extent determined by the con through the heat-conducting surrounding gas. ditions of heat removal which, thus, plays an important Consequently, there exists another mechanism for role in determining the shape of the filament. taking heat away from the filament, and it is natural to It has been pointed out already that the filament can assume that near the filament such a mechanism could be stretched by the electric fo~·ces created by the HF be provided by the convection of the gas, which, as is field. The stretching force is equal to F z, and its mag-

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 999 nitude is given by expression (5.41). For our filaments the filament would have the greatest diameter near the its magnitude is of the order of 102 dyn. ends while its center would be compressed. The next force which acts on the filament is the com But in actual fact this does not occur. In the photo pression of the filament by the so-called pinch effect. It graph of the filament (Fig. 3.6) it can be seen that it has is brought about by the fact that when a current flows the greatest cross-section in the middle. It is, there over the surface of the filament and the magnetic field fore, clear that the electrical and magnetic forces in does not penetrate inside a normal pressure arises. Its our case do not exert any appreciable influence on the value averaged over time is equal to shape of the filament and, consequently, cannot lead to an instability of its shape as is the case in the usual PH=H.2/8:t (6.29) filamentary discharges. where H~ is the average square of the magnetic field As has been shown in Sec. 4, the high temperature of tangent to the surface of the filament. This field is de the electrons in the hot plasma of the filamentary dis termined by the density of the surface current: charge is possible due to the existence at the boundary of a double layer from which electrons are reflected H • = !n.J /2.-rr = 2! I r, (6.30) elastically. Expression (4.17) gives the value of the where I is the total current. Assuming that the radius surface tension of the double layer which could affect of the cross section varies along the filament in accord the shape of the filament, but, as has been noted al ance with (5.20) as in the case of an ellipsoid, we obtain ready, its magnitude is too small for this. by using (5.30) for the distribution of pressure along the Taking into account the estimate of the forces given filament above which act on the filamentary discharge and ob serving the behavior of the filament we think that the (6.31) following simple mechanism explains sufficiently well why the filament has a shape close to that of an elon From this expression it can be seen that the pressure gated ellipsoid, and why this shape is stable and does PH which compresses the plasma has the greatest value not depend on the electromagnetic forces which act at the middle of the filament and falls to zero at the upon it. The photograph 3.6 of the filament shows that ends of the filament. For large currents which occur in there exists a sufficiently well defined boundary sur ordinary filamentary discharges between electrodes of face for the hot plasma; at such a boundary a tempera capacitors this pressure, as is well known, can be many ture discontinuity must occur since the gas surrounding times greater than the pressure of the gas surrounding the hot plasma has a low temperature at which it has no the plasma. Then the phenomenon of pinching occurs. appreciable electrical conductivity. In order for the gas But in our case, when the current is not great, the pres surrounding the plasma to have a well defined tempera sure at the middle section of the filament is of the order ture it is natural to assume that the radius of the cross of 102 dyn. section of the filament is the larger the more heat has In addition to magnetic forces electric forces can been liberated at that point. The distribution of energy also affect the shape of the filament. They arise due to liberated along the filament is given by expression the fact that at the surface of the filament charges o (5.31). One can foresee that a simple relationship be appear (5.24) which give rise to electrical forces nor tween the energy liberated and the cross section of the mal to the surface. They produce a negative pressure in filament is what determines the shape of the filament the plasma at the ends of the filament. Averaged over to be similar to an ellipsoid of revolution. At the pres time it is equal to ent stage of our investigations an exact solution of this problem not only presents considerable mathematical P< = En’/8:>:, (6.32) difficulties but, primarily, requires a more detailed un where En is the amplitude of the normal component of derstanding of the mechanism of heat transfer between the intensity of the electric field equal to the plasma and the gas surrounding it. With such a picture for the formation of the filament (6.33) the mechanism providing its stability is apparently triv Substituting the value of r and o from (5.20) and (5.24) ial. If at any point along the filament an expansion oc and using (5.5) we obtain curs, then the density of the surface current diminishes and likewise the liberation of heat. At the same time (6.34) removal of heat increases due to the increase in the surface. All this leads to a cooling of the plasma and In the derivation of (5.22) we have used an approxima the expansion disappears. Converse phenomena occur tion for o which is not valid at the ends of the ellipsoid; in the case of an accidental contraction of the cross here the formula has been made more precise. This section of the filament: the surface current increases has led to the eccentricity E appearing in (6.34). From and this again leads to a smoothing out of the cross sec this expression it can be seen that the force at the ends tion. The nearness of the shape of the discharge to el attains large values, and, therefore, it is not possible liptical and the fact that its long axis is parallel to the to use as a model for the plasma an ellipsoid which has electric field in the resonator are also from this point a sharp boundary at the ends. But still the negative of view associated with stability, since only in this case pressure at the ends will be greater than the magnetic when the current flows parallel to the length of the fila compression. From this it follows that if the shape of ment is complete homogeneity of the current density the filament were determined by the pressure which is guaranteed everywhere on the surface. exerted on its surface by electromagnetic forces, then As has been noted already at the end of Sec. 2 in the

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1000 P. L. KAPITZA course of investigating the longitudinal stability of the (7.1) discharge in the resonator, it can be seen from analo gous considerations that the filament will tend to move where mp is the proton mass and Z is the charge of to that region in the resonator where the electric field the ion. If the time between collisions is T and the ve has a maximum value. This will occur because on that locity of the particles is v, then in the absence of the side of the plasma in the filamentary discharge where field the mean free path A is equal to the higher field exists a greater density of the surface current will also occur, the heat influx from that side (7 .2) will increase and the amount of plasma in this direction The radii of the Larmor orbits are respectively equal will grow. Thus, a filament shape will result which is to analogous to the shape of a flame. In the case of a fila ment its shape is determined by the supply of energy (7.3) from the high frequency field, and in a flame it depends In order that the magnetic field could introduce a notice on the introduction of a fuel mixture. If this mechanism able change into the motion of particles in the plasma it in fact determines the shape of the filamentary dis is necessary that A >> r and, consequently, charge its great stability must be preserved also when the dimensions of the filament are increased. Lately (7.4) we have discovered an instability in the shape of the If this condition is not satisfied then the magnetic filament. This occurred in experiments in which we field has no effect on the gas kinetic processes in the tried to obtain a discharge of the greatest possible plasma. cross section. This was achieved by increasing the in In studying the filamentary discharge we are inter put of HF power. ested in the effect of the magnetic field on the ion heat As has been already described in Sec. 2, as the pow conductivity of hot plasma. The magnitude of the ion er input was increased the length of the filament heat conductivity of a plasma in a magnetic field is the reached its limit which was equal to half a wavelength oretically determined. It is an isotropic, and while at the frequency of the input current. A further in along the field it has the usual value already quoted by crease in power led to an increase in the cross section us in Sec. 4 (expression (4.26)), at right angles to the of the discharge without an increase in its length (cf., direction of the field it is equal to: l 133 Figs. 2.4 and 2.5). It turned out that after a certain di ameter has been attained the filament begins to be flat (7.5) tened and then to break up into two parts. In place of one filament two filaments were formed emanating from where Ti-the time between collisions of ions-is given one point at a small angle, both somewhat shorter and as before by expression (4.27). Comparing this heat thinner than the initial one. conductivity in (7 .5) with the heat conductivity in the ab A natural explanation of this phenomenon consists of sence of a field one can see that it is less by a factor the fact that when the filament attains its limiting length, of (wi Ti)2• the value of the HF current in it is determined, as al We consider the same problem which we solved in ways at resonance, by the active resistance, i.e., by the Sec. 4 for the radial heat conductivity in cylinders, but skin-resistance. Therefore, an inhomogeneity in the in the presence of a magnetic field directed along the heating of the surface of the filament and the inhomoge axis of the cylinder. Utilizing expressions (4.24) and neity caused by this in the value of the skin-resistance (4.27) we obtain can give rise to a redistribution of the current density over the surface of the plasma, and this can lead to an (7.6) unstable shape of the filament. Thus, for a given frequency of the supply current ap In determining the temperature Ti we consider two parently there exists not only a limiting length for the limiting cases. The first is when the density n remains filamentary discharge but also a limiting diameter. constant inside the cylinder. This is the case when the One of the principal difficulties in the experimental electron temperature Te is considerably higher than study of the shape of the plasma itself inside the fila the ion temperature Ti. Then, setting K = % according ment is its small cross-section. Only with a transition to (4.25) with the boundary condition Ti = T 0 we have to larger dimensions will it be possible to establish for r = b: with greater confidence the mechanism which deter 1’· = [-!__!!_( 1-)+To”’ 1 2 mines the shape of the discharge and its limiting dimen r 8.“‘1 C /,‘2 .J ’ sions. 1’, = consl, IIi’= ne = COllSl, Te \}> 1’;, (7. 7) where q is the power input per unit length of the cylin 7. INFLUENCE OF A MAGNETIC FIELD ON THE der. The process of heat removal proceeds in a some FILAMENTARY DISCHARGE what different manner when the ion temperature is The mechanism for the effect of a magnetic field on higher than the electron temperature. In this case the plasma processes consists of the fact that between col density of the plasma determines the ion temperature: lisions electrons and ions move not along straight lines, It;= n0T0! T,, P = 1 /T'''. (7.8) but along circles with a Larmor frequency equal to Substituting these values into (7.6)r w”e ‘o btain K = -2.5, ” (oJe o- ---Jf ~~ 1./li • JlFJI, 1’; = [ T~’·-( l- ~~J 8~~-r ~ T; > 1’,.. (7.9) 11/tC

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 1001 From this expression it may be seen that for a certain els a distance 2 r then the velocity of its motion in the radius r = bm the temperature Ti becomes infinitely plasma in the direction of the x axis will be given by great. Setting the expression in square brackets equal f 2f 4 J1•;j to zero we obtain V.,=—=-;---. (7 .17) 3 1:; 3:t !O\{!i (.!!!::)2=1-~£_ T·= oo (7.10) Substituting the values of E, A, Yx, Dx into expression b 3 qJ”.~, t • (7.12) and taking into account vf = 2kTi/mi we obtain The calculations described above have been made with out taking into account the finite dimensions of the Lar (7 .18) mor orbits, but in both cases considered above there exists a limitation on the increase of the temperature This expression agrees with the already well-known ex Ti which is imposed by the condition that a Larmor or pression (7 .5), but due to the simplified derivation the bit with its center at the radius r must be contained numerical coefficient in (7 .18) is less by 20% than in within a cylinder of radius b, and consequently, vi the case of the rigorous derivation. We now assume ~ (b - r) Wi> from where we obtain the value of the ion that within a certain region of the plasma b greater temperature at the boundary: than a Larmor diameter there arises due to fluctua tions in the density of ions and electrons an alternating (7 .11) electric field E. Then the ions in this whole region will start moving along the radius with the velocity The heat conductivity in a magnetic field given in (7.5) is derived on the assumption that in the interval l’,= cE/ l!, between collisions the Larmor orbits remain motion !ib <: 2ri, V, < L”i, (7 .19) less. But in actual fact it is sufficient for small fluctu where Erp is the component of the electric field normal ations of the electric field to be present in order to to the radius and to the magnetic field. Therefore, the make the centers of the Larmor orbits acquire a chaotic diffusion coefficient along the radius will consist of two or, as it is said, a turbulent motion which increases the parts: heat conductivity by a large factor. In order to take into account the effect of this turbulent motion in the filament (7 .20) we give a simple derivation of heat conductivity in a magnetic field which brings out well the physical nature Approximate calculations show that at high values of of these processes. heat conductivity it is sufficient to have quite small As is well known,l17J the amount of heat transferred field fluctuations in order to bring about a large in by the heat flux in a gas along the x axis is determined crease in the diffusion coefficient and, consequently, by the following general expression: also in the heat conductivity. The only region in which · iJe dT; dT; the heat conductivity retains its low value is near the qx=Dx----=:Jtx—, (7 .12) iJT; dx dx stationary boundary of the cylinder since here we have where the diffusion coefficient is given by V, = 0, r =b. (7 .21) (7 .13) We determine the width of the boundary layer ~b in which fluctuations of the field have no appreciable ef Here A is the mean free path, n is the particle density, fect on diffusion. If such a layer exists it must be not Yx is the average velocity along the x axis as a result thinner than 2q-a diameter of a Larmor orbit. Each of thermal motion, equal to I Vi l/3, the quantity E is ion can be regarded as a particle of cross section rrri. the energy of the particles. In the case of a completely The smallest possible monatomic layer will have a ionized gas the energy of the particles is equal to their thickness 2ri. Therefore one can assume kinetic energy: L’1b > 2ri. (7 .22) e = n;kTi. (7.14) Then from (7.3) we obtain If the hot plasma is situated in a magnetic field under the condition which is given by expression (7.4) then the 2 — nb = p-f’2kT;/m;, (7 .23) mean free path between collisions will be determined by !0; the diameter of a Larmor orbit. The distances between > where p 1. points at which collisions occur can be determined by We further assume that due to the large turbulent any two points on the orbit. The orbit has a radius q; heat conductivity in the central section of the cylinder then the average distance 2 ri between two points of the from r = 0 to r = b- ~b the temperature in it is uni orbit will be given by form and equal to Ti. In a boundary layer of thickness 2r· 1r1/ ! 4 ~~b the heat removal will be determined by the heat 2r;= n::,1 -’: 2 ._ J 0 COsada= ~ - r;. (7 .15) conductivity X 1 , so that Thus we obtain T;- To q=2:tb~~X_L. (7 .24) • _ 4 Ju;j J.=2ri=---. (7.16) Jt (!) i Using expressions (7.5) and (7.24) and assuming Ti >> Since during a time Ti a particle on the average trav- T we obtain 0

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1002 P. L. KAPITZA k2n;T,2 reduced. This process becomes effective when the mag q = 1.3nb----. (7 .25) netic field attains such a value for which the diameter pm;<•J, < ;1 ‘!.kl’;jm; 2re of the Larmor orbit is close to the thickness of From this expression it can be seen that the heat con the layer: ductivity in the plasma for large values of Wi, in con trast to expression (7.5), falls off with the first power 6 ;:::;2r,. (7 .28) of the intensity of the magnetic field and in this is sim Utilizing expressions (6.1), (7.1), and (7.3) we obtain ilar to the empirical expression proposed by Bohm [(]21, p. 47]. H4:T.<ume/cepa. (7.29) The proposed picture of the phenomenon of heat From the picture given above it follows that the mag transfer in a plasma reminds one of the process of heat netic field affects the skin-resistance when it is di conductivity which occurs in the flow of gas in pipes. rected parallel to the plane in which the current is Here also, when turbulence occurs, the temperature flowing. It can be shown theoretically that as the field drop is concentrated across the boundary layer where is increased the anomalous skin-resistance in the limit the laminar flow is not much disturbed. The thickness disappears completely and only the ordinary skin of the laminar layer is what determines the magnitude resistance of the plasma remains. A quantitative deter of the heat transfer. mination of this effect presents certain difficulties, Setting b/~ b = Pc we can determine the lowest criti since it depends strongly on the conditions for the re cal value of Pc for which no turbulence arises in the flection of electrons from the boundary, and it has not plasma. From (7 .23) we obtain its value: as yet been established whether this reflection should Pc-t \{;( f = J )i 1 - / v 2 j k il - , T i - , = r - b 1 , Pc > 1. (7 .26) be A tr n e a e t x e p d e a ri s m s e p n e t c a u l l s a t r u d o y r d of i ff th u e s e f . i lamentary discharge in a magnetic field was carried out using the solenoid Very likely it will be possible to determine the quantity described in Sec. 2. The magnetic field which it pro Pc only experimentally, as is the case with Reynolds duced was parallel to the filament and attained a value critical number. of 22 kOe. So far the experiments have been restricted From expression (7 .25) it is possible to show that to measurements (for different values of the power and even when the plasma goes over into a turbulent state of the pressure up to p = 3 atm) of the external diame the heat removal from a filament in a magnetic field ter 2a of the filament, of its length 2Z and of the width remains small. ~A of the D\{3 line. In the course of this we have invari The magnetic field can also affect the heat conduc ably noted in the magnetic field a decrease in the diam tivity which is due to electrons, but in our case we do eter 2a, a lengthening of the filament and an increase not take it into account. As we have already indicated, in ~A. The experimental record of the D\{3 line in the the thermal insulation properties of the boundary layer filament in a magnetic field of 20 kOe is given in are so great that a decrease in the heat conductivity Fig. 2.3. The results of the measurements are shown brought about by the magnetic field cannot significantly in Figs. 7.1 and 7.2. The dependence of the narrowing affect the distribution of the temperature of the elec of the filament and of A on the intensity of the field is trons in the plasma. As we have already noted, we con shown in Fig. 7.3. As can be seen from these curves sider the temperature Te inside the filament to be con the external diameter of the filament in the magnetic stant. field is decreased by 30%, while its length is increased It is well known that a magnetic field by acting on the by 10%, while the power input Paf2Z remains constant. motion of the electrons alters the specific ohmic resist Therefore, in accordance with (5.34), since the experi ance of the plasma. The conditions required for such ments were carried out at a constant value of the inten an effect are the same as those that are given by ex sity 8 in the supply resonator, it turned out that the pression (7.4). The time Te between collisions of elec resista 0 n ce in the magnetic field was decreased to 30%. trons is determined by the following expression:l 131 For a skin-resistance Ps = 0.59 ohm the depth of pene ‘Te 0 = .28 - - T. - ’” . (7 .27) tration according to (6.1) will be given by l5 = 9.4 A n, x 10-3 em. The diameter of a Larmor orbit in a field of It has been shown theoretically that for the case of a 20 kOe for Te = 106 °K and ve = 5.5 x 108 em/sec is current flowing along a magnetic field the ordinary re equal according to (7.3) to 2re = 6.3 x 10-3 em. Thus, sistance is not altered, it is increased only when the according to (7.28) experimental data confirm the as current flows at right angles to the field but even then sumption that a decrease in the diameter of the filament by not more than a factor of two. is a result of the influence of the magnetic field on the It is not difficult to see that a magnetic field affects anomalous skin-effect. A more exact quantitative inves the anomalous skin-resistance strongly and results in tigation of this phenomenon is made difficult primarily its being reduced. The nature of this effect can be seen by the lack of a possibility of measuring the internal di from the derivation of the anomalous skin-resistance ameter of the filament 2b. For the time being we given in Sec. 6. As can be seen in Fig. 6.1 the ohmic sume that the internal diameter 2b is proportional to losses are due to the fact that the electrons in the the external diameter 2a and is determined in accord course of their thermal motion leave the skin-layer l5 ance with expression (3.12). and carry away with them the increment in the momen In future we shall study this phenomenon in greater tum mev which produces the current. The bending of detail by utilizing measurements in the microwave and the electron trajectories in the magnetic field hinders the extreme ultraviolet regions. An explanation of this this removal of the momentum, and ohmic losses are phenomenon by any processes involving heat transfer by

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE1003 t-~~ ,A ;Za, rom From expression (4.21) it can be seen that at a constant . r-·-----1.. 4~-----1 JJ=o?O kOe II fl ~ pressure and constant cross section of the filament 1rb2 \(J, /z : ··— ~ the electron density ne is inversely proportional to the 3 ~~---1_’—’\:~~:-:;;:;.-r-/-j-------- ~ temperature T e, and the power transferred to the ions I · i ’ 4 o·o ’ ’”? u \{ . . - . J , ’”>< Y ’ .Y ‘i 1 will decrease as T2•5• z ~~---------Hj/ y~~:r<f.”J;. ~~-------- The energy which is supplied to the filament all goes via the skin-resistance into heating the electrons. Thus, t-~~ dlur—t in order to increase the temperature of the ions it is , - necessary to supply power directly to them. The sim plest and most direct method is to excite magnetoacous zo 0 5 10 15 tic oscillations in the plasma the kinetic energy of which P0, kW is produced by the oscillations of the ions. In our case FIG. 7.1. Dependence of the diameter of the filament and of the this can be done if a magnetic field H is produced par broadening of the D13 line on the power in the discharge with a magnetic field and without it. Deuterium, 1.3 atm < p < I .5 atm. allel to the filamentary discharge and an alternating field is superimposed in the same direction of ampli tude llH and of such a frequency wa for which the field would not penetrate deeply into the plasma. Then near the surface of the filament a pressure arises equal to !‘!p = t-.H -II I 4n. (8.1) For a field H = 2 x 10” Oe the pulsing of the pressure will attain a magnitude of ilPn = 0.05 atm. We calculate the limiting power which could be di rected across the boundary into the plasma of the fila FIG. 7.2. Dependence of the length of the filamentary discharge on ment. The electric field at the boundary of the filament power input at low and high magnetic fields. Deuterium, I .3 atm < p will be given by < 1.46 atm. (8.2) where b is the radius of the filament. The average d ’-,p.A ; -Zo, m - m -s. flux of power across the boundary will be determined 1- by the Poynting vector. This is the limiting power; it is J ----=-----===~ ! I equal to i I FIG. 7.3. Variation of the dia- I . i i meter of the discharge and line I’ .~liE.,. (.\II)’, (8.3) 2 ----j--- broadening as functions of the in- ”.!,/ = ~.:r-.;..:tU =-1-b‘“Wa• 1 Za t te e r n i s u i m ty , o p f = t h 1 e . 2 m 3 a a g t n m et , i c 9 . f 7 i e k ld W . D < e u- For a value of llH = 30 Oe, a frequency of wa = 1.5 11.3 kW. x 108 and b = 0.4 em we have P /2l = 500 W. If such additional power were absorbed in the filament it could 0 15 25 be observed experimentally, and, therefore, we began to II, kOe carry out experiments. For this purpose an apparatus was constructed which is schematically shown in Fig. 8.1. In essence this is our previous apparatus de ions encounters a difficulty in the fact that according to scribed in Sec. 2 and shown in Fig. 2.1. A magnetic our measurements the quantity Wi Ti is close to unity field is produced in its resonator by the previously de- and according to (7 .4) the magnetic field cannot exert a strong influence on ionic processes. If we attempt to explain this phenomenon on the basis of a cold plasma at a temperature of T e = 6500°, then in this case no processes are known which reduce the specific resistance of the plasma. Moreover, such an explanation does not satisfy criterion (7 .4) since the value of weT e is small. Thus, at the present stage we can explain the observed effect of a magnetic field on a filamentary discharge only by processes occurring in a hot plasma. 8. MAGNETOACOUSTIC OSCILLATIONS IN THE PLASMA OF THE FILAMENT In this section we consider problems of increasing the ion temperature by magnetoacoustic oscillations. One of the characteristic properties of a hot plasma is FIG. 8.1. Schematic diagram of the high frequency circuit for the the fact that as its temperature is increased the heat excitation of magnetoacoustic oscillations in a filamentary discharge, exchange between the ions and the electrons decreases. !-coil, 2-capacitors, 3-feeder line.

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1004 P. L. KAPITZA scribed solenoid with an iron yoke. The difference con H ___, sists of the fact that a circuit consisting of the coil 1 of L No ,To =JHslncu0t Gas (]\ 2-3 turns and two cylindrical capacitors 2 serves to …,l t___j zu produce a variable magnetic field of amplitude AH. ”’ —l -==j: — Such a construction enables one when the whole oscilla flj,/!o.-Tt tory circuit is placed within the resonator to obtain Plasma powerful oscillations of high frequency which reached FIG. 8.2. Notation adopted for making calculations concerning values of wa = 1.5 x 108• The circuit is supplied by the radial magnetoactoustic waves in the plasma of the filament. line 3 which is connected to a fraction of the turns of the coil. The supply line was made of copper tubes through which water circulates and thus cooling of the If the filament has a skin-resistance Ps [ohm], then the depth of penetration of the field o is equal to circuit is achieved. The principal difficulty in realizing such a system is 109 associated with the choice of such dimensions and posi 6= 2 - rt - (J) p a - .‘i• (8.4) tion of the circuit that it would not interfere with the In the case that the plasma has a high conductivity this main oscillations feeding the filament. The power input quantity can be small, but not smaller than the depth o to the circuit in the feeder line 3 was measured in 0 which determines the density of electrons in the plas terms of the active component of the supply current. At ma. It is possible to make an estimate of this quantity an input power level of several kilowatts we attained an amplitude of wH = 30 Oe. The first experiments showed from the relation 6 0 ~ ( A.z /2JT)2 b-1 where A.z is the wavelength of the proper plasma oscillations. that, indeed, the filamentary discharge absorbs power. At the surface of the filament an azimuthal current At first this phenomenon was interpreted by us as an ef is produced with an amplitude equal to fect on the plasma of acoustic oscillations, but this in terpretation had to be abandoned, since it turned out that j = c\H I b. (8.5) the absorbed power is considerably higher than that per which on interacting with the magnetic field H gives mitted by expression (8.3 ). Making a further study of rise to a normal pressure jH sin wat which excites ra this phenomenon we discovered that it is not even asso dial magnetoacoustic waves. ciated with the intensity of the oscillations of the mag As has been noted already, the plasma is adjacent to netic field in the circuit. The matter was reduced to a a gas whose density is by a factor of 103 greater than simpler phenomenon. As can be seen from the construc the density of the plasma, and, therefore, we assume in tion of the oscillatory circuit shown in Fig. 8.1 in addi our calculations that at the boundary at r = b the plas tion to the variable magnetic field AH in the region ma remains stationary: where the filamentary discharge is situated an axial al ternating electric field is also produced by the capaci c\1-= 0, r =b. (8.6) tances 2 situated on the sides. It turns out that this field If the normal force Hj acting on the plasma were acts on the ionized gas surrounding the filamentary dis concentrated only at the boundary surface itself, then charge and is strongly absorbed. When the circuit was no oscillations could be generated in the plasma. But replaced by another one in which this horizontal compo since the current penetrates to a certain depth oscilla nent of the field was absent, the absorption of power tions will be generated even in the case of a stationary disappeared. Observations were carried out on the ef boundary. fect of the oscillation of AH in this circuit on the width Figure 8.2 represents a filament in terms of the co of the discharge, on its length, on the intensity of emis ordinates adopted by us. For the sake of simplicity we sion of Df3 and on AA.. No appreciable effect on these assume the filament to be a cylinder. We denote the quantities was observed. These experiments were car wave number by k = 2JT I A.a, the plasma density by di ried out during that stage of our investigations when we = ni mi and the gas pressure by p Then under the assumed the radius a of the cloud to be the radius of 0• condition that the frequency is considerably lower than the plasma in the filamentary discharge. Therefore, the plasma frequency ne and greater than the cyclo calculations of the power according to expression (8.3) were greater by a factor of 4-5. tron frequency wi we obtain the velocity of magneto A deeper investigation of the problem of the excita acoustic radial waves tion of magnetoacoustic waves in the plasma showed V’ = P\’ I d,, V =~ (•la I k, (8.7) that this is a difficult problem which, as will be seen, where does not have a simple solution. First, it is difficult to excite acoustic waves by pressure because at the bound ary the gas has a density which is by 2-3 orders of ( y is the adiabatic exponent). We consider the case of magnitude greater than that of the plasma. Therefore in making calculations concerning radial high frequen~y excitation of oscillations when the depth of penetration of the current o is small compared to the radius of the oscillations the boundary should be regarded as a sta plasma filament: tionary one. Oscillations can be excited in the plasma only if the pressure Ap (expression (8.1)) is applied 6<; b. not at the boundary itself but somewhat deeper. We Under this condition we can treat the process of the in give an example of a possible mechanism for the exci teraction between the current and the field at the bound tation of oscillations in the following theoretical inves ary of the filament as a plane case. We denote the dis tigations. tance from the boundary by x. The normal force acting

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 1005 in the plasma will be equal to The propagation of an acoustic radial wave in a cylin der is, as is well known, determined by the following F = - \}]“1 e-•·‘6 sinffiul. (8.9) expression: 6 We obtain the equation for the propagation of longitudi - 8 _ Ap - = -d;!‘1i’, 8(rM) = _ !p (8.20) or ror ’\‘P nal waves in the usual manner by considering the equi librium of the element dx: where the velocity of propagation of the waves is deter mined as before by expression (8. 7). For a wave pro li.r .. d1 +-u:-.c. - p = F, 81’1_ x +— O,· (8.10) gressing into the cylinder we have the following solu (\}X (\}X \‘P tion: from this equation and from expression (8. 7) we o~~tain !J.po = A [lo (kr) sin ( <p —wat) +No (kr) cos (<p-<rlat)], .. .., iJ’I’!.x F /:!.1; -l·— 8. . r.· , =-: rl - ; . (8.11) Mo =~~[JI(kr)cos(<p-wat)-N•(kr)sin(<p-wat)], (8.21\} d;l Substituting the value of F from (8.9) we solve this where A and cp constants. It can be shown that this equation under the boundary conditions (8.6). Utilizing expression indeed corresponds to a progressive wave. (8. 7) we obtain under the condition at the boundary .:lx We substitute these values into (8.15) and utilize the = 0, X= 0 Wronskian: [V=- d; [ P+ l ( / / 1 \{ ) j ( ua)” 1 re-x 0sinwat+sin(kx-w 0 t)], (8.22) J ( l’!.p =--- J - l + j6 - < (. o -), ,V .-, ,)-’ ~ - 1 - e-x, . ; st . n Wat-cos(k.r-<•lat) 8.12) We obtain that the average power of the wave flux will 12 6k be constant and equal to At a distance x from the boundary between the plas ma and the gas when it is considerably greater than o Ji, = -A’·4l/ uJad;. (8.23) (the depth of penetration of the current) a progressive Equating this expression to (8.17) we determine the wave is formed which is determined by the expressions quantity /‘li; = - c J 1 / , 1 1 - ’ · - 1 - - - i- f c J i J o 2 s(k.r-Wat), Ap0 = l/j-_ t - + fi B -2 cos(kx-<•latl. A = - , 1 2 ; ~ k l - /J 1 +p B’. (8.24) (8.13) In this expression we have introduced the notation When the wave is propagated inwards from the surface of the plasma the energy density of the oscillation be ~ = OWa IV= 2:tl\ I Aa. (8.14) comes infinite. The velocity .:lr near the axis of the Thus the quantity \{3 is determined by the ratio of the cylinder varies as depth of penetration of the current into the plasma to B the wavelength of the magnetoacoustic wave in the plasma. and, therefore, we obtain from (8.21) When the process of generation occurs at the sur 2A 1 face of the plasma filament and the radius of the fila i’li’o= ---sinwat. (8.25) ment b is large compared to the depth of penetration o, nwadi rn then the average power Pr which passes through the The kinetic energy of the ions in the plasma on the axis cylindrical surface of radius r will be given by of the filament will be equivalent to the temperature: P _ , = 4:trl T 1 T ~ e t1p0_\f0 dt. (8.15) T 1 = . 2 \ 1 i·’ , d ,1 , 1 _ ,- _ 2;tk _ oll; _ kr b n _ 2 [Jo

(l l 1 j 1 ) 2/ 2 4 n (1
~2 ~2)2’ ( 8•26) 0 We set where ko is the Boltzmann constant. The smallest value of the radius r is apparently de x = b-r, !J..i = -M; (8.16) termined by that quantity of ions and electrons for and obtain which the plasma ceases to oscillate as a continuous medium. This quantity is determined by the Debye ra P - ,=-2nbl (l V ij )2 --- ~ - 2 ’ - (8.17\} dius equal to d; (1+P’l’ (8.27) This expression has a maximum when \{3 = 1; utilizing (8. 7) we obtain _ n j2JJ2 where ne is the electron density, Te is the electron Pnn = —bl :;=::::::;=~~;:;,=;:-;=—:- temperature. On reaching this radius the waves will be 2 fpod;(1 +112/hpo) absorbed. Can one assume that as a result of this ab i-.a = 2rrb, b> b, (8.18) sorption their energy goes over into the thermal motion for plasma y = 1. of the ions in the plasma? This is as yet an unanswered When the pressure H2/8JT produced by the magnetic question, but it is a very important one, since for the field is either small or large compared to the gas pres heating of ions it is necessary that a significant frac sure Po we have two limiting cases: tion of acoustic oscillations would be absorbed by them. Prm = -rr’l,bl l ’ 2 _ If , - 112 ~ p,, In the case of the method described above for the exci ‘/dt 4n tation of plasma oscillations ohmic losses in the skin

J/2 ~ p •. (8.19\} layer are also unavoidable. They can be estimated. 4n If, as before, we treat the filament as a cylinder of

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1006 P. L. KAPITZA radius b and of length 2l then the average ohmic losses ions can be evaluated most reliably from (3.3) in terms will be given by of the limiting value of the frequency of emission in the microwave region (Fig. 3.6). If the temperature of the (8.28) ions is low then in the hot region of the plasma in the By using (6.1) in an approximate fashion we obtain in filament the electron temperature is above a million accordance with expression (8.14) degrees. The possibility of the existence of a plasma of such a high temperature is explained by us by analogy (8.29) with gas discharge tubes in terms of the appearance at the boundary of the plasma of a double layer which re from which we have flects electrons elastically. Thus a discontinuity in the electron temperature is produced. Theoretical calcula 2:d” Pp= 2nbi-;;;-F. (8.30) tions of the structure of the double layer (Sec. 4) show that it is realizable and that its characteristics agree The ratio of the acoustic power to the power of the ohm with the known experimental data which determine the ic losses will be equal in accordance with (8.17) and interaction between ions and electrons. In the model of (8. 7) to the structure of the filament adopted by us with an el lipsoidal region filled with hot plasma and surrounded P, 1 1/2 ~ (8.31) by a cloud of cold plasma the high frequency current x=p;=2np +ll’/4n1+B’ 2 flows over the boundary of the ellipse in a skin-layer. From here we obtain In Sec. 5 a method is described for measuring the cur rent and the results are given in Fig. 5.2. The high re Jl2 2 x=i+B” -4;t~ p. (8.32) sistance of the boundary layer of the hot plasma is ex plained by analogy with metals by the existence of an The maximum value will be x = 1 for \{3 = 1. Thus, the anomalous skin-resistance. Numerical calculations ohmic losses can be equal to or greater than the power confirm this well (Sec. 6). which is expended in maintaining acoustic oscillations. The elliptic shape of the filament and its great sta If in our experiments described at the beginning we bility are explained more simply than we had at first calculate in accordance with (8.17) the power input to supposed. The filament is formed in that region of the the filament it will turn out to be in the range from 100 electromagnetic field in which power can be supplied to to 200 W for the whole filament, and in our experiments it most efficiently. Thus, its shape and its stability are it does not appear to be possible to observe it. As can very similar to the stability of the flame of an ordinary be seen from (8.3) the transfer of energy by magneto candle, the shape of its flame is also determined by the acoustic oscillations increases with the square of the supply of fuel from the wick and by the air flow on the cross section and reaches a practical value when the outside. The length of the plasma filament is limited by dimensions of the filament are considerably greater half a wavelength of the high frequency field, because in than those which were realized in our apparatus. such a case the greatest power input to the discharge is The problem as to how to achieve effective heating achieved. Experiment shows that after the plasma fila of ions in the filament does not to date have a definite ment has attained this length a further increase in the solution. The most promising direction is the excitation power input leads to an increase in the cross section in the plasma of acoustic oscillations either radial or which also reaches a limiting value after which the fila axial. Of great interest also is the action of the field ment begins to break up into two parts (Sec. 6). Thus, on the cyclotron motion of the ions since here one might for a given frequency of the supply current there exists utilize resonance absorption. Of course, heating of the a limiting size of the filament. The investigations car ions can also occur as a result of a collective interac ried out by us have determined the electron structure of tion with electrons. As is well known, it has been ob the filament sufficiently fully. The existing theoretical served, but so far there is no quantitative estimate of ideas concerning the properties of plasma enable us to it. At this stage of the investigations of a filamentary give a quantitative interpretation of the observed phe discharge these problems must be regarded as some of nomenon. the fundamental ones. For the time being their solution The ions have turned out to present the greatest dif should be sought experimentally utilizing filaments of ficulty for an experimental study. The determination of large dimensions. the density of ions in the discharge does not present any difficulty since it is equal to the electron density. But inside the filament the hot plasma is not in equilibrium, 9. CONCLUSION and the ion temperature Ti can be considerably lower The analysis of the experimental material presented than the electron temperature Te. The most reliable in the preceding sections leads to the important result method for determining Ti utilizes the partial pres that the plasma at the center of the filament should be sure which the ions exert. As has been pointed out al regarded as hot. This follows most convincingly from ready, to achieve this one must in accordance with ex the intensity of its emission in the extreme ultraviolet pression (3.3) make a sufficiently accurate determina (1000 A) (Sec. 3) and also from the effect of a magnetic tion of the plasma density Ne and the electron tempera field on the shape of and on the emission from the fila ture Te. The plasma density can be determined suffi ment (Sec. 7). According to present theoretical ideas ciently accurately by the cutoff in the microwave region these phenomena cannot occur in a cold plasma. The (the curve of Fig. 3.5), but so far there is no possibility sum of the temperatures of the electrons and of the of accurately measuring the electron temperature in

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FREE PLASMA FILAMENT IN A HIGH FREQUENCY FIELD AT HIGH PRESSURE 1007 terms of the bremsstrahlung. If one could find a relia 10-4-10-5• It is natural to suppose that the diffuse state ble theory which quantitatively determines the effect of of the discharge in contrast to the filamentary state a magnetic field on the filamentary discharge which consists only of cold plasma. manifests itself in the experimental data described in A curious phenomenon was observed in experiments Sec. 7, then this could give a very reliable method of when the discharge was struck in helium which we took determining T e· But so far no such theory exists. from a gas cylinder. In this case the shape of the dis The method of determining the ion temperature in charge reminded one more of its diffuse state, although terms of the intensity of neutron emission is also suf in the middle of the discharge one could nevertheless ficiently reliable and simple. But this emission be see a filament. Unexpectedly it turned out that the visi comes measurable only at an ion temperature above a ble spectrum of this discharge does not contain a helium million degrees. At lower temperatures this method is line, but only a hydrogen line, even though the content of inapplicable. Therefore, for the time being we estimate hydrogen in the mixture was not greater than 1%. In or the ion temperature by means of a calculation on the der to obtain the purest possible helium we took it from basis of the Coulomb interaction between ions and elec evaporating liquid He. Only then did helium lines ap trons. This interaction has been well studied theoreti pear in the spectrum. In this case the hydrogen Balmer cally, it gives simple numerical relationships. By this lines still did not disappear, but the discharge became method we find that the temperature of deuterium ions even more diffuse and the filamentary structure at the at the center of the filament is in the neighborhood of center even less pronounced. These experiments have 105 °K (cf. Sec. 4). This temperature is insufficient to shown that the presence of even a small quantity of hy explain the existence of the weak neutron emission ob drogen creates favorable conditions for the production served by us which we described in the Introduction of a filamentary discharge. From the point of view of (Sec. 1) and which indicates a corresponding ion temper the model adopted by us as described in Sec. 4 it is ature in the neighborhood of 7 x 105 °K. One can draw natural to explain this phenomenon by the fact that hy conclusions regarding the temperature of the ions in an drogen atoms have the most suitable properties for the indirect manner by measuring the gradient of their establishment of a boundary layer. In accordance with temperatures. As is well known, this gradient deter expression (4.10) the large cross section qp for charge mines the thermal diffusion processes in the plasma. exchange leads to small losses in the boundary layer. Experiments on the thermal diffusion of hydrogen in The recombination coefficient also affects the losses in deuterium described in Sec. 4 gave an unexpected result the boundary layer. Possibly the value of these coeffi since they demonstrated its absence. Thus, determina cients in the case of hydrogen atoms favors the creation tion of the ion temperature is at present one of the fun of a boundary layer. We propose to make a more de damental and most interesting problems in the study of tailed study of this phenomenon. It is probable that a a filamentary discharge. filamentary discharge can be produced in helium without In addition to the experiments described in the pre an admixture of hydrogen only if the gas pressure is ceding sections we have observed in plasma a number high. of other phenomena which we have not as yet had time Production of a filamentary discharge in pure argon to study in detail, although a quantitative study of these also encounters difficulties. The discharge has a rather phenomena will further deepen our understanding of diffuse structure which is shot through with luminous plasma processes in a filamentary discharge. threads randomly situated in it. A small admixture of We shall indicate the more interesting ones of them. hydrogen immediately facilitates the production of a We modulated the high frequency power supplied from filamentary discharge. the nigotron to the discharge, and observed variations A more detailed study of these phenomena will most in the intensity of emission from the filament in the likely enable us to achieve a deeper understanding of the visible region of the spectrum. Variations of intensity mechanism of the processes leading to the production of were observed only when the modulation frequency was a filamentary discharge. not higher than 105 Hz. Approximate estimates have Further development of these investigations is at shown that this corresponds to the relaxation time for present limited by the scale of our present experiments. a hot plasma. In our apparatus described in Sec. 2 the radius of the The diffuse form of the discharge was also investi filament of hot plasma is not greater than 1.5-2 mm and gated. As has been pointed out in the Introduction, it ap and the double layer covering it is of approximately the peared at low power. Before assuming the shape of a same thickness. It is clear that with such small dimen filament the discharge had a diffuse shape of relatively sions of the filament it is difficult to study its structure low luminosity. It did not have a sharp boundary for the in detail. In the course of further developments of our luminous cloud and the shape of the discharge was investigations the scale of our experimental apparatus closer to oval than to filamentary. Experiment showed will be increased and consequently the cross section of that this type of discharge is produced more easily at the filament will be increased. low pressures (below 1 atm). Under these conditions it The difficulty in the study of the structure of the can exist over a wider range of power. At pressures of plasma filament is associated with the fact that the 3-4 atm we did not succeed in producing such diffuse emission from the external cloud is superimposed on discharges in hydrogen and in deuterium. The power the emission from the hot plasma. Therefore, one needed to maintain diffuse discharges is less than for a should transfer the study into the domain of the extreme filamentary discharge and lies in the range of 2.5-3 kW. ultraviolet where there is practically no emission from In the diffuse discharge the D13 line had a width of only the cloud. These investigations can be carried out with 0.5 A which corresponds to a degree of ionization of greater success when the electron temperature of the

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1008 P. L. KAPIT ZA hot plasma is higher, and this, as has been shown in at exceptionally high temperatures and high pressures Sec. 3, is achieved by increasing the cross section of must lead to a deeper scientific understanding of a num the filamentary discharge. ber of plasma processes. According to our ideas an increase in the dimensions of the filament will lead to an increase in the electron 1 P. L. Kapitza, In the collection of articles “Elek temperature. At the same time, as has been indicated tronika bol’shikh moshchnostei” (High Power Electron in Sec. 4, the ion temperature will not necessarily in ics) 1, Nauka, 1962. crease, it could even decrease, since the power trans 2P. L. Kapitza, Dokl. Akad. Nauk SSSR 101, 245 ferred from the electrons to the ions in accordance with (1955). expression (4.20) falls with an increase in their temper 3P, L. Kapitza, s. I. Filimonov, and S. P. Kapitza. ature. But an increase in the dimensions of the filament In the collection of articles “Elektronika bol’shikh opens up a possibility of realizing an independent power moshchnostei (High Power Electronics) 3, Nauka, 1963. input to the ions by means of magnetoacoustic oscilla 4P. L. Kapitza, s. I. Filimonov, and S. P. Kapitza. tions in the plasma. As has been indicated already in ibid. 6, Nauka, 1969. Sec. 8 in order to excite magnetoacoustic oscillations 5 V. I. Kogan. In the collection of articles “Fizika one should produce in the filament a longitudinal mag plazmy i problema upravlyaemykh termoyadernykh re netic field. This field will also reduce the radial ther aktsii” (Physics of Plasma and the Problem of Con mal conductivity of the ion gas (cf., Sec. 7), and this trolled Thermonuclear Reactions) 3, Published by will considerably raise the temperature of the ions in Academy of Sciences, USSR, 1968, p. 99. the internal portion of the hot plasma. Since at the 6 Collection of articles “Diagnostika plazmy” (Plas boundary of the hot plasma the temperature will be the ma Diagnostics) (translations), Mir, 1967. same as in the absence of a magnetic field, it is natural 7 P. L. Kapitza. In the collection of articles “Elek to assume that this increase in the temperature of the tronika bol’shikh moshchnostei” (High Power Electron ions will not affect the shape and the stability of the ics), 4, Nauka, 1965. filamentary discharge. As can be seen from expres 8 p. L. Kapitza and S. I. Filimonov, Us p. Fiz. Nauk sions (8.3) and (8.17) the input to the ions of sufficiently 95 3 5 (1968) [Sov. Phys.-Usp. 11, 299 (1968)]. high power in order to heat them appreciably can be achieved only with a sufficiently large diameter of the ‘9 A. I. Zaidel’ and E. Ya. Shreider, Spektroskopiya vakuumnogo ul’trafioleta (Spectroscopy of the Vacuum filament. The temperature Ti of the ions must be Ultraviolet), Nauka, 1967. raised sufficiently that it should reach 1-2 millions 10 E. w. MacDaniel, Collision Processes in Ionized of degrees. Then neutron emission will appear suffi Gases (Wiley, 1964). ciently intense for a reliable measurement of the ion 11A. v. Gurevich and L. P. Pitaevskii, Zh. Eksp. temperature. The theory of excitation of magnetoacous Teor. Fiz. 46, 1289 (1964) [Sov. Phys.-JETP 19, 874 tic oscillations which we developed in Sec. 8 and also (1964) ]. the theory of thermal insulation for the ions given in ex 12 L. Spitzer, Physics of Fully Ionized Gases, 2nd ed., pressions (7.7) and (7.25) enable us to calculate the di 1965. mensions of the filament needed to obtain such an ion 13S. I. Braginskii, in the collection of articles “Yo temperature. The principal indefiniteness in these cal prosy teorii plasmy” (Problems of Plasma Theory) 1, culations is the fact that so far no theoretical solution Atomizdat, 1963. has been found as to what fraction of the energy of the 14 G. E. H. Reuter and E. H. Sondheimer, Proc. Roy. acoustic oscillations will be utilized to heat the ions, Soc. (London) A195, 336 (1948). and what part will be used to heat the electrons. So far 15 L. Boltzmann, Festschrift, Leipzig 5, 904 (1904). no account has been taken in these calculations of the 16K. H. Riewe and L. Rompe, Z. Physik 103, 478 collective interaction which will apparently also raise (1937). the ion temperature. The production and study of the 17 J. H. Jeans, An Introduction to the Kinetic Theory thermonuclear process in the filament can, of course, of Gases, Cambridge, 1940, p. 186. also have a great practical significance for nuclear energy but in addition to that a study of the filamentary Translated by G. Volkoff discha;ge itself in which hot plasma exists continuously 213