PPPL-1755 CONF-791225-- MARCH 1981 PROCEEDINGS OF THE US-JAPAN JOINT SYMPOSIUM ON COMPACT TORUSES AND ENERGETIC PARTICLE INJECTION PRINCETON, NEW JERSEY, 12-14 December 1979 PLASMA PHYSICS LABORATORY PRINCETON UNIVERSITY PRINCETON, NEW JERSEY This work was supported by the U.S. Department of Energy Contract No. DE-AC02-76-CHO 3073. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted. PROCEEDINGS OF THE US-JAPAN JOINT SYMPOSIUM ON COMPACT TORUSES AND ENERGETIC PARTICLE INJECTION HOSTED BY PLASMA PHYSICS LABORATORY PRINCETON UNIVERSITY PRINCETON, NEW JERSEY 08544 ON 12-14 DECEMBER 1979 DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED PREFACE The sixty papers contained in these Proceedings serve to convey some idea of the highly original and diversified discussions that took place at the US-Japan Joint Symposium on Compact Toruses and Energetic Particle Injection. Perhaps the most striking feature of the Symposium, however, was not its diversity, but its essential unity. Researchers from such seemingly disparate fields as tokamaks, mirrors, theta pinches, zed-pinches, and relativistic-beam injection found themselves confronting identical problems of physics and converging towards a similar reactor goal. The participants were also pleased to experience a second form of convergence: the joining of the Japanese and United States fusion programs in a collaborative effort. This collaboration promises to be particularly fruitful in the area of compact toruses and energetic particle injection — where so much depends on the emergence of new ideas and new experimental techniques. Harold P. Furth 21 January 1980 TABLE OF CONTENTS Title Page ... i Preface ... ii Table of Contents ... iii Introductory Remarks by J. F. Clarke ... 1 The Compact Torus Concept and the Spheromak by H. P. Furth ... 3 Injection of Relativistic Electron Beam into Toroidal Systems by A. Mohri, K. Narihara, Y. Tomita ... 8 The LASL Compact Torus Program by R. K. Linford and CT Staff ... 12 Initial Results of Field Reversed Plasma Gun Experiment by W. C. Turner, C. W. Hartman, J. Taska ... 16 Experiment on Plasma Confinement by Intense Relativistic Electron Beam Ring by Y. Tomita, K. Narihara, T. Tsuzuki, M. Hasegawa, K. Ikuta, A. Mohri ... 20 Intense Relativistic Electron Beams in Toroidal Magnetic Geometries by V. Bailey, J. Benford, R. Cooper, B. Ecker, H. Helava ... 26 Compact Torus Research at U.C.I. by A. Fisher, S. Robertson, N. Rostoker ... 29 The Longshot Injector: A 3/4-kJ, 120-keV Pulsed Source of 3 x 10^16 Ions for Ion Ring Formation by J. B. Greenly, D. A. Hammer, R. N. Sudan ... 33 Reversed-Field Configuration with Rotating Relativistic Electron Beams by J. D. Sethian, K. A. Gerber, D. N. Spector, A. E. Robson ... 37 Results and Present Status of the Relativistic Electron Ring Experiments and Their Application to Spheromak Problems by H. H. Fleischmann ... 41 Reversed Field Configurations Generated by Proton Pulses by J. A. Pasour, J. Golden, J. Marsh, C. A. Kapetanakos ... 45 Thermal Background Effects on the Kink Instability of a Field-Reversing Ion Layer by S. J. Yakura, T. Kammash ... 49 Magnetized Gun Experiments by T. R. Jarboe, I. Henins, H. W. Hoida, J. Marshall, A. R. Sherwood ... 53 Formation of a Compact Torus using a Toroidal Plasma Gun by M. A. Levine, P. A. Pincosy ... 57 Reconnection Conditions for Flowing Field-Reversed Plasma from a Plasma Gun by J. W. Shearer, J. L. Eddleman, J. R. Ferguson ... 61 Physics of the OHTE by T. Ohkawa and the OHTE Group ... 65 Formation of Toroidal Plasma Confinement Configurations by using Hot Electrons by C. W. Hartman, M. A. Levine ... 68 Particle-Fluid Hybrid Simulation of Field Reversal in a Mirror Plasma by B. I. Cohen, T. A. Brengle ... 72 Two-Dimensional Time-Dependent Transport in Field Reversed Equilibria by S. P. Auerbach, H. L. Berk, J. K. Boyd, B. McNamara, D. Shumaker ... 76 A Steady-State Beam Driven Field-Reversed Mirror by J. H. Hammer, H. L. Berk ... 80 Calculation of Ideal MHD Growth Rates and Eigenfunctions in Field Reversed Mirrors in the Large Toroidal Mode Number Limit by D. V. Anderson, W. A. Newcomb ... 82 Toroidal Reversed Field-Pinch Experiments by D. A. Baker ... 86 Some Properties of the Heating and Confinement in the RFP Configuration by S. Ortolani ... 89 Relaxation of Toroidal Discharges by L. Turner ... 94 Effects of Impurity Radiation on Reversed-Field Pinch Evolution by E. J. Caramana, F. W. Perkins ... 98 Field Reversal Experiments, FRX-A and FRX-B Results by W. T. Armstrong, R. K. Linford, J. Lipson, D. A. Platts, E. G. Sherwood ... 102 FRX-C and Multiple-Cell Experiments by R. E. Siemon and LASL Compact Torus Staff ... 106 Compact Torus Theory — MHD Equilibrium and Stability by D. C. Barnes, C. E. Seyler ... 110 Two-Dimensional Simulation of Compact Torus Formation by D. W. Hewett ... 115 Two-Dimensional Compression in General Compact Tori by E. Hameiri, W. Grossmann ... 118 Tearing-Mode Stability Analysis to a Cylindrical Plasma by H. L. Berk, J. Sayer, D. D. Schnack ... 122 The Tilting Mode in the Reversed-Field Theta Pinch by A. I. Shestakov, D. D. Schnack, J. Killeen ... 126 Periodic Field-Reversed Equilibria for a Multiple-Cell Linear Theta Pinch by H. Meuth, F. L. Ribe ... 130 Zero-Dimensional Modeling of Field-Reversed Theta-Pinch Machines by E. H. Klevans ... 135 Spheromak Formation by Theta Pinch by Y. Nogi, H. Ogura, Y. Osanai, K. Saito, S. Shiina, H. Yoshimura ... 139 Field-Reversed Plasma Gun Based on the Inverse-Pinch Discharge by W. D. Getty ... 143 A Triggered-Reconnection Compact Toroid Experiment by A. L. Hoffman, G. C. Vlases ... 147 Plasma Rotation in Field-Reversed Theta Pinches by L. C. Steinhauer ... 151 Stellarmak a Hybrid Stellarator — Spheromak by C. W. Hartman ... 155 Utilization of Electron Coils for an Advanced Tokamak and Conjecture About the Cause for Current Step (Down) by S. Yoshikawa ... 159 Dynamically Formed Spheromak Plasma (PS-1) by G. C. Goldenbaum, Y. P. Chong, G. Hart, J. H. Irby ... 162 Spheromak Equilibrium and Stability and Numerical Studies of a Spheromak Formation Scheme by M. Okabayashi, S. Jardin, H. Okuda, T. Sato, G. Sheffield, A. Todd ... 166 Design and Fabrication of the S-1 Spheromak Device by M. Yamada, J. Sinnis, H. P. Furth, M. Okabayashi, G. Sheffield, T. H. Stix, A. M. M. Todd ... 171 Two-Dimensional Simulation of the Formation of the PPPL Spheromak by A. Aydemir, C. K. Chu, H. C. Lui ... 176 Bifurcation of Toroidal Plasma in a Poloidal Quadrupole Field by H. Ikezi, K. F. Schwarzenegger ... 180 Startup Scenario of Compact Tori Based on REB-Injection Developed in SPAC Group by K. Ikuta ... 184 The SPS Compact Torus Experiment by A. DeSilva ... 186 Minimum Energy Equilibria by A. Reiman, R. N. Sudan ... 189 Compact Toroidal Plasma Equilibrium and Implications on Stability by G. K. Morikawa ... 193 Radio-Frequency Flux Control of Toroidal Plasmas by S. Inoue, K. Itoh ... 197 Field-Reversed Configurations: Theoretical Considerations and Reactor Applications by G. H. Miley ... 200 The Holomak — A Toroidal Spheromak by T. H. Stix, A. M. M. Todd ... 204 The LINUS Reactor: Compression of a Compact Torus by a Liquid Metal Liner by A. E. Robson ... 208 Preliminary Studies of Spheromak Reactors by M. Katsurai, M. Yamada ... 212 The All Plasma Spheromak: The Plasmak by P. Koloc, J. Ogden ... 216 Neutral Beam Sustained, Field-Reversed Mirror Reactors by G. A. Carlson, K. R. Schultz, A. C. Smith, Jr. ... 220 The Moving-Ring Field-Reversed Mirror Reactor Concept by A. C. Smith, Jr., G. A. Carlson, H. H. Fleischmann, T. Kammash, K. R. Schultz, D. M. Woodall ... 224 Preliminary Reactor Implications of Compact Tori: How Small is Compact? by R. A. Krakowski, R. L. Hagenson ... 228 TRACT: A Small Fusion Reactor Based on a Compact Torus Plasma by H. J. Willenberg, A. L. Hoffman, L. C. Steinhauer, P. H. Rose ... 233 List of Attendees ... 237 INTRODUCTORY REMARKS John F. Clarke, Deputy Director, Office of Fusion Energy, Department of Energy, Washington, D.C. 20545 I wish to add my welcome and that of the Department of Energy to Mel's. Exchange visits of the past have proven to be valuable to the participants from both countries, and it is gratifying that this is the first to be held under the newly inaugurated series with the Government of Japan. It may not be coincidental that the topic for this conference is in the area of alternative concepts. The diversity of our national program is probably matched only by the Japanese program among the several national fusion programs worldwide. Further, the focus of the meeting, what we call compact toroids, is indicative of the readiness of the worldwide fusion community to deal with worthy, innovative ideas. In the U.S. program we continuously evaluate alternate confinement approaches for development as fusion power systems. How do we arrive at a decision to launch development of an approach such as compact toroids and neglect others? This is a difficult technical management issue that we are frequently asked to address. The answer is not simple and ultimately must rely on professional judgments. The process for selecting concepts has evolved as technical successes were obtained in the development of the mainline confinement concepts. That introduces a key element in the selection process: we examine and select alternate confinement approaches by taking full account of the status of the principle confinement approaches, and we do not undertake selection of alternate fusion confinement as an abstract exercise. Historically, the mainline confinement approaches, the tokamak and mirror, have reached a prominent role in the development program because of demonstrated experimental success in confining hot, fusion-quality plasma earlier than other approaches. However, the flexibility implicit in the physical principles that unite all confinement concepts has permitted a great variety of feasible fusion approaches to be conceived and proposed for development. These are collectively identified as alternate concepts. Any number of them might be chosen for development and ultimately lead to successful fusion power systems. It is taken as an imperative by the Office of Fusion Energy that any attempt to develop all of them with equal emphasis would be detrimental to the eventual technical success of the most promising and an irresponsible utilization of valuable resources. Several courses of action are conceivable in order to optimize the development of the highest potential of fusion for commercial application. The one approach that is clearly unsound is to ignore potential advantages that can come to the development program from ideas outside the mainline effort. It is precisely this factor that is employed in the review and selection process for alternate concepts. The selection of alternate confinement approaches for development involves three factors: potential reactor advantages with respect to the mainline approaches, technical feasibility, and the readiness (or timeliness) of undertaking the development with respect to the status of worldwide fusion development. The analysis of these factors is a continuing process; the level of performance by which the concepts are evaluated becomes increasingly more demanding as the concepts mature (and as the successes of the mainline effort elevate the general standard for all fusion development). Novel alternate concepts such as compact toroids must be perceived by the fusion community as having the potential of significant reactor advantages with respect to the mainline concepts. As the concept matures and becomes ready for proof-of-principle level tests, the perception must be replaced by quantitative studies supporting the reactor advantages. The compact toroid concept is clearly in an embryonic state. As the research we will hear about during the next several days evolves, this concept will be submitted to this scrutiny also. We wish the research success for it is equally clear that this approach has significant potential benefits for users. Despite the enthusiasm for such a fusion system it still takes the dedicated work of the fusion community to make the promise of it a reality. THE COMPACT TORUS CONCEPT AND THE SPHEROMAK H. P. Furth, Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08544 Photographs of solar activity, using polarized filters [1], have provided indirect evidence of the emission of long-lived toroidal plasma configurations confined by linked poloidal and toroidal magnetic fluxes. Plasma configurations of this sort were first produced in the laboratory by H. Alfvén [2] and his coworkers (cf. Fig. 1) and reported at the Second International Conference on Peaceful Uses of Atomic Energy in 1958. The injection of a current layer of highly energetic electrons (an "E-layer") to produce a steady-state toroidal plasma confined by poloidal field was proposed at the same conference by N. Christofilos [3]. A modern variant of this idea, using a neutral-beam-injected, medium-energy ion current [4], is shown in Fig. 2. Reversed-poloidal-field configurations of the same form have long been produced successfully by means of ordinary plasma currents in theta pinches — both with and without toroidal magnetic field component [5,6] (Fig. 3). The common feature of all these plasma confinement schemes is that the magnetic field lines are closed, yet the field generating coil system is not required to link the plasma toroid. The principal variants of this "compact torus" concept are tabulated in Fig. 4. The present paper is concerned mainly with a brief review of the case B_pol < B_plasma, where the current carriers have poloidal-field gyroradii that are smaller than the scale height of the plasma. Experimental theta-pinch plasmas with essentially null toroidal-field component (B_pol >> B_tor) have exhibited remarkable longevity in terms of the characteristic time scale for MHD instability [7,8]. While the ideal MHD theory for this configuration does not actually allow all modes to be stabilized, the elimination of the strongest instabilities by axial elongation, combined with the finiteness of the plasma ion gyroradius (a_pol ~ a_plasma) may be providing effective stability in the experiments. For the reactor application, the null-B_t variant has the obvious advantage of very high beta-value (\beta \le 1), but the possible drawback of insufficiently stable confinement, since there may be a contradiction between the requirements for stability against gross modes and microinstabilities. The fast time scales and high voltages of the field-reversed theta-pinch formation method (Fig. 2) could be avoided in the beam-injected field-reversed mirror approach (Fig. 3), provided that the problem of ion-current cancelation by the electron-drag current can be resolved satisfactorily [4]. The compact torus with comparable toroidal and poloidal field components (Fig. 1), which has lately come to be called the "spheromak," has long received theoretical attention [9,10,11]. The toroidal field is supported by poloidal currents flowing inside the plasma and must, of course, vanish outside the plasma boundary. Ideal MHD stability is achievable when the plasma entity is somewhat oblate, as in Fig. 5, and is surrounded by a moderately close-fitting conducting shell [12]. Under these conditions, the stability limit for \beta_0 \equiv 8\pi \langle p^2 \rangle^{1/2}/B_0^2 (where B_0 is the field strength on the magnetic axis) is typically of order 2-5%, but it can be several times greater in highly optimized configurations [13]. The basic advantage of the finite-B_tor regime is that stability against all ideal MHD modes can be ensured even for the case a_pol << a_plasma, which is congenial to good microstability properties. The main drawbacks are that special provision must be made for generating the toroidal flux and that beta must remain well below unity. It should be noted, however, that a limiting value of \beta_0 in the 5-10% range for the spheromak gives as much \langle p^2 \rangle^{1/2} as a tokamak \beta_0-value of 50-100%, if the maximum field strength at the magnet coils is the same in the two cases. This is because the spheromak field is maximal at the plasma center (Fig. 5) while the tokamak field is maximal at the coils. The spheromak is closely related to the conventional reversed-field Z-pinch (RFP) [14]: it corresponds to the particular case of null field-reversal and fairly low aspect ratio. The RFP has more shear, and thus is able to tolerate somewhat higher limiting beta values, but has the drawback of requiring plasma linkage by external toroidal-field coils. Experimentally [15], the null-field case of the RFP is found to lie precisely at the transition point between the "quiescent" state that is achieved with external B_tor \le 0 and the turbulent state that prevails for external B_tor > 0. The finite-resistivity MHD kink modes of the spheromak have been studied for large aspect ratio: stability is found to be realizable with optimal current profiles and very close-fitting shells [16] — quite comparable to the case of the conventional RFP. The low-aspect-ratio limit appears to have similar resistive instability characteristics [12], but has not yet been treated for optimized profiles. The stabilization of the resistive interchange mode in the spheromak depends mainly on collisionlessness and moderation of the beta value [17]. (For the B_tor = 0 version of the compact torus, the resistive MHD analysis has been carried out thus far only for the special case of axisymmetric modes [18].) The experimental study of spheromak plasmas began with Alfvén [2]. It has been resumed recently, by means of the same coaxial-gun technique [19,20] (Fig. 1), as well as by means of a theta-pinch formation process (Fig. 3) that includes toroidal-field generation [21]. References 22-24 describe a new type of "quasi-static" spheromak-formation technique that is aimed at avoiding the high pulsed powers associated with a dynamic forming process in plasmas of reactor size. The degree of gross stability observed during the limited pulse time of the theta-pinch spheromak experiment [21] has been excellent — or even too good, since the ideal MHD theory clearly predicts a tilting mode [12] for prolate plasmas of the type of Fig. 3, whether a toroidal field component is present or absent. The antitheoretical stability against tilting has also been noted experimentally in the B_pol >> B_tor case [7,8]. Very recently, however, the injection of a gun-produced spheromak plasma into a prolate conducting shell has exhibited the predicted tilting [20]. The suppression of the tilting mode, as well as of higher surface modes, may be a consequence of the presence of hot plasma at the separatrix (cf. Fig. 3) and just outside it. An effect might be expected when the ion gyroradii are large or when the field outside the separatrix retains finite shear, due to the presence of external axial plasma currents or helical windings [12]. External-plasma stabilization could turn out to be very important for the compact-torus reactor application, since stabilization by close-fitting conducting shells would be inconveniently restrictive. As is shown in several reactor studies [25-27], one of the attractions of the compact torus is its potential ability to undergo compression, expansion, or displacement, free of mechanical constraints. ACKNOWLEDGMENT This work supported by US Department of Energy Contract No. EY-76-C-02-3073. REFERENCES [1] RIDDLE, A. C., Solar Physics 13 (1970) 448-457. [2] ALFVÉN, H., Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31 (1958) 3. [3] CHRISTOFILOS, N., Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 32 (1958) 279. [4] COHEN, B. I., BRENGLE, T. A., Particle-Fluid Hybrid Simulation of Field Reversal in a Mirror Plasma, this conference. [5] KOLB, A. C., DOBBIE, C. B., GRIEM, H. R., Phys. Rev. Lett. 3 (1959) 5. [6] KOLB, A., et al., in Plasma Physics and Controlled Nuclear Fusion Research (Proc. 3rd Int. Conf., Novosibirsk, 1968) II (IAEA, Vienna, 1969) 567. [7] ES'KOV, A. G., et al., in Controlled Fusion and Plasma Physics (Proc. 7th European Conf., Lausanne, 1975) I, 55. [8] LINFORD, R. K., and CT Staff, The LASL Compact Torus Program, this conference. [9] LÜST, R., SCHLÜTER, A., Z. Astrophys. 34 (1954) 263. [10] CHANDRASEKHAR, S., in Proc. of the National Academy of Sciences 42 (1956) 1. [11] MORIKAWA, G. K., et al., Phys. Fluids 12 (1969) 1643. [12] BUSSAC, M. N., et al., in Plasma Physics and Controlled Nuclear Fusion Research (Proc. 7th Int. Conf., Innsbruck, 1978) III (IAEA, Vienna, 1979) 249. [13] GAUTIER, P., et al., in Controlled Fusion and Plasma Physics (Proc. 9th European Conf., Oxford, 1979) paper EP 30, to be published. [14] BAKER, D. A., Toroidal Reversed Field-Pinch Experiments, this conference. [15] ORTOLANI, S., Some Properties of the Heating and Confinement in the RFP Configuration, this conference. [16] GLASSER, A., SELBERG, H., to be published. [17] BUSSAC, M. N., Bull. Am. Phys. Soc. 23 (1979) 872. [18] BERK, H. L., et al., Tearing-Mode Stability Analysis of a Cylindrical Plasma, this conference. [19] TURNER, W. C., et al., Initial Results of Field Reversed Plasma Gun Experiment, this conference. [20] JARBOE, T. R., et al., Magnetized Gun Experiments, this conference. [21] GOLDENBAUM, G. C., et al., Dynamically Formed Spheromak Plasma (PS-1), this conference. [22] OKABAYASHI, M., et al., Spheromak Equilibrium and Stability and Numerical Studies of a Spheromak Formation Scheme, this conference. [23] YAMADA, M., et al., Design and Fabrication of the S-1 Spheromak Device, this conference. [24] AYDEMIR, A., et al., Two-Dimensional Simulation of the Formation of the PPPL Spheromak, this conference. [25] MILEY, G. H., Field-Reversed Configurations: Theoretical Considerations and Reactor Applications, this conference. [26] KATSURAI, M., YAMADA, M., Preliminary Studies of Spheromak Reactors, this conference. [27] SMITH, A. C., Jr., et al., The Moving-Ring Field-Reversed Mirror Reactor Concept, this conference. FIGURE CAPTIONS: Fig. 1. Spheromak generation, using a coaxial plasma gun with poloidal field at the muzzle. Fig. 2. Neutral-beam-driven field-reversed mirror machine. Fig. 3. Field-reversed theta pinch. Fig. 4. Tabulation of compact toruses. Fig. 5. Oblate spheromak. Plasma current is localized within the solid-field-line region. (PPL 786431) A wide variety of research was presented at the symposium covering theoretical modeling, numerical simulations, experiments on magnetic guns, relativistic electron beams, theta pinches, and reactor design concepts: 1. Injection of Relativistic Electron Beam into Toroidal Systems (A. Mohri, K. Narihara, Y. Tomita - IPP Nagoya) 2. The LASL Compact Torus Program (R. K. Linford et al. - Los Alamos Scientific Laboratory) 3. Initial Results of Field Reversed Plasma Gun Experiment (W. C. Turner, C. W. Hartman, J. Taska - Lawrence Livermore Laboratory; A. C. Smith, Jr. - PG&E) 4. Experiment on Plasma Confinement by Intense Relativistic Electron Beam Ring (Y. Tomita et al. - IPP Nagoya) 5. Intense Relativistic Electron Beams in Toroidal Magnetic Geometries (V. Bailey et al. - Physics International Company) 6. Compact Torus Research at U.C.I. (A. Fisher, S. Robertson, N. Rostoker - UC Irvine) 7. The Longshot Injector: A 3/4-kJ, 120-keV Pulsed Source of 3x10^16 Ions for Ion Ring Formation (J. B. Greenly, D. A. Hammer, R. N. Sudan - Cornell University) 8. Reversed-Field Configuration with Rotating Relativistic Electron Beams (J. D. Sethian et al. - Naval Research Laboratory) 9. Results and Present Status of the Relativistic Electron Ring Experiments and Their Application to Spheromak Problems (H. H. Fleischmann - Cornell University) 10. Reversed Field Configurations Generated by Proton Pulses (J. A. Pasour et al. - Naval Research Laboratory) 11. Thermal Background Effects on the Kink Instability of a Field-Reversing Ion Layer (S. J. Yakura, T. Kammash - University of Michigan) 12. Magnetized Gun Experiments (T. R. Jarboe et al. - LASL) 13. Formation of a Compact Torus using a Toroidal Plasma Gun (M. A. Levine, P. A. Pincosy - LBL) 14. Reconnection Conditions for Flowing Field-Reversed Plasma from a Plasma Gun (J. W. Shearer et al. - LLL) 15. Physics of the OHTE (T. Ohkawa and the OHTE Group - General Atomic Company) 16. Formation of Toroidal Plasma Confinement Configurations by using Hot Electrons (C. W. Hartman, M. A. Levine - LLL/LBL) 17. Particle-Fluid Hybrid Simulation of Field Reversal in a Mirror Plasma (B. I. Cohen, T. A. Brengle - LLL) 18. Two-Dimensional Time-Dependent Transport in Field Reversed Equilibria (S. P. Auerbach et al. - LLL) 19. A Steady-State Beam Driven Field-Reversed Mirror (J. H. Hammer, H. L. Berk - LLL) 20. Calculation of Ideal MHD Growth Rates and Eigenfunctions in Field Reversed Mirrors in the Large Toroidal Mode Number Limit (D. V. Anderson, W. A. Newcomb, D. C. Barnes - LLL/LASL) 21. Toroidal Reversed Field-Pinch Experiments (D. A. Baker - LASL) 22. Some Properties of the Heating and Confinement in the RFP Configuration (S. Ortolani - CNR-Padova) 23. Relaxation of Toroidal Discharges (L. Turner - LASL) 24. Effects of Impurity Radiation on Reversed-Field Pinch Evolution (E. J. Caramana, F. W. Perkins - PPPL/LASL) 25. Field Reversal Experiments, FRX-A and FRX-B Results (W. T. Armstrong et al. - LASL) 26. FRX-C and Multiple-Cell Experiments (R. E. Siemon et al. - LASL) 27. Compact Torus Theory — MHD Equilibrium and Stability (D. C. Barnes, C. E. Seyler, D. V. Anderson - LASL/LLL) 28. Two-Dimensional Simulation of Compact Torus Formation (D. W. Hewett - LASL) 29. Two-Dimensional Compression in General Compact Tori (E. Hameiri, W. Grossmann - Courant Institute, NYU) 30. Tearing-Mode Stability Analysis of a Cylindrical Plasma (H. L. Berk, J. Sayer, D. D. Schnack - LLL) 31. The Tilting Mode in the Reversed-Field Theta Pinch (A. I. Shestakov, D. D. Schnack, J. Killeen - NMFECC/LLL) 32. Periodic Field-Reversed Equilibria for a Multiple-Cell Linear Theta Pinch (H. Meuth, F. L. Ribe - University of Washington) 33. Zero-Dimensional Modeling of Field-Reversed Theta-Pinch Machines (E. H. Klevans - Penn State University) 34. Spheromak Formation by Theta Pinch (Y. Nogi et al. - Nihon University) 35. Field-Reversed Plasma Gun Based on the Inverse-Pinch Discharge (W. D. Getty - University of Michigan) 36. A Triggered-Reconnection Compact Toroid Experiment (A. L. Hoffman, G. C. Vlases - MSNW) 37. Plasma Rotation in Field-Reversed Theta Pinches (L. C. Steinhauer - MSNW) 38. Stellarmak a Hybrid Stellarator — Spheromak (C. W. Hartman - LLL) 39. Utilization of Electron Coils for an Advanced Tokamak and Conjecture About the Cause for Current Step (Down) (S. Yoshikawa - PPPL) 40. Dynamically Formed Spheromak Plasma (PS-1) (G. C. Goldenbaum et al. - University of Maryland) 41. Spheromak Equilibrium and Stability and Numerical Studies of a Spheromak Formation Scheme (M. Okabayashi et al. - PPPL/Grumman/Univ. of Tokyo) 42. Design and Fabrication of the S-1 Spheromak Device (M. Yamada et al. - PPPL/Grumman) 43. Two-Dimensional Simulation of the Formation of the PPPL Spheromak (A. Aydemir, C. K. Chu, H. C. Lui - Columbia University) 44. Bifurcation of Toroidal Plasma in a Poloidal Quadrupole Field (H. Ikezi, K. F. Schwarzenegger - Bell Labs) 45. Startup Scenario of Compact Tori Based on REB-Injection Developed in SPAC Group (K. Ikuta - IPP Nagoya) 46. The SPS Compact Torus Experiment (A. DeSilva - University of Maryland) 47. Minimum Energy Equilibria (A. Reiman, R. N. Sudan - Cornell University) 48. Compact Toroidal Plasma Equilibrium and Implications on Stability (G. K. Morikawa - Courant Institute, NYU) 49. Radio-Frequency Flux Control of Toroidal Plasmas (S. Inoue, K. Itoh - Hiroshima University / JAERI) 50. Field-Reversed Configurations: Theoretical Considerations and Reactor Applications (G. H. Miley - University of Illinois) 51. The Holomak — A Toroidal Spheromak (T. H. Stix, A. M. M. Todd - PPPL) 52. The LINUS Reactor: Compression of a Compact Torus by a Liquid Metal Liner (A. E. Robson - NRL) 53. Preliminary Studies of Spheromak Reactors (M. Katsurai, M. Yamada - Princeton/University of Tokyo) 54. The All Plasma Spheromak: The Plasmak (P. Koloc, J. Ogden - Prometheus II, Ltd.) 55. Neutral Beam Sustained, Field-Reversed Mirror Reactors (G. A. Carlson et al. - LLL/GA/PG&E) 56. The Moving-Ring Field-Reversed Mirror Reactor Concept (A. C. Smith, Jr. et al. - PG&E/LLL/Cornell/Univ. of Michigan/GA/Univ. of New Mexico) 57. Preliminary Reactor Implications of Compact Tori: How Small is Compact? (R. A. Krakowski, R. L. Hagenson - LASL) 58. TRACT: A Small Fusion Reactor Based on a Compact Torus Plasma (H. J. Willenberg, A. L. Hoffman, L. C. Steinhauer, P. H. Rose - MSNW) ATTENDEES Hiroshima University: - Dr. S. Inoue Institute of Plasma Physics, Nagoya University: - Dr. K. Ikuta - Dr. A. Mohri - Dr. K. Narihara - Dr. Y. Tomita Nihon University: - Dr. Y. Nogi Bell Telephone Laboratories, Inc.: - Dr. H. Ikezi University of California at Irvine: - Dr. S. Robertson - Dr. N. Rostoker University of California, Los Angeles: - Dr. R. Taylor Columbia University: - Dr. C. K. Chu Cornell University: - Dr. H. Fleischmann - Dr. B. Kusse - Dr. J. Greenly - Dr. R. Sudan - Dr. A. Reiman Office of Fusion Energy, U.S. Department of Energy: - Dr. J. Clarke - Dr. W. Dove - Dr. T. George - Dr. D. Thomson - Dr. W. Ellis Grumman Aerospace Corporation: - Dr. A. Todd Electric Power Research Institute (EPRI): - Dr. D. Paul - Dr. R. Scott General Atomic Company: - Dr. T. Ohkawa University of Illinois: - Dr. G. Miley Institute for Advanced Study: - Dr. Y.-P. Ho - Dr. M. Rosenbluth - Dr. J. VanDam Lawrence Livermore Laboratory: - Dr. S. Auerbach - Dr. H. Berk - Dr. G. Carlson - Dr. T. K. Fowler - Dr. J. Hammer - Dr. C. Hartman - Dr. R. Post - Dr. J. Shearer - Dr. W. Turner - Dr. D. Schnack - Dr. A. Shestakov - Dr. D. Anderson Los Alamos Scientific Laboratory: - Dr. D. Baker - Dr. D. Barnes - Dr. T. Armstrong - Dr. T. Jarboe - Dr. R. Krakowski - Dr. W. Quinn - Dr. R. Linford - Dr. S. Ortolani - Dr. A. Sherwood - Dr. R. Siemon - Dr. L. Turner University of Maryland: - Dr. A. DeSilva - Dr. G. Goldenbaum - Dr. Z. An (Southwest Institute of Physics, PRC) Massachusetts Institute of Technology: - Dr. A. Janos - Dr. D. Pappas Mathematical Sciences Northwest, Inc. (MSNW): - Dr. P. Rose - Dr. L. Steinhauer - Dr. G. Vlases Max-Planck-Institut für Plasmaphysik, Garching: - Dr. G. Spies University of Michigan: - Dr. T. Kammash - Dr. W. Getty Naval Research Laboratory: - Dr. C. Kapetanakos - Dr. J. Finn - Dr. A. Robson - Dr. J. Sethian - Dr. P. Turchi Jaycor, Inc.: - Dr. E. Scannell Courant Institute of Mathematical Sciences, NYU: - Dr. W. Grossmann - Dr. G. Morikawa Oak Ridge National Laboratory: - Dr. D. Sigmar Pennsylvania State University: - Dr. E. Klevans - Dr. T. York Physics International Company: - Dr. V. Bailey - Dr. B. Ecker - Dr. H. Helava Pacific Gas and Electric Company: - Dr. A. C. Smith, Jr. Public Service Electric and Gas Company: - Dr. B. Jensen Princeton Plasma Physics Laboratory: - Dr. A. Boozer - Dr. H. Furth - Dr. M. Gottlieb - Dr. R. Jacobsen - Dr. J. L. Johnson - Dr. M. Katsurai - Dr. S. Jardin - Dr. M. Okabayashi - Dr. F. Perkins, Jr. - Dr. J. Sinnis - Dr. T. Stix - Dr. M. Yamada - Dr. K. Yamazaki - Dr. S. Yoshikawa University of Washington: - Dr. F. Ribe - Dr. H. Meuth University of Miami: - Dr. D. Wells Prometheus II, Ltd.: - Dr. P. Koloc - Dr. J. Ogden Society to Advance Fusion Energy: - Mrs. L. Slaner Lawrence Berkeley Laboratory: - Dr. B. Feinberg - Dr. M. Levine Stevens Institute of Technology: - Dr. M. Seidl