RESEARCH ARTICLE | APRIL 29 2015 Plasma-gun-assisted field-reversed configuration formation in a conical θ-pinch  T. E. Weber; T. P. Intrator; R. J. Smith Phys. Plasmas 22, 042518 (2015) https://doi.org/10.1063/1.4919262  CHORUS   View Export Online Citation Articles You May Be Interested In Applied magnetic field design for the field reversed configuration compression heating experiment Rev. Sci. Instrum. (April 2013) A multi-frame soft x-ray pinhole imaging diagnostic for single-shot applications Rev. Sci. Instrum. (July 2012) Numerical studies of the effects of precursor plasma on the performance of wire-array Z-pinches Phys. Plasmas (June 2010) 22 August 2025 23:26:50 S S S S S S e e e e c e c c e r r r c e c e e c r t M r t M t M r e e e i i i l l l t i t i i t t t t M a M a a M r r r y y y i T i T T i l l l i e i e e i t t t c c c a a a h h h r n r n n r y o y o o y l l l T o T o o T g g g e y e y y e . . . c c c c c c S o S o S o h h h e m e m e m nc c n c n r r r e e e o o o t t t M M M l l l o o o i i i l l l i i i gt t g t g a a a yr r y r y y y y .T T . T . ce e c e c oc c o c o S h S h S h mn n m n m e e e o o o c l o c l o c l o g g g r r r e y e y e y . . . c c c t S o tS o S t o M M M e m e m e m c c c i r ir r i l e le e l i i i t t M ttM t M t a a a i i i r l i lri l i r t t t y a ya a y r r r T y Ty y T T T T e e e e e e c c cc c c h h h h h h n n n n o on o n l l l o o o o o o g g g l y ly y l o . o. . o c c c S g o S go S o g e m e m e m y y y c c c r . r . r . e e e c c c t t t M o M o M o S S S i i i l m l m l m i i i e t e t te a a a c r c r rc y y y r T r T Tr e e e e ee c c c t t t h h h M M M n n n o o o i l i l li l o l o ol i i i g g g t t t a y a y ya . . . c c c r r r S o S o S o y y y e m e m e m T c c T c T r r r e e e e e e t t t c M M c M c h i l i l h i l h i i i t t t n a a n a n r r r o y y o y o T T T l l l o e e o e o c c c g h h g h g n n n y y y o o o . l l . l . o o o c c c g g g o y y o y o . . . m c c m c m o o o m m m PHYSICSOFPLASMAS22,042518(2015) Plasma-gun-assisted field-reversed configuration formation in a conical h-pinch T.E.Weber,1,a)T.P.Intrator,1,b)andR.J.Smith2 1LosAlamosNationalLaboratory,LosAlamos,NewMexico87545,USA 2DepartmentofAeronauticsandAstronautics,UniversityofWashington,Seattle,Washington98195,USA (Received23February2015;accepted16April2015;publishedonline29April2015) Injection of plasma via an annular array of coaxial plasma guns during the pre-ionization phase of field-reversed configuration (FRC) formation is shown to catalyze the bulk ionization of a neutral gasprefillinthepresenceofastrongaxialmagneticfieldandchangethecharacterofoutwardflux flow during field-reversal from a convective process to a much slower resistive diffusion process. ThisapproachhasbeenfoundtosignificantlyimproveFRCformationinaconicalh-pinch,resulting ina(cid:2)350%increaseintrappedfluxattypicaloperatingconditions,anexpansionofaccessiblefor- mation parameter space to lower densities and higher temperatures, and a reduction or elimination ofseveraldeleteriouseffectsassociatedwiththepre-ionizationphase.VC 2015AIPPublishingLLC. [http://dx.doi.org/10.1063/1.4919262] I. INTRODUCTION shocks12,13 through the acceleration and subsequent stagna- tion of FRC plasmoids against a strong magnetic mirror and A field-reversed configuration (FRC)1,2 is a compact to- flux-conservingboundary.MSXusesmuchoftheequipment roidal plasmoid with a simply connected separatrix and pre- fromthediscontinuedField-ReversedExperimentwithLiner dominantly poloidal magnetic field. Its robust nature under (FRX-L)14,15 program, which served as a test bed for tech- extremeaccelerationandstabilityduringtranslationmakethe nology and techniques that were eventually adopted on FRC a useful plasma configuration for a variety of applica- FRCHX. Accordingly, MSX and FRCHX use nearly identi- tions.Primarilystudiedasasteady-statemagneticfusioncon- cal conical h-pinch hardware to form and accelerate FRCs. finement concept, the majority of previous research has The goal of FRCHX is to investigate a version of magneto- consequentlyfocusedonnon-translatingFRCscreatedinacy- inertialfusion16inwhichaFRCisinjectedintoaconverging lindrical h-pinch. These techniques have since been adapted solid,conductiveliner,andcompressedtofusionconditions. to produce translating FRCs through simultaneous formation andaccelerationusingaconicalh-pinch.3–5FRCformationin Bothoftheseeffortsrequireefficientflux-trappingatsignifi- a conical h-pinch, however, presents several unique chal- cantly higher densities and magnetic fields than have previ- lenges that have historically resulted in relatively poor per- ouslybeenattempted. formancecomparedtostaticformationinacylindricalpinch. Following this Introduction, Sec. II briefly reviews This paper explores the impact of initial ionization con- static FRC formation and flux-trapping in a cylindrical h- ditions and pre-ionization technique on FRC formation/ pinch, discusses specific difficulties involved with forma- acceleration in a conical h-pinch at high densities and mag- tion in a conical h-pinch, and motivates the need for netic fields. We hypothesize that introduction of a small improved pre-ionization. Section III introduces an alterna- amount of seed plasma can catalyze a Townsend ionization tive ionization method using plasma injection via an annu- cascade6drivenbyanazimuthalelectricfieldinthepresence lar array of coaxial plasma guns and describes the hardware of a strong axial magnetic field, thereby allowing bulk ioni- used in this study. Section IV presents the results of initial zation of a neutral gas prefill to occur at significantly higher testing, their bearing on a modified formation strategy, and levels of axial magneticbias thanwouldotherwise be possi- interpretation of data from integrated formation experiments ble using the traditional method of ringing the axial field. using a variety of pre-ionization techniques conducted over This has the potential to significantly improve flux-trapping a range of operating conditions. Finally, conclusions from andprovideadditionalflexibilitytoaccommodatethespecial this study and implications for future research are discussed requirementsoftranslatingFRCexperiments. in Sec. V. Investigation of this approach was carried out on the Magnetized Shock Experiment (MSX)7 at Los Alamos II. BACKGROUND NationalLaboratorywiththeintentionofsubsequentfielding The field-reversed h-pinch (FRTP)1,2 technique has his- on the Field-Reversed Configuration Heating Experiment (FRCHX)8–11 at the Air Force Research Laboratory, torically been the most common method of forming FRCs, anddespitethedevelopmentofseveralalternativeformation Kirtland, if the technique proved successful. The purpose of techniques(e.g.,RotatingMagneticFields(RMF),17Coaxial MSX is to study the physics of magnetized collisionless SlowSource(CSS),18mergingspheromaks19),itremainsthe a)Electronicmail:[email protected] only demonstrated method to produce hot long-lived FRCs b)Posthumous. at high densities and magnetic fields. Figure 1 illustrates the 1070-664X/2015/22(4)/042518/10/$30.00 22,042518-1 VC 2015AIPPublishingLLC 22 August 2025 23:26:50 S S S S S S e e e e c e c c e r r r c e c e e c r t M r t M t M r e e e i i i l l l t i t i i t t t t M a M a a M r r r y y y i T i T T i l l l i e i e e i t t t c c c a a a h h h r n r n n r y o y o o y l l l T o T o o T g g g e y e y y e . . . c c c c c c S o S o S o h h h e m e m e m nc c n c n r r r e e e o o o t t t M M M l l l o o o i i i l l l i i i gt t g t g a a a yr r y r y y y y .T T . T . ce e c e c oc c o c o S h S h S h mn n m n m e e e o o o c l o c l o c l o g g g r r r e y e y e y . . . c c c t S o tS o S t o M M M e m e m e m c c c i r ir r i l e le e l i i i t t M ttM t M t a a a i i i r l i lri l i r t t t y a ya a y r r r T y Ty y T T T T e e e e e e c c cc c c h h h h h h n n n n o on o n l l l o o o o o o g g g l y ly y l o . o. . o c c c S g o S go S o g e m e m e m y y y c c c r . r . r . e e e c c c t t t M o M o M o S S S i i i l m l m l m i i i e t e t te a a a c r c r rc y y y r T r T Tr e e e e ee c c c t t t h h h M M M n n n o o o i l i l li l o l o ol i i i g g g t t t a y a y ya . . . c c c r r r S o S o S o y y y e m e m e m T c c T c T r r r e e e e e e t t t c M M c M c h i l i l h i l h i i i t t t n a a n a n r r r o y y o y o T T T l l l o e e o e o c c c g h h g h g n n n y y y o o o . l l . l . o o o c c c g g g o y y o y o . . . m c c m c m o o o m m m 042518-2 Weber,Intrator,andSmith Phys.Plasmas22,042518(2015) axial field swings toward zero. When the forward field rises to a value exceeding the trapped reverse field (the plasma is still relatively cold at this point), the plasma is driven radi- allyinward or “lifts-off” the wall. This marks the end of the reconnection phase of formation, after which point trapped fluxcanonlydecrease.Thetrappedfluxatlift-offisapproxi- mately / (cid:3)AB , where A is the area of the discharge LO t LO t tubeandB isthefieldatlift-offtime. LO Theinertial-confinement flux-trapping model, originally proposed by Green and Newton,20 assumes that flux is con- vected through the wall at the radial Alfv(cid:2)en speed1 during field-reversal. Under this model, the trapped flux at lift-off canbeestimatedusing / LO ¼1(cid:4)G2; (1) / o o where G ¼B =B ; (2) o o GN B istheinitialreversebiasfield,and/ istheinitialreverse o o bias flux. B is the Green-Newton field; the value of bias GN field at which the radial Alfv(cid:2)en transit time equals the time neededtoreversetheinitialbiasfield B ¼ðl q Þ1=4E1=2; (3) GN o o h wherel isthevacuummagneticpermeability,q istheini- FIG.1.ResistiveMHDsimulationillustratingFRTPformationinaconical o o tial mass density, and E is the applied azimuthal voltage at h-pinch matching the MSX geometry using typical gas fill and magnetic h conditions.Magnetsareindicatedbyheavyblacklines,thequartzdischarge the tube wall during field-reversal. This model predicts lift- tubebyadoubleblackline,magneticfieldcontoursbythinblacklines,and off flux for reversal timescales faster than the inertial radial plasma density is represented in grey-scale (auto-scaled for each frame). Alfv(cid:2)en time and has historically matched experimental data Theinitialplasmawasassumedtobefullyionizedwithnoringing-hcycle preceding field-reversal. The following stages are shown: (a) reverse bias intherangeG o (cid:2)0:5.21 andpre-ionization;(b)field-reversal,radialcompression,andreconnection; Whenthereversaltimescalebecomescomparableorlon- (c) axial contraction and equilibration; (d) acceleration and ejection. See ger than the inertial radial Alfv(cid:2)en time (i.e., when G (cid:3)1), a o Fig.5forMSXschematicandscale. significant amount of plasma comes into contact with the wall,duringwhichtimethetrappedreversefieldissupported nominalsequenceofeventsduringFRTPformationinacon- byapressure-bearingsheathuntiltheaxialfieldrisestoasuf- ical geometry similar to that of MSX and FRCHX. Prior to ficient value for lift-off to occur. Practically, this behavior formation, a pre-ionized volume of plasma with an embed- begins to become important at G (cid:3)0:5. Under these condi- ded reverse axial magnetic field is established. The polarity o tions, the trapped flux at lift-off time can be estimated using of the axial field is then quickly reversed over a timescale thesheath-confinedmodeldescribedbySteinhauer,22,23which shorterthantheinductivedecaytimeoftheplasma(i.e.,L/R is similar to that of Vekstein,24 valid for reversal timescales time), and the imposed forward field reconnects with the slowerthantheinertialradialAlfv(cid:2)entime trapped reverse field to form a closed toroidal magnetic to- pologyinsideasimplyconnectedseparatrix.Thesuddenrise / (cid:2) (cid:3) LO ¼exp (cid:4)0:74G N(cid:3)(cid:4)1=4 ; (4) in forward field drives a radial implosion that rapidly heats / o o the plasma through a combination of compression, strong shocks, and flux annihilation. The h-coil is then crowbarred where N(cid:3) ¼N=N(cid:5) is the normalized line density with N(cid:5) atmaximumcurrenttomaintainastrongforwardfieldforra- ¼2pm=e2l ¼6:46(cid:6)1017 m(cid:4)1fordeuterium,m istheion i o i dialconfinement,andtheplasmaundergoesashortperiodof mass, and e is the elementary charge.25 The normalized line radial oscillation, eventually leading to equilibrium (radial densitycanbeconvenientlyexpressedas pressure-balance), followed by slower axial contraction, os- N(cid:3) ¼2:4(cid:6)103p r2; (5) cillation,andequilibrationtoastateofaxialandradialpres- o t surebalance. wherep istheinitialgasfillpressureandr isthedischarge o t tuberadius. A. Flux-trappinginacylindricalh-pinch The radial compression and axial contraction phases of During field-reversal (between a and b in Fig. 1), the formation (b and c in Fig. 1) are also associated with rapid plasma can expand at up to the radial Alfv(cid:2)en speed as the flux loss, primarily due to high anomalous resistivity and 22 August 2025 23:26:50 S S S S S S e e e e c e c c e r r r c e c e e c r t M r t M t M r e e e i i i l l l t i t i i t t t t M a M a a M r r r y y y i T i T T i l l l i e i e e i t t t c c c a a a h h h r n r n n r y o y o o y l l l T o T o o T g g g e y e y y e . . . c c c c c c S o S o S o h h h e m e m e m nc c n c n r r r e e e o o o t t t M M M l l l o o o i i i l l l i i i gt t g t g a a a yr r y r y y y y .T T . T . ce e c e c oc c o c o S h S h S h mn n m n m e e e o o o c l o c l o c l o g g g r r r e y e y e y . . . c c c t S o tS o S t o M M M e m e m e m c c c i r ir r i l e le e l i i i t t M ttM t M t a a a i i i r l i lri l i r t t t y a ya a y r r r T y Ty y T T T T e e e e e e c c cc c c h h h h h h n n n n o on o n l l l o o o o o o g g g l y ly y l o . o. . o c c c S g o S go S o g e m e m e m y y y c c c r . r . r . e e e c c c t t t M o M o M o S S S i i i l m l m l m i i i e t e t te a a a c r c r rc y y y r T r T Tr e e e e ee c c c t t t h h h M M M n n n o o o i l i l li l o l o ol i i i g g g t t t a y a y ya . . . c c c r r r S o S o S o y y y e m e m e m T c c T c T r r r e e e e e e t t t c M M c M c h i l i l h i l h i i i t t t n a a n a n r r r o y y o y o T T T l l l o e e o e o c c c g h h g h g n n n y y y o o o . l l . l . o o o c c c g g g o y y o y o . . . m c c m c m o o o m m m 042518-3 Weber,Intrator,andSmith Phys.Plasmas22,042518(2015) tearing instabilities driven by large density gradients in thin (/=/ <0:1 and B=B <0:1 for the 4.98 half-angle of the t p t p antiparallel layers. The flux-retention factor during these MSX h-pinch, wheresubscriptstandpindicate toroidal and phasescanbeestimatedusing1,23,25 poloidal components respectively); however, since magnetic pressure and energy are proportional to the square of the / eq ¼2:33rp1=2; (6) magnetic field, the toroidal field is not expected to appreci- / t o ably affect the dynamics or pressure balance of the FRC LO (B2=B2 <0:01). where/ eq isthetrappedfluxatequilibrium. t Si p mulations using the MOQUI30 resistive- Figure 2 shows contours of predicted / over a range eq magnetohydrodynamics code predict that FRC formation in ofreversebiasfluxandneutralgasfilldensitynD o 2 fortypical MSX proceeds similarly to the formation in a cylindrical operating parameters on MSX and FRCHX. It should be pinch and that the radial and axial equilibration phases are noted that nowhere in this parameter space does G LO completedpriortoejection(e.g.,Fig.1),althoughitispossi- ¼B =B exceed unity, which has been described as a LO GN ble that additional flux loss may occur during the highly practical limit for formation.23,26,27 It can be seen that dynamicperiodsofaxialaccelerationandejectioninaman- trapped flux is increased both by increasing / (increases o ner similar to the rapid flux loss observed during the radial amount of flux available to trap) and by increasing nD o 2 and axial equilibration phases of formation. The relatively (increasesflux-trappingefficiency).Atlowfilldensities,flux small diameter of MSX and FRCHX combined with opera- trappingishighlysensitivetoincreases innD o 2 andrelatively tion at unprecedented high fill pressures gives rise to large insensitivetoincreasesin/ o ,whileathighfilldensities,the density gradients during formation and ejection, which can oppositeistrue. increase anomalous resistivity and susceptibility to tearing instabilities that drive flux-loss. Due to this and the addi- B. Formationinaconicalh-pinch tional time required for acceleration and ejection, trapped flux levels in the final translating FRC may be lower than Although the preceding trapped flux estimates were predicted by models derived from previous experiments developed for static formation in a cylindrical h-pinch, they studyingstaticformation. can be used as a starting point to develop an understanding of the formation process in a conical geometry. In a conical C. Pre-ionization h-pinch, the diverging magnetic field exerts an axial force thatacceleratesandeventuallyejectstheFRC,4,5andtheini- Theanalysisof Sec.IIA alsoassumesan initial state of tialfluxavailablefortrapping(/ )variesalongthelengthof uniform,fullyionizedplasmapriortofield-reversal,although o the h-coil due to the constant diameter of the quartz dis- this assumption is often invalid. The characteristics and charge tube. A small amount of toroidal field is also gener- reproducibilityofthefinalFRChavehistoricallybeenfound ated during FRC formation in a conical h-pinch28,29 tobehighlydependentonthespatialdistribution,resistivity, and degree of ionization of the initial plasma. While several methods of pre-ionization have been attempted (ringing-h, axial discharge, ringing multi-pole fields, UV irradiation, plasma injection),31 the most common method is ionization viaringingh-pinch.1,32 Ringing-h pre-ionization superimposes a time-varying axial magnetic field onto the pseudo-steady-state reverse biasfield(Fig.3(a)),inducinganazimuthalelectricfieldthat accelerates free electrons in the neutral gas-fill to produce a Townsend ionization cascade. Since a large axial magnetic field impedes cross-field electron motion and can suppress ionization,33theamplitudeoftheringingaxialfieldtypically needs to be greater than the reverse bias, such that the mag- netic field crosses zero with enough overshoot to induce a substantial electric field during times when the magnetic field is small. However, while zero-crossing facilitates ioni- zation,ithastheunfortunateeffectthattheplasmaiscreated during a time that the axial field is nearly zero, resulting in FIG.2.ContoursofpredictedtrappedfluxfortheMSXcoilgeometryover typical operating parameter ranges; solid contours (—) indicate sheath- very little trapped flux. Typically, many ringing cycles are confinedformation,dashedcontours(––)indicateinertiallyconfinedforma- needed to couple enough energy to the plasma to ensure tion,andtheshadedregionindicatestheparameterspaceofhistoricalagree- good ionization and allow time for turbulent mixing to uni- mentbetweentheinertialmodelandexperimentaldatausingacylindrical pinch. Note that the inertial and sheath models agree fairly well in the formlydistributeplasmaandmagneticfield. shadedregion.InMSXandFRCHXformationtakesplaceinacylindrical Whentheaxialfieldcrosseszero,thevolumewithinthe dischargetubewithintheconicalh-pinch.InitialreversefluxinMSXtypi- h-coil also becomes magnetically connected to the down- callyvariesfrom/ o ¼1:7mWb(B z(cid:3)0:2T)atthelargeendofconicalh- stream regions of the experiment, which allows plasma to pinchto/ o ¼3:9mWb(B z(cid:3)0:5T)atthesmallend,with/ o ¼2:5mWb (B z(cid:3)0:3T)onaverage. freely stream along open field lines. In a conical geometry, 22 August 2025 23:26:50 S S S S S S e e e e c e c c e r r r c e c e e c r t M r t M t M r e e e i i i l l l t i t i i t t t t M a M a a M r r r y y y i T i T T i l l l i e i e e i t t t c c c a a a h h h r n r n n r y o y o o y l l l T o T o o T g g g e y e y y e . . . c c c c c c S o S o S o h h h e m e m e m nc c n c n r r r e e e o o o t t t M M M l l l o o o i i i l l l i i i gt t g t g a a a yr r y r y y y y .T T . T . ce e c e c oc c o c o S h S h S h mn n m n m e e e o o o c l o c l o c l o g g g r r r e y e y e y . . . c c c t S o tS o S t o M M M e m e m e m c c c i r ir r i l e le e l i i i t t M ttM t M t a a a i i i r l i lri l i r t t t y a ya a y r r r T y Ty y T T T T e e e e e e c c cc c c h h h h h h n n n n o on o n l l l o o o o o o g g g l y ly y l o . o. . o c c c S g o S go S o g e m e m e m y y y c c c r . r . r . e e e c c c t t t M o M o M o S S S i i i l m l m l m i i i e t e t te a a a c r c r rc y y y r T r T Tr e e e e ee c c c t t t h h h M M M n n n o o o i l i l li l o l o ol i i i g g g t t t a y a y ya . . . c c c r r r S o S o S o y y y e m e m e m T c c T c T r r r e e e e e e t t t c M M c M c h i l i l h i l h i i i t t t n a a n a n r r r o y y o y o T T T l l l o e e o e o c c c g h h g h g n n n y y y o o o . l l . l . o o o c c c g g g o y y o y o . . . m c c m c m o o o m m m 042518-4 Weber,Intrator,andSmith Phys.Plasmas22,042518(2015) simply by introducing gas through the plasma guns a few milliseconds prior to the initiation of the discharge (i.e., puff-fill) rather than using a traditional static-fill.36 This allows FRC translation to take place through vacuum rather than a background of neutral gas, resulting in higher final velocitiesandplasmatemperatures.37 Itisworthnotingthat,inparallelwithplasmagundevel- opment at MSX, a similar technique was attempted on FRCHX using a capacitively coupled axial RF discharge combined with a much larger puff-fill in which the leading edge of the gas pulse was used to form the FRC. Results showed that the RF discharge had a marginal effect on flux- trapping (producing a (cid:2)3% increase in excluded flux radius corresponding to a (cid:2)10% increase in trapped flux),38 and while the absence of neutral gas downstream enables higher translation velocities, the non-uniformity of the gas fill within the h-coil8 makes comparison with previously estab- lishedscalinglawsdifficult. A. Plasmagunarray Each plasma gun is constructed from concentric stain- FIG.3.(a)Typicalaxialfieldhistoryforringing-hpre-ionizationandfield- less steel tubes separated by a layer of flexible polyurethane reversalinacylindricalpinch(datafromFRX-B35);(b)Single-cycle,non- to provide electrical insulation (Fig. 4). A 5-in.-diameter zero-crossingpre-ionizationandfield-reversalinMSX. 8 outer conductor is maintained at machine-ground, while a 1- 4 in.-diameter central tube, which doubles as a gas feed, is plasma is forced downstream due to the magnetic gradient. switched to 1kV. Near the end of the gun the polyurethane This has been observed to deplete the plasma inventory in insulator transitions, via nested convolute joint forincreased the h-coil which later obstructs the translation of the FRC. tracking distance, to an aluminum oxide insulator with cap- Excessive overshoot (“hard” zero-crossing) and multiple tured O-ring seals that serves both as a vacuum boundary ringing cycles only exacerbates this problem and can also and as a standoff insulating layer to prevent the arc from ablate material from the quartz wall, introducing impurities occurringupstreamoftheelectrodes.Astainlesssteelnozzle into the plasma leading to excessive radiative losses. In isthreadedintotheoutertubetoprovideflowrestrictionand MSX (and previously in FRX-L34) hard zero-crossing has function as an outer electrode, and a cylindrical 1-in. thori- beenassociatedwithsiliconandoxygenemissionanddrasti- 8 atedtungstencentralelectrodeispress-fitintoastainlessgas callydecreasedFRClifetime. diffuser with four radial ports, which is then silver-soldered totheinnerconductor/gasfeed.Inasimilardesigntoplasma III. APPARATUSANDMETHODS guns used in the previous studies,39,40 the central electrode These considerations prompt the need for a pre- extends(cid:2)2cmpasttheouterelectrodetoreducecurrentden- ionization scheme that does not rely on multiple ringing-h sity and prevent destructive sputtering. Once assembled, the cycles and/or hard zero-crossing of the axial field. Such a guns are bent to 90(cid:7) and mounted in a conflat spool with 12 system should also be capable of ionization in the presence radial ports to form a downstream-pointing annular array ofastrongaxialmagneticfieldforincreased/ overarange (Fig. 5). The guns are mounted in sliding seals to allow ra- o of high-density gas fill conditions. To address this need, a dial adjustment, and the conflat spool is mated to the quartz multistage pre-ionization method has been developed on dischargetubeusingacapturedO-ringtoallowaxialtransla- MSX that uses a combination of non-zero-crossing, single- tionoftheentire array.Deuteriumgasisintroduced through cycle ringing-h pre-ionization supplemented by an annular a polyethylene manifold to prevent image currents, then array of coaxial plasma guns. The plasma gun array injects through 6 fast pulse valves (2 guns per valve) that are plasma into the formation section prior to the initiation of the ringing-h cycle and provides a seed population of free electrons that facilitates ionization of the bulk gas by the electric field induced by the ringing-h system. Since this approach decouples the initiation of ionization from the energy deposition process, ionization can take place in the presence of a large magnetic field, arbitrary fill density, and atatimewhentheinducedelectricfieldisatamaximum. This method has the additional benefit that a uniform FIG. 4.Cross section of a plasma gun near the electrodes. The nested neutral gas fill can be achieved within the h-coil while pre- coaxialconductors,insulators,andcapturedO-rings(black)allowforacom- serving near vacuum in the downstream translation section pactstructureandclosely-spacedarray. 22 August 2025 23:26:50 S S S S S S e e e e c e c c e r r r c e c e e c r t M r t M t M r e e e i i i l l l t i t i i t t t t M a M a a M r r r y y y i T i T T i l l l i e i e e i t t t c c c a a a h h h r n r n n r y o y o o y l l l T o T o o T g g g e y e y y e . . . c c c c c c S o S o S o h h h e m e m e m nc c n c n r r r e e e o o o t t t M M M l l l o o o i i i l l l i i i gt t g t g a a a yr r y r y y y y .T T . T . ce e c e c oc c o c o S h S h S h mn n m n m e e e o o o c l o c l o c l o g g g r r r e y e y e y . . . c c c t S o tS o S t o M M M e m e m e m c c c i r ir r i l e le e l i i i t t M ttM t M t a a a i i i r l i lri l i r t t t y a ya a y r r r T y Ty y T T T T e e e e e e c c cc c c h h h h h h n n n n o on o n l l l o o o o o o g g g l y ly y l o . o. . o c c c S g o S go S o g e m e m e m y y y c c c r . r . r . e e e c c c t t t M o M o M o S S S i i i l m l m l m i i i e t e t te a a a c r c r rc y y y r T r T Tr e e e e ee c c c t t t h h h M M M n n n o o o i l i l li l o l o ol i i i g g g t t t a y a y ya . . . c c c r r r S o S o S o y y y e m e m e m T c c T c T r r r e e e e e e t t t c M M c M c h i l i l h i l h i i i t t t n a a n a n r r r o y y o y o T T T l l l o e e o e o c c c g h h g h g n n n y y y o o o . l l . l . o o o c c c g g g o y y o y o . . . m c c m c m o o o m m m 042518-5 Weber,Intrator,andSmith Phys.Plasmas22,042518(2015) FIG.5.Schematicoftheplasmagunarray,MSXh-coil,andpartialtransla- tion section. Note that plasma is injected beyond the upstream magnetic cusp.Thequartzdischargetubeis10cmindiameter,thesmallestfastcoil hasaninnerdiameterof12.3cm,andthelargestcoilhasaninnerdiameter of18.9cm;thehalf-angleoftheMSXconicalh-pinchis4.98. overdriven to increase pulse speed.39 Each gun is driven by an optically triggered, SCR-switched and crowbarred, 1.1 mF (550J per gun and 6.6kJ for the 12 gun array) electro- lyticcapacitorbank.Althoughthetriggeringsystemiscapa- ble of firing the guns independently, all guns were triggered simultaneouslyforthisstudy. FIG.6.(a)PlasmadistributionfromsingleguntestinginRSXat20cmand 30cmdownstreamoftheplasmagun;(b)superpositionofsingle-gundataat Both MSX and FRCHX use “programmed” forma- 20cmfor12gunsarrangedinanannulus;(c)predictedplasmadistribution tion41,42 to force reconnection to occur at externally applied at20cm(roughlyhalfwaydowntheh-coil)forconditionspriortoinitiation magnetic cusps. This promotes symmetry and prevents tear- oftheringing-hcycleinMSX. ing instabilities for more reproducible and well-formed FRCs. In such a configuration, the plasma guns need to r(cid:3)1:5 cm at 20cm and r(cid:3)2:1 cm at 30cm downstream extend beyond the upstream cusp to inject plasma into the of the gun (Fig. 6(a)), which shows scaling consistent with region of reverse field (Fig. 5). During the FRC formation conservationofmass. experiments described in Sec. IV, the axial position of the Superposing these distributions, the plasma emanating array was such that the gun electrodes were located (cid:2)3cm fromafull12-gunarray ispredicted tobeasmooth annulus pasttheupstreamcusp,andtheplasmagunsarelocatednear withamaximumdensityof(cid:2)6(cid:6)1019m(cid:4)3(Fig.6(b)).Later to the quartz tube so the injected plasma forms an annulus tests in MSX using the 12-gun array and an axially translat- that encloses the maximum amount of reverse flux prior to able Langmuir probe revealed that the translation speed of field-reversal. the plasma was slower than previously observed during The plasma gun array also satisfies several other engi- single-gun testing in RSX (v z (cid:3) 0.25cm/ls in MSX vs. neering constraints including: the need to facilitate radial (cid:3)1.5cm/ls in RSX). We believe this to be caused by and axial placement of the plasma streams, location of the increasedneutraldragduetooperationwithalargernumber gasvalvesawayfromregionsofstrongmagneticfield,short of plasma guns in a significantly smaller diameter vacuum axial length (<25cm) to fit on FRCHX, and an obstruction- vessel than RSX. Assuming approximately similar plasma free line of sight on-axis to facilitate diagnostic access for parameters, the cross-field diffusion coefficient46 D ? scales high-speedphotographyandpulsedpolarimetery.43 proportionally to B(cid:4)2 (valid for both partially ionized and fully ionized plasmas). Since the transverse diffusion of the IV. EXPERIMENTALRESULTS plasma takes place over the timescale Dt¼Dz=v z , and the spread of an outwardly diffusing Gaussian plasma column A. Initialconditions p ffiffiffiffiffiffiffiffiffiffiffi evolves as r¼ 2D t, the plasma distribution in MSX can ? Early testing of a prototype plasma gun was carried out be predicted using the RSX measurements at z¼20cm and on the Relaxation Scaling Experiment (RSX) experi- 30cm to determine D , then scaling to account for the ? ment,44,45 which has improved diagnostic access compared higher magnetic field, decrease in translation speed, and toMSXandiscapableofproducingaxialmagneticfieldsof divergenceoftheaxialmagneticfieldinMSX.Thedistribu- 0.12T, approaching the lower range of reverse bias used in tion of plasma 20cm downstream of the gun array (halfway MSX. At typical operational parameters (150psi line pres- down the h-coil) at reverse bias levels used for subsequent sure, several hundred ls puff duration, and peak currents of testing (cf. Fig. 2 caption and Fig. 3(b)) is predicted to be a (cid:2)2kA), peak plasma density 20cm downstream of the gun lumpyannuluswithpeakdensitiesofroughly1020m(cid:4)3(Fig. nozzle was measured via Langmuir probe to be 6(c)). This configuration is optimal for efficient trapping of (cid:2)3(cid:6)1019m–3 with a (cid:2)50% reduction over the next 10cm. reverse magnetic field as the greatest amount of flux is The axial velocity was v (cid:3) 1.5cm/ls, and the transverse enclosedusingtheleastamountofplasmatoformacontinu- z spread was Gaussian with a half-width at half-max of ousconductingpathfortheinducedtoroidalcurrenttoflow. 22 August 2025 23:26:50 S S S S S S e e e e c e c c e r r r c e c e e c r t M r t M t M r e e e i i i l l l t i t i i t t t t M a M a a M r r r y y y i T i T T i l l l i e i e e i t t t c c c a a a h h h r n r n n r y o y o o y l l l T o T o o T g g g e y e y y e . . . c c c c c c S o S o S o h h h e m e m e m nc c n c n r r r e e e o o o t t t M M M l l l o o o i i i l l l i i i gt t g t g a a a yr r y r y y y y .T T . T . ce e c e c oc c o c o S h S h S h mn n m n m e e e o o o c l o c l o c l o g g g r r r e y e y e y . . . c c c t S o tS o S t o M M M e m e m e m c c c i r ir r i l e le e l i i i t t M ttM t M t a a a i i i r l i lri l i r t t t y a ya a y r r r T y Ty y T T T T e e e e e e c c cc c c h h h h h h n n n n o on o n l l l o o o o o o g g g l y ly y l o . o. . o c c c S g o S go S o g e m e m e m y y y c c c r . r . r . e e e c c c t t t M o M o M o S S S i i i l m l m l m i i i e t e t te a a a c r c r rc y y y r T r T Tr e e e e ee c c c t t t h h h M M M n n n o o o i l i l li l o l o ol i i i g g g t t t a y a y ya . . . c c c r r r S o S o S o y y y e m e m e m T c c T c T r r r e e e e e e t t t c M M c M c h i l i l h i l h i i i t t t n a a n a n r r r o y y o y o T T T l l l o e e o e o c c c g h h g h g n n n y y y o o o . l l . l . o o o c c c g g g o y y o y o . . . m c c m c m o o o m m m 042518-6 Weber,Intrator,andSmith Phys.Plasmas22,042518(2015) The dynamics of the neutral gas fill using the full 12- alongtheh-coilandonlygiventimetotranslateasmallfrac- gun array operating in puff-fill mode were also studied in tion of the length of the h-coil. However, when the guns MSX using a custom, miniaturized, fast ionization gauge.36 were not fired (i.e., only used for the gas fill), a FRC could Itwasfoundthatauniformdensityprofilecouldbeachieved not be formed and nearly zero plasma diamagnetism was throughout the h-coil while maintainingnear vacuum down- observed. This shows that bulk ionization can take place stream, and that the profile could be scaled self-similarly evenifplasmaispresentoveralimitedaxialextentoftheh- over pressure ranges of interest by simply varying the line coil, but that some form of pre-ionization (either plasma pressureinthegasmanifold.36Theuniformityofthegasfill guns or ringing-h) is still needed. The nominal duration of allows FRC formation/translation using a puff-fill to be the plasma gun discharge for subsequent testing was chosen benchmarked against the scaling laws described in Sec. IIA to be 160ls (from (cid:4)150ls to þ 10ls in Fig. 3(b)), since it developed for stationary FRC formation in a static-fill. For was found that the plasma takes roughly 150ls to reach the operation in deuterium using the previously stated puff tim- downstreamendoftheh-coil. ings,theminimummanifoldpressureneededforreliabledis- chargeofall12gunsresultedinafilldensityof(cid:2)8.0(cid:6)1020 C. Flux-trapping D /m3(equivalent toa 25mTorr static fillbut onlyin the h- 2 A series of tests were conducted at fairly high reverse coil). Themanifold pressureused during RSXtesting andto biasfieldlevels(cf.Fig.2caption)tobetterstudytheeffects arrive at the above plasma density estimates produces in of plasma gun assisted pre-ionization on flux-trapping effi- MSX a gas fill of (cid:2)2.5(cid:6)1021 D /m3, implying a peak ioni- 2 ciencyandtoattempttomaximizetotaltrappedflux.During zationfractionofafewpercentintheannularplasma. these tests the ringing-h system was run at 50kV (when used),producinganaxialfieldswingthatapproachedbutdid B. Qualitativeeffectonionization not cross zero-field (Fig. 3(b)). The main field-reversal ca- Upon initial FRC formation testing using the plasma pacitorbankwasalsochargedto50kV(similartotheprevi- gunarray,itwasfoundthatbulkionizationoftheneutralgas ous studies, Sec. IVB) in order to compare FRC formation prefill (characterized by sudden visible light emission) using gun-assisted ringing-h pre-ionization to plasma gun occurred immediately upon applying voltage to the h-coil catalyzedionizationthroughfield-reversalalone.Thetypical rather than when the axial field crossed zero. This confirms sequence of events preceding field-reversal consisted of a the initial hypothesis that a seed plasma at the few percent 500lsgaspuff followedbya3.4msdelaytoallowtime for level can catalyze a Townsend ionization cascade driven by the neutral gas to fill the h-coil. The gas puff timings were the induced azimuthal electric field despite the strong axial fixed to maintain a self-similar gas profile in the h-coil. magnetic field that had previously suppressed ionization. Plasma was then injected by the annular gun array followed This also opens the possibility that bulk ionization can be by a single non-zero-crossing ringing-h pre-ionization cycle affectedwithoutuseofringing-hpre-ionization,sincetheca- (ifringing-hisusedatall)andfield-reversal(Fig.3(b)). pacitor bank that drives the main field-reversal is typically The radial magnetic profile of the drifting FRC can be operated at similar charge voltages to the ringing-h system. computed at several locations along the 40cm long transla- In such a scenario, ionization would occur after voltage is tion section by measuring the axial field external to the applied to the h-coil, but before significant reduction in plasma during the FRC transit (cf. Fig. 7(a)). The profile reversebiasoccurs.Thismodeofoperationwasusedinsev- (Fig. 7(c)) of the FRC was estimated using the well- erallaterstudies. established rigid-rotor model1,2 BðrÞ¼B tanhðKuÞ, where e Asexpected,testsinwhichtheringing-hamplitudewas u¼2ðr=r Þ2(cid:4)1 is the transformation of the radial coordi- s increased beyond the reverse bias level (with or without nate,andKistherigid-rotorprofileparameterchosentosat- plasma guns) correlated with substantially decreased flux- isfy the “average beta” axial pressure-balance relation35,47 lifetimeinthedriftingFRCevenwhenonlyslightlycrossing hbi¼1(cid:4)x2=2. The average beta of a rigid-rotor FRC can s zero. Several other deleterious features were also displayed also be expressed as hbi ¼tanhðKÞ=K, allowing K to be RR suchasstrongimpurityemissionanddecreasedreproducibil- determined knowing x. The ratio of the separatrix radius r s s ity. Since significant amounts of flux decays over the course to the radius of the conducting boundary r , commonly c of translation under these conditions, trapped flux levels at denoted as x (cid:8)r =r , is related to the values of the unper- s s c theendofthetranslationsection(where shockphysics stud- turbed axial field B and the excluded field between the zo iesorlinercompressiontakesplace)werefoundtobemaxi- FRCandtheconductingboundaryB throughfluxconserva- ze mized when using plasma gun assisted non-zero-crossing tion:x ¼ð1(cid:4)B =B Þ1=2.Thetotaltrappedfluxwascalcu- s zo ze ringing-hpre-ionization. latedafterthedriftingFRChadequilibratedbutbeforelarge The effects of changes to the axial distribution of the amount of trapped flux had decayed using42 p seed plasma on FRC formation were also investigated by / (cid:3)0:62px B ðr = ffi 2 ffiffi Þ2, which is equivalent to integrat- eq s ze s varying the startof theplasma gundischargefrom (cid:4)1ms to ing the rigid-rotor magnetic profile. The validity of this (cid:4)1ls in Fig. 3(b). For these tests, the ringing-h system was approach was occasionally checked by measuring the peak notusedinanattempttoaccentuatetheeffectsofchangesto reversed field at the downstream end of the translation sec- theseedplasmadistribution.Verylittlechangewasobserved tion using an 1-in.-diameter internal magnetic probe inserted 8 in the final FRC properties between cases where the seed alongthemachineaxis(r¼0)fromdownstreamtominimize plasma was allowed more than enough time to translate the effect on the plasma (e.g., Fig. 7(b)). Although there 22 August 2025 23:26:50 S S S S S S e e e e c e c c e r r r c e c e e c r t M r t M t M r e e e i i i l l l t i t i i t t t t M a M a a M r r r y y y i T i T T i l l l i e i e e i t t t c c c a a a h h h r n r n n r y o y o o y l l l T o T o o T g g g e y e y y e . . . c c c c c c S o S o S o h h h e m e m e m nc c n c n r r r e e e o o o t t t M M M l l l o o o i i i l l l i i i gt t g t g a a a yr r y r y y y y .T T . T . ce e c e c oc c o c o S h S h S h mn n m n m e e e o o o c l o c l o c l o g g g r r r e y e y e y . . . c c c t S o tS o S t o M M M e m e m e m c c c i r ir r i l e le e l i i i t t M ttM t M t a a a i i i r l i lri l i r t t t y a ya a y r r r T y Ty y T T T T e e e e e e c c cc c c h h h h h h n n n n o on o n l l l o o o o o o g g g l y ly y l o . o. . o c c c S g o S go S o g e m e m e m y y y c c c r . r . r . e e e c c c t t t M o M o M o S S S i i i l m l m l m i i i e t e t te a a a c r c r rc y y y r T r T Tr e e e e ee c c c t t t h h h M M M n n n o o o i l i l li l o l o ol i i i g g g t t t a y a y ya . . . c c c r r r S o S o S o y y y e m e m e m T c c T c T r r r e e e e e e t t t c M M c M c h i l i l h i l h i i i t t t n a a n a n r r r o y y o y o T T T l l l o e e o e o c c c g h h g h g n n n y y y o o o . l l . l . o o o c c c g g g o y y o y o . . . m c c m c m o o o m m m 042518-7 Weber,Intrator,andSmith Phys.Plasmas22,042518(2015) FIG. 9.Trapped flux measurements for formation using ringing-h pre- ionization alone over varying fill densities. The dashed curve (– –) repre- sentsthetrappedfluxpredictedbytheinertialflux-trappingmodelwhere/ o was varied to fit the experimental data shown in this figure (the sheath- confinedmodelcouldnotbemadetofitthedata);thebestfitwasobtained FIG.7.SampledatacollectedonthedriftingFRCwithinthetranslationsec- for/ o ¼3.7mWb(B z¼0:47Tina10cmdischargetube).Thesolidcurve tion:(a)externalmeasurementsoftheunperturbedaxialguidefieldB zo and (—)isrepeatedfromFig.8forreference. excludedfieldB provideplasmadiamagnetism,totalpressure,andenable ze calculation of a rigid-rotor profile;1,2 (b) downstream internal axial field For otherwise similar machine parameters, plasma gun measurementswereoccasionallyusedtoconfirmtheaccuracyoftherigid- rotormodel;(c)therigid-rotorFRCmodelwasusedtodeterminetheradial assisted ringing-h pre-ionization (Fig. 8) was found to con- magnetic profile and trapped flux; the density profile is described by2 sistently result in higher levels of trapped flux and enabled n¼n p sech2ðKuÞ, where n p is the peak density, using the profile factor K FRC formation to take place at lower densities than previ- frommagneticdataandline-integrateddensity(ndl)measurementstocon- ously possible using ringing-h alone (Fig. 9). Although the strainn (forthisexamplendlwasmeasuredonaseparateshotduetothe p axialprobeobstructingtheinterferometerbeam). trapped flux trends for gun-assisted and unassisted ringing-h pre-ionizationexhibitsimilarslopes(d/ =dnD2)atmoderate eq o fill densities, gun-assisted formation was best fit by the were no observable differences in FRC properties during sheath-confined flux-trapping model of Steinhauer (Sec. shots for which the probe was present, none of the data in IIA), while unassisted formation was best fit by the inertial Figs.8–10weretakenwiththeinternalprobeinplace. modelofGreenandNewton. However, FRC formation is known to deviate signifi- cantly from the Green-Newton model for G (cid:3)0:5 (cf. o Fig.2),aswasthecaseduringthesetests,duetotheformation FIG. 8.Trapped flux measurements for formation using gun-assisted ring- ing-hpre-ionizationovervaryingfilldensities.Thesolidcurve(—)repre- sentsthetrappedfluxpredictedbythesheath-confinedflux-trappingmodel where/ wasvariedtofittheexperimentaldatashowninthisfigureforlow o fillpressures(theinertialmodelcouldnotbemadetofitthedata).Thebest FIG.10.Trappedfluxmeasurementsforformationusingplasmaguncata- fitwasobtainedfor/ o ¼2.6mWb,correspondingtoB z¼0:33Tinthe10- lyzedionizationviathemainfield-reversalbankalone(i.e.,noringing-h). cmdischargetubeorperhapsmoreappropriatelyB z¼0:47Tinthe8.4-cm- Boththesolid(—)anddashed(––)curvesarerepeatedfromFigs.8and9 diameterplasmaannulus.Thedashedcurve(––)isrepeatedfromFig.9for forreference.Inthiscase,neithertheoreticalfluxtrappingmodelcouldbe reference. madetofitthedata. 22 August 2025 23:26:50 S S S S S S e e e e c e c c e r r r c e c e e c r t M r t M t M r e e e i i i l l l t i t i i t t t t M a M a a M r r r y y y i T i T T i l l l i e i e e i t t t c c c a a a h h h r n r n n r y o y o o y l l l T o T o o T g g g e y e y y e . . . c c c c c c S o S o S o h h h e m e m e m nc c n c n r r r e e e o o o t t t M M M l l l o o o i i i l l l i i i gt t g t g a a a yr r y r y y y y .T T . T . ce e c e c oc c o c o S h S h S h mn n m n m e e e o o o c l o c l o c l o g g g r r r e y e y e y . . . c c c t S o tS o S t o M M M e m e m e m c c c i r ir r i l e le e l i i i t t M ttM t M t a a a i i i r l i lri l i r t t t y a ya a y r r r T y Ty y T T T T e e e e e e c c cc c c h h h h h h n n n n o on o n l l l o o o o o o g g g l y ly y l o . o. . o c c c S g o S go S o g e m e m e m y y y c c c r . r . r . e e e c c c t t t M o M o M o S S S i i i l m l m l m i i i e t e t te a a a c r c r rc y y y r T r T Tr e e e e ee c c c t t t h h h M M M n n n o o o i l i l li l o l o ol i i i g g g t t t a y a y ya . . . c c c r r r S o S o S o y y y e m e m e m T c c T c T r r r e e e e e e t t t c M M c M c h i l i l h i l h i i i t t t n a a n a n r r r o y y o y o T T T l l l o e e o e o c c c g h h g h g n n n y y y o o o . l l . l . o o o c c c g g g o y y o y o . . . m c c m c m o o o m m m 042518-8 Weber,Intrator,andSmith Phys.Plasmas22,042518(2015) of a pressure-bearing sheath that confines the expanding pre-ionization strategy based on this concept has been devel- plasma.Theseresultscanbeunderstoodbyrecallingthatdur- opedonMSXthatusesacombinationofplasmainjectionvia ing unassisted ringing-h pre-ionization, breakdown occurs an annular coaxial plasma gun array and non-zero-crossing, when the axial field is very low. The weakly magnetized single-cycle, ringing-h pre-ionization. The gun array injects plasma is then driven radially inward during the second half plasmaintotheformationsectionpriortotheinitiationofthe of the ringing-h cycle, establishing prior to field-reversal a ringing-h cycle and provides a seed population of free elec- narrow column of plasma on-axis surrounded by a region of trons that facilitates ionization of the bulk gas by the electric vacuummagneticfield.Whenthefieldisreversed,theplasma field induced by the ringing-h system. Since this decouples columnisfree to expand(i.e., inertiallyconfined) untileither theinitiationofionizationfromtheenergydepositionprocess, the forward field rises to a sufficient value to halt the expan- ionization can take place in the presence of a large magnetic sion or the plasma encounters the tube wall. This results in field, arbitrary fill density, and at a time when the induced exactlythesameamountoftrappedfluxaswouldbethecase electric field is at a maximum. By ionizing at high field and if the axial field were to convect through the wall at the placingtheseedplasmanearthewallofthedischargetube,a Alfv(cid:2)en speed, as assumed in the Green-Newton model. Gun- continuousconductingpathfortheinducedtoroidalcurrentis assisted formation overcomes this limitation by ionizing at formed that encloses the maximum amount of reverse flux highfieldandplacingtheseedplasmanearthewall.Thiscre- usingtheleastamountofplasma,andpromotestheformation atesinitialconditionsthatpromotesheath-confinedformation, of a pressure-bearing sheath which changes the character of which reduces the rate of flux loss during field-reversal by outwardfluxflowduringfield-reversalfromaconvectivepro- changingthecharacterofoutwardfluxflowfromaconvective cess (inertial confinement) to a much slower resistive diffu- processtoamuchslowerresistivediffusionprocess. sionprocess(sheathconfinement). Formation using plasma gun catalyzed ionization via This approach has been shown to significantly improve field-reversalonly(i.e.,noringing-h)resultedintrappedflux FRC formation, resulting in a (cid:2)350% increase in trapped levels between those of the other two modes of operation flux at typical operating conditions (p o (cid:3)50 mTorr) com- and was not well described by either theoretical model (Fig. pared to ringing-h pre-ionization alone, an expansion of ac- cessible formation parameter space to lower densities and 10).Thisisbelievedtobeduetomarginalbreakdowninthe higher temperatures, and a reduction or elimination of sev- plasma guns at the lowest densities, resulting in “lossy” eral deleterious effects associated with the pre-ionization sheath-confinedformation. phase. Higher levels of trapped flux improves confinement, In all cases, trapped flux levels are observed to roll-off leads to increased FRC diameter (increased inductance), athighdensities, aphenomenathatisnot predicted ineither higher temperatures (reduced resistivity), and longer overall theoreticalmodel.Thisislikelyattributabletohighlevelsof FRCflux-lifetime(/ ðtÞ¼/ expðt=sÞ,wheres¼L=R). plasma resistivity resulting from insufficient heating during FRC eq Since the acceleration process is predominately adiabatic in pre-ionization and in the early stages of field-reversal. The MSXandFRCHX(h-coilcurrentiscrowbarredpriortoejec- fact that this roll-off occurs at relatively lower density when tion), higher post-formation temperatures lead to higher onlytheplasmagunsareusedsupportsthisconjecture,since translation velocities. The use of non-zero-crossing, single- there is less overall energy available for heating during the cycle ringing-h pre-ionization lowers impurity levels and early stages of formation without the ringing-h system. downstream plasma, further increasing lifetime and transla- Conversely, the formation at lower density proceeds at tionvelocity.Thesefactorscombinetogreatlyimprovepros- highertemperaturessincethereislessgastoionizeandheat. pects for heating to thermonuclear conditions during liner Post-formationplasmatemperaturesinferredfromtotalpres- compression in FRCHX and have already enabled unprece- sure measured via excluded flux array and chord-averaged dentedaccesstohighlysupersonic,collisionless,magnetized density via heterodyne interferometer48 in the translation flows in cosmically relevant dimensionless parameter section were observed to be several hundred eV at low den- regimesforshockphysicsstudiesinMSX.49 sitiesandtensofeVfordensitiesatorbeyondroll-off. Achieving further increases in trapped flux requires ei- The validity of these models to formation in a conical ther formation at higher densities and/or higher levels of pinch is somewhat surprising due to the additional phase of reverse bias field. Flux-trapping efficiency has been shown non-equilibrium and the time required for acceleration/ejec- to increase with density in a manner consistent with sheath- tion. One would not na€ıvely expect trapped flux levels to be confined formation up to a point at which plasma heating asgreatasthescalinglawsforstaticformationpredict;how- becomes insufficient to maintain high temperature and low ever,thisisobservedtobethecase,whichindicatesthatthe resistivity. Efficient flux-trapping at densities beyond this acceleration and ejection processes are gentle enough not to pointrequiresadditionalplasmaheating,providedthisisnot causesubstantialfluxloss. accomplished by increasing the ringing-h amplitude beyond the value of the reverse bias field. Operation at higher V. CONCLUSIONS reverse bias levels provides more initial flux to potentially It has been demonstrated that a small amount of plasma trap and permits the use of higher charge voltages on the in a neutral gas (ionization levels of a few percent) can cata- ringing-h system without zero-crossing, but also requires lyzeaTownsendionizationcascadedrivenbyaninducedazi- higher field-reversal voltages to achieve the same crow- muthal electric field despite the presence a strong axial barred current; all of which leads to large increases in total magnetic field that would normally suppress ionization. A storedenergy.Sincetheringing-hsystemstillhassignificant 22 August 2025 23:26:50 S S S S S S e e e e c e c c e r r r c e c e e c r t M r t M t M r e e e i i i l l l t i t i i t t t t M a M a a M r r r y y y i T i T T i l l l i e i e e i t t t c c c a a a h h h r n r n n r y o y o o y l l l T o T o o T g g g e y e y y e . . . c c c c c c S o S o S o h h h e m e m e m nc c n c n r r r e e e o o o t t t M M M l l l o o o i i i l l l i i i gt t g t g a a a yr r y r y y y y .T T . 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