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Characterization of a spheromak plasma gun: The effect of refractoryelectrode coatingsM. FL Brown,) A. D. Bailey Ill,b) and P. M. BellanCalifornia Institute of Technology, Pasadena, California 9112.5(Received 27 September 1990; accepted for publication 23 January 1991)In order to investigate the proposition that high-Z impurities are responsible for theanomalously short lifetime of the Caltech spheromak, the center electrode of the spheromakplasma gun has been coated with a variety of metals (bare steel, copper, nickel, chromium,rhodium, and tungsten). Visible light (230-890 nm) emitted directly from the plasma in thegun breech was monitored for each of the coated electrodes. Plasma density and temperatureand spheromak lifetime were compared for each electrode. Results indicate little difference ingun performance or macroscopic plasma parameters. The chromium and tungsten electrodesperformed marginally better in that a previously reported helicity injection effect [ Phys. Rev.Lett. 64,214 ( 1990)] is only observed in discharges using these electrode coatings. There aresubtle differences in the detailed line emission spectra from the different electrodes, but thespectra are remarkably similar. The fact that ( 1) contrary to expectations, attempts to reducehigh-Z impurities had only marginal effect on the spheromak lifetime coupled with (2) anestimate of Z,, < 2 based on a O-D model suggests that it is not impurities but some othermechanism that limits the lifetime of small, cold spheromaks. We will discuss the generalcharacteristics of the spheromak gun as well as effects due to the coatings.

I. INTRODUCTIONAn important consideration for plasma configurationsgenerated from high current density electrodes (e.g., sphero-maks, dc helicity injection discharges,2 Marshall gun,3 andMather focus4 plasmas) is contamination from impurities.At high current densities, high-Zelectrode material (as wellas low-Z adsorbed impurity gases) can be sputtered orevolved into the discharge thereby raising Z,, and increas-

ing the resistivity and radiated power from the plasma. Theinteraction of hot plasma with material limiters in large to-kamaks and the concomitant increase in Z,, is a related is-sue.5 Impurities have been a particular concern of sphero-mak researchers. The Caltech Spheromak Injectionexperiment* may be susceptible to this problem sincehigh discharge currents ( < 150 kA) are generated fromsmall electrodes ( - 100 cm2). We have noted that ( 1) ourspheromak magnetic lifetimes ( r,ife ) are anomalously shortcompared with predictions of the resistive decay time andthat (2) copious impurity line emission is observed through-out the discharge lifetime. In addition, we have observedablation of the center electrode and sputtering of electrodematerial onto quartz vacuum fixtures. It has remained un-clear whether there was a correlation between impurity con-tent (i.e., Z,, ) and short rlife.Spheromaks are force-free magnetofluid configurationswith comparable toroidal and poloidal magneti c fluxesiwhich are generated largely by currents flowing in the plas-ma itself. In force-free systems, internal JxB forces nearlybalance so that the magnetic field structure of spheromaks isapproximately governed by the eigenvalue equation) United States Department of Energy Fusion Energy Postdoctoral Re-search Fellow.b, United States Department of Energy Fusi on Science Research Fellow.

VX B = R B (with il = constant ). This equation must besolved subject to boundary conditions; if a perfectly con-ducting wall is assumed then image currents must flow toprovide equilibrium fields. Because of their high plasma den-sity and magnetic helicity content compared with tokamaks(the helicity K = SA *Bd 3x is related to volume integratedfield aligned current), spheromaks have been proposed asboth a tokamak refueling and current drive scheme. 13-15 heCaltech Spheromak Injection experiment has demonstratedboth tokamak refueling and refluxing (current drive) byspheromak injection.Early spher omak researchers determined that impurityradiation (dependent on Z,, ) was the most important ener-gy loss mechanism in their di scharges.16 From bolometerymeasurements it appeared that all the plasma magnetic ener-gy was radiated by impurities during decay. In the larger,warm, nonradiation dominated CTX spheromaks, Barnes,et al. ascertained that enhanced particle loss and particlereplacement power were the primary loss mechanisms.Particle replacement power is that required to ionize neutralgas and heat cold electrons to the bulk temperature in a par-ticle confinement time. More recently, it has been recog-nized that an important loss mechanism in spheromaks ismagnetic helicity dissipation due to electric fields in the plas-ma edge. The CTX group has inferred large edge electricfields due to the spheromak relaxation process. Since helicitydissipation depends on the electric field, helicity dissipationis greater at the edge in their discharges.To understand the anomalous lifetimes in the CaltechSpheromak Injection Experiment and ascertain whether thecause is large impurity content, we embarked on a programofelectrode coating and spheromak cleanup. In Sec. II, theo-retical issues concerning spheromak lifetimes, impurity pro-duction rates, Z,, and other mechanisms affecting r,ife are

6302 J. Appl. Phys. 69 (9), 1 May 1991 0021-8979/91/096302-11$03.00 @ 1991 American Institute of Physics 6302Downloaded 17 Jul 2003 to 130.58.92.72. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp


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discussed. In Sec. III, the Caltech spheromak gun and theadverse role of impurities are described. In Sec. IV, our mainspectroscopic results from the various coated electrodes arepresented. In Sec. V, we close with a discussion of our resultsin the context of other experiments and a summary. Gunperformance and operation are characterized in the appen-dices. Electromagnetic properties of the gun are discussed inAppendix A and we characterize the role of neutral gas inour experiment in Appendix B.

II. THEORETICAL ISSUESA. Spheromak lifetimes

The spheromak resistive lifetime can be viewed as anL /R decay time where L is the spheromak inductance deter-mined by the dimensions of the current path in the dischargeand R is the Spitzer resistance of the spheromak plasma.Turner et aZ.l6 have pointed out that the magnetic diffusionequation governing spheromak resistive decay can be writ-ten:dB-= - T,JA Bat PO (1)

where q is the Spitzer resistivity (7 a Z,, T - 32) and il isthe eigenvalue in the equation for the force-free state(V X B = /z B). The e-folding time for the spheromak mag-netic fields is thenr mag =po/($ 2). (2)We have noted that the magnetic decay time of ourspheromaks is anomalously short compared to this simpleSpitzer lifetime calculation. We have performed extensivemagnetic measurements of the spheromak equilibrium in-

jected into the empty Encore tokamak vessel and have de-termined from a fit of the data to a simple equilibrium modelthat R = 22 m .- . For a value of T, = 7 eV (measured with adouble Langmuir probe) and assuming Z,, = 1 we calcu-late rmap= 100 ps while the measured e-folding timer mag= 10 ps in our spheromak (the total rlife r20 ps).Spheromaks which are not fully relaxed, and thus havesmaller dimensions, have been measured with values ofR upto 30 m - and fully relaxed spheromaks late in the decayphase of the discharge have T, as low as 4 eV. In these ex-treme cases, we calculate T,,,~~50 ps. We conclude thatthere is an anomaly factor of 5-10 between the predicted andmeasured e-folding times of the magnetic fields of our spher-omak discharges. Other researchers have noted a discrepan-cy between measured spheromak lifetimes and those predict-ed by simple Spitzer resistivity. Barnes et aZ.6 have reporteda resistance anomaly of 1.6-4.0 coupled with a Z,, of 1.3-2. It is important for spheromak injection experimentsthat the spheromak can traverse the distance from its source(a coaxial magnetized plasma gun in our case) to the centerof the tokamak before the spheromak resistively decays. Animportant experimental figure of merit is the Lundquistnumber, Lu = rlir r/rAlf, where rAlf is the AlfvCn transit t imeacross the spheromak. Since the AlfvCn transit time is justthe time required for the spheromak to move its length, the

Lundquist number is a dimensionless measure of the dis-tance the spheromak can traverse in its lifetime. In our ex-periment, Lur 10 so that this condition is marginally met. Arelated dimensionless number is the magnetic Reynoldsnumber, Rm = ,uO v/~, where r is a typical spheromak di-mension (its radius) and u is its velocity. A large Rm isindicative of a high degree of magnetic turbulence. Magneticturbulence and the associated magnetic tearing is critical forhelicity injection experiments. It is because magnetic helicityis conserved even in the presence of turbulent tearing*,19that spheromak injection into a tokamak can be expected todrive current.As noted earlier, it has recently been suggested by theLos Alamos CTX group that spheromaks might rapidly losemagnetic helicity (and therefore have anomalous lifetimes)due to strong electric fields in the edge. The CTX group hasobserved peaking of the current profile (parameterized byJ/B) during the decay phase of the discharge (cooler plasmaat the edge causes higher resistivity there) .20 As the sphero-mak relaxes back to a flat J/B profile consistent with theforce-free Taylor state, electric fields arise in the edge inorder to drive the current. The helicity decay rate is given by:

$== -2 E-BdV. (3)If we assume that most of the dissipation occurs in the edgewhere the electric fields are highest then the loss rate can beapproximated:

its K /rK s - 2@,,,, E*dl, (4)

where aedge s the spheromak magnetic flux either on openfield lines or otherwise immersed in the edge volume wherethere is a significant proportion of neutral gas. The electricfield becomes clamped at the value given by the Paschenbreakdown condition. Note that the resistivity directly at-tributable to electron-neutral collisions is small compared tothe Spitzer resistivity since typically veVenY,, < 0.1 in our ex-periment (where Y,,, is the electron-neutral collision fre-quency).We can determine the fraction of flux required in theedge in order for the edge loss mechanism to have a signifi-cant effect on our experiment. The minimum Paschen vol-tage for breakdown in hydrogen is about 250 V while theminimum path for edge breakdown is a poloidal circumfer-ence, 2~ (0.12 m) = 0.75 m. If we assume that only the outer5% is the edge then the edge flux becomes 5 X lo- 5 Wb,where we have used 0.03 T as the average spheromak mag-netic field. We can now estimate an upper bound on rK dueto this edge loss mechanism by calculating a lower bound tok in Eq. (4). Using a total helicity content0*17 of about10 - Wb*, we therefore conservatively estimate rK < 10 ,usdue to this effect in our experiment (with the assumption of5% edge flux). This is close to our measured rk r 7-a 2 = 5~CLSo the edge loss mechanism is a plausible candidate forour anomalously short lifetimes.

6303 J. Appl. Phys., Vol. 69, No. 9,1 May 1991 Brown, Bailey Ill, and Bellan 6303Downloaded 17 Jul 2003 to 130.58.92.72. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp


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fields decay excessively before reaching the tokamak. Final-ly, if the spheromak decays substantially before relaxing toits lowest energy state then it is difficult to fit experimentaldata to a simple (nondynamic) model.

IV. ELECTRODE COATINGSMaterials used for coating the center electrode of the

spheromak gun were chosen for a number of characteristics(see Table I and Refs. 22-24). First, the material should berefractory (high melting point) to prevent melting and va-porization during the high current discharge. Second, thematerial should have a low sputtering coefficient (wherec s,,ul s the number of electrode atoms evolved per incidentplasma ion). The sputtering coefficients presented in Table Irepresent the number of electrode metal atoms liberatedupon impact of a 600-V argon ion. The coefficient for tung-sten is a factor of two lower than for other materials in thetable so that tungsten is an excellent coating from the stand-point of sputtering.Secondary emission plays a role in the avalanche break-down of gas between coaxial electrodes (see appendix B).Ion bombardment of the cathode (the inner electrode in ourcase) generates secondary electrons which sustain the dis-charge. Tungsten has about a factor of two higher secondaryemission coefficient than other materials for which we havedata, so again tungsten has desirable coating characteristics.Because the discharge has a relatively fast rise time( < 10 ps, see appendix A), the gun current flows in a skinlayer. The skin depth in the cold rolled steel substrate

S,, = Jw, is less than the coating thickness ( Scoatingbecause p is large. However, the skin depth in the coating islarge (S,, = = 0.4mm = 0.0 15 > ?jcoatlng for copper),therefore most of the current flows in the coating for eachelectrode in our experiment. So, for a skin depth large com-pared to the coating thickness, the resistive power depositedper unit volume is given byI R /volume = I T/( 27r&,,t,ng ) . Note that ifs r-3 < Llttng (as it is for nickel), then the power per unitvolume for a given current becomes independent of the resis-tivity 7.

The thermal properties of the coating are governed bythe thermal conductivity, /cth,and the thermal mass of thematerial (the product of the density and specific heat). Athermal skin depth can be defined:25 S,, = 2,/wwhere At is the time the heat pulse is applied. In each case,the thermal skin depth (for a 10~s heat pulse) is comparableto the thickness of the coating. S,, varies from 1.2 mil fornickel to 2.7 mil for copper while the electroplated coatingswere l-2 mil thick. Ideally, we would prefer to have thecoating thickness large compared to St,, so that the coatingwould act as a thermal reservoir to conduct heat away fromthe surface. Unfortunately, it is difficult to electroplate ahigh quality coating thicker than a few thousandths of aninch and thick plasma-coated surfaces tend to flake off of thesubstrate (due to internal stresses developed during the coat-ing process).The steel center electrode of the spheromak gun waselectroplated with copper, nickel, chromium, and rhodium(0.001 in. to 0.002 in. thickness) and was plasma coatedwith tungsten (0.006 in. thick). After plating, the electrodeswere thoroughly cleaned (methanol in an ultrasoniccleaner) and baked to remove residual electrochemicals.Typical base pressures with the coated electrodes were2 X 10 - 6 cm - with residual gas analysis showing predomi-nantly hydrogen and nitrogen. Each coated electrode wastested under identical conditions ( V,,, = 4.5 kV, I,,,, = 70kA, and Qgun = 0.3 mWb) and the visible emission spec-trum from the spheromak was measured ( 18 shots are re-quired to measure the entire visible spectrum from 230 to890 nm in roughly 40 nm increments). Typical plasma den-sities were lOI cm - 3and electron temperatures were 8 eV inthe gun discharge.The visible spectrum (230-890 nm) in the annular re-gion between inner and outer electrodes is measured with anoptical multichannel analyser (OMA) (Princeton Instru-ments Model 120, with a 0.22 meter SPEX monochrometer,Model 1681). A l-mm sealed quartz tube is inserted in themiddle of the electrode gap with the tip exposed a few mm atthe back of the gun (see Fig. 2). A quartz optical fiber isinserted into the quartz tube such that emission can beviewed axially along the length of the gun. The line of sight ismidway between the inner and outer electrodes. Attenuation

TABLE I. Comparison of refractory electrode coating characteristics.Material T n& c pu rl hardness P Ktll cc.Steel 1550C 1.3 0.061 10 160 7.86 0.52 0.12Copper 1084 C 2.3 0.050 1.7 80 8.96 4.01 0.38Nickel 1453 C 1.5 0.053 6.8 140 8.90 0.91 0.44Chromium 1860 C 1.3 - 13 220 7.19 0.94 0.45Rhodium 1965 C 1.5 - 4.6 260 12.9 1.50 0.24Tungsten 3450C 0.6 0.096 5.6 440 19.3 1.74 0.13Notes: Sputtering coefficient is for dc yield from bombar dment of 600-V argon ions, secondary emission coefficient (1: ) is from bombardment of slowhydrogen ions, electrical resistivity (7) is in units of 10 - 0 m, hardness is in units of kg/mm*, density (p) i s in units ofg/cm , thermal conductivity (K,,, )is in units of Wcm K at room temperature and specific heat (C,.) is in units of Jg K .References: CRCHandbook ofApplied EngineeringScience, R. E. Bolz and G. L. Tuve, Eds. ( 1970), Metals Reference Book, C. J. Smithells, Ed. ( 1967) andGlou Discharge Processes,B. Chapman ( 1980).

6305 J.Appl.Phys.,Vol.69,No.9,1 May 1991 Brown,Baiiey III, and Bellan 6305Downloaded 17 Jul 2003 to 130.58.92.72. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp


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Fiber

12opF.lOkV

along the length of the optical fiber and OMA dynamicrange limit our measurements to 230 nm at the short wave-lengths and 890 nm at the longer. The OMA was gated ( 10,us) so that light from the gun breech was monitored duringonly the first half-cycle of the discharge.The principal result of this sequence of tests is that thespheromak parameters and line emission were largely thesame for each electrode (see Table II). There were no sys-tematic differences in spheromak density, temperature, orlifetimes with electrode coating. However, the helicity injec-tion effect was only observed with the tungsten andchrome electrodes. Small variations in the helicity decaytime have a large effect on the amount of helicity that isultimately deposited into the tokamak since the helicity de-cay time appears in an exponent ( Ksph = K, e - rK). Evi-dently, 7-k n the case of the dirty electrodes was ust smallenough so that Ksph decayed below our threshold of mea-surement.Before the present clean up program was undertaken,we measured ifetimes as ow as 15 us and never as ong as 25,us, we now routinely measure lifetimes up to 25 ,X and sel-dom as short as 15 /.Ls. This improvement is not due to aspecific electrode coati ng but due to a combination of the useof Macor ceramic insulators, titanium gettering and, mostimportant, effective discharge cleaning from firing hundredsof shots. The best results have been with an uncoated Monelelectrode with a Macor insulator after firing s 2 00 shots (weobserve similar results with a tungsten coated electrode withMacor insulators). Other researchers have made the obser-

TABLE II. Summar y of refractory electrode coating results.ThicknessMaterial in. Lines suppresse d Sputtering Helicity

Steel - - yes ll0%wr 0.001 576.3 (FeI) Ye noNickel 0.002 - yes noChromium 0.002 426.7 (CII), 504.1 (FeI), no Ye505.1 (FeI), 576.3 (FeI),634.8 (FeI), 637.0 (NiI)Rhodium 0.001 426.7 (CII) yes noTungsten 0.006 426.7 (CII), 504.1 (FeI), no Yes505.1 (FeI), 576.3 (FeI),634.8 (FeI), 637.0 (NiI)

FIG. 2. Schematic ofexperimental set-up showing location of quartz capil-lary used for optical measurement s.

vation that firing many shots is the best technique for clean-ing spheromak guns.a. 2b t is therefore likely that the dis-charge cleaning removes some low-Z impurities (carbonand oxygen) from our electrode surface.In Fig. 3 we present spectra from six electrodes ( tung-sten, rhodium, chromium, nickel, copper, and bare steel)and two typical wavelength ranges (487-533 and 606-652nm). The main point i s that the spectra are remarkably simi-lar from 230-890 nm. There are several hundred identifiablelines commo n to each electrode coating. Next, it is interest-ing that a few lines are suppressed n the case of the tungs tenand chromium coated electrodes (Fe1 and Nil ) . The sup-pressed lines that have been identified are summarized inTable II. Also no ted in Table II is an indication whethersputtering onto the quartz capillary was observed andwhether the helicity injection effect was observed. Weshould note that the limited resolution of the OMA (only afew angstroms) made absolute identification of lines diffi-cult. The identification of a given line is the most likely can-didate of several annotated lines.

In addition to monitoring visible light emission in thebreech of the gun, we also scanned the visible spectrum ofemission from the tokamak di scharge (l/4 of the tokamakcircumference f rom the injection point) with and withoutspheromak injection. There was much less line emissionfrom the tokamak plasma than from the gun breech andthere were only - 10 additional lines observed upon sphero-mak injection. In Fig. 4, we present typical data from thewavelength range 527-572 nm. Note first that there aremany fewer lines than in t he scans presented in Fig. 3. Sec-ond, note that two new lines appear as a result of spheromakinjection (NiI and FeI). The fact that we see ewer lines inthe tokamak could be due to inefficient transport of high-2impurities from the ablated electrodes. Other researchershave noted that heavy impurities (mostly Fe1 in our case)are not efficiently accelerated by the current sheath in thegun.We noticed that after 30-40 shots, the quartz optics,particularly the l-mm quartz capillary used to view the gunbreech, became coated with metal. The coatings on thequartz capillaries were analyzed using energy dispersive x-ray analysis. For the most part, material from each electrodewas detected on the capillary used for the experiment. Weconcluded that some (perhaps most) of the sputtering isfrom the inner electrode but at least some material is beingablated from the outer electrode. All of the electrodes sput-

6306 J. Appl. Phys., Vol. 69, No. 9, 1 May 1991 Brown, Bailey III, and Bellan 6306Downloaded 17 Jul 2003 to 130.58.92.72. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp


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TUNGSTEN

RHODIUM

CHROMIUM

NICKEL

COPPER

STEEL

487 nm 533 nm

TUNGSTEN

RHODIUM

CHROMIUM

NICKEL

COPPER

STEEL

606 nm 652 nm

FIG. 3. Typical spectral comparison for each electrode coating, emissionfrom the gun breech, (a) the range from 487 to 533 nm showing the sup-pression ofsome Fe1 lines in the tungsten and chromium electrodes, (b) therange from 606 to 652 nm, showing supression of Fe1 and NiI lines in thetungsten and chromium electrodes.6307 J. Appl. Phys., Vol. 69, No. 9,l May 1991

I . I 1 I.

TOKAMAK DISCHARGE 546.3 (FeI)(JTOKAMAKWITH SPHEROMAK

527 nm 572 nmFIG. 4. Typical emission spectrum in the tokamak di scharge (top) andtokamak discharge with spheromak injection (bottom) for the tungstencoated electrode, range from 527 to 572 nm.

tered some material onto the quartz capillary with the nota-ble exceptions of the chromium and tungsten coated elec-trodes.In Fig. 5, we present the time history of a resonant CIIIline (229.7 nm) from different electrode/insulator systems.The CIII line is among the brightest impurity lines in our

;ob0.loo-

2liY -s'i; -$EE -

(b)

I I I I0 20 time@) 40FIG. 5. Time histories of 230 nm emission (including CIII at 229.7 nm) inthe tokamak discharge upon spheromak injection for representative elec-trode/insulator systems, (a) I,,, , (b) 230 nm emission with the Monel-/Macor system, (c) Monel/Delrin, (d) copper coated/Delrin.

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discharge and we expect emission from carbon lines to beindicative of ablation from plastic insulators. For this mea-surement, we view emission through a quartz window andnarrow band filter (FWHM of 9 nm, centered at 230 nm)with a UV enhanced photodiode (UDT-455UV) sensitivedown to 200 nm. The window is located on the tokamakvessel, l/4 of a toroidal circumference from the spheromakinjection point.Our cleanest system is a bare Monel electrode and aMacor insulator [Fig. 5 (b) 1. We expect our dirtiest sys-tem to be the high sputtering coefficient, low melting pointcopper coated electrode with the Delrin (a machinable plas-tic) insulator [Fig. 5 (d) 1. Note however that the emissiontraces are remarkably similar in magnitude and shape. Ineach trace there is an initial burst of CIII emission when thespheromak enters the tokamak chamber fol lowed by an-other burst during the decay phase as the spheromak plasmaexpands past the viewing window. We see that the time evo-lution of this typical line is similar for the various electrodes.The macroscopic parameters were also the same for each ofthese electrode systems. Contrary to expectations, the plas-tic insulator did not contribute appreciably to the carbonimpurity content of the discharge.V. DISCUSSION

In summary, we have coated the center steel electrode ofthe coaxial, magnetized plasma gun used in our spheromakinjection experiments with var ious refractory metals (cop-per, nickel, chromium, rhodium, and tungsten). This wasdone in an attempt to reduce the level of sputtered high-Zimpurities into the spheromak discharge so that magneticlifetimes might be increased. The chromium and tungstencoated electrodes performed marginally better than the oth-ers in that we measured only trace amounts of sputteredchromium on our quartz capillaries and we were able to ob-serve the helicity injection effect with these electrodes. Inaddition, despite the very similar spectra among electrodematerials, a small number of spectral l ines were supressed inthe chromium and tungsten electrodes and not in the others.However, we found that none of the coatings had a measura-ble effect on spheromak magnetic li fetime, temperature, ordensity. In addition, discharge cleaning had only a marginaleffect on spheromak lifetime (not enough to account for thefactor of 5-10 discrepancy between theory and experiment).On this experimental evidence coupled with a O-D calcula-tion that Z,, < 2 in our discharge (Sec. II B) we conclude amechanism unrelated to impurities causes our anomalouslyshort lifetimes.It is instructive to compare our magnetic lifetime mea-surements with those of other experimenters. In Fig. 6, wecompare our longest magnetic lifetime to those measured inseveral spheromak experiments (data from these experi-ments are obtained from Refs. 1,6,9,16,28-3 1). We compareonly with other low temperature experiments ( < 50 eV)since spheromak lifetime in hot spheromaks is governed bydynamic processes rather than simple Spitzer resistivi ty(e.g., current driven instabilities32 and ballooningJR ). Thereported experimental spheromak l ifetime, rlife, is plotted asa function of J Tj2 where r is the flux conserver radius.6308 J. Appl. Phys., Vol. 69, No. 9,i May 1991

Since ~-,~r~puo/(77/2 2, and ~a T -32, the data should belinear when plotted this way. A straight line with 2T22scaling and passing through the Caltech measurement isplotted (i.e., if we made our spheromak bigger and hotter wewould expect to move along this line) as is the Spitzer pre-diction with Z,, = 1. Note first that spheromak lifetimes inthis low-temperature regime indeed have the predictedSpitzer-like scaling but with an anomalously low coefficient.This cannot be explained with a large Z,, since the tempera-ture is not high enough to make Z,, greater than about two.It appears from the plot that the 20,~~sifetime of the Caltechspheromak is not anomalous in the context of results fromother experiments and that a mechanism unrelated to Z,,may be a ubiquitous feature limiting lifetimes ofcold sphero-maks.We should point out that contrary to this observation,some experimenters have found spheromak r,ife invariantwith size* and with temperature34 under certain conditions.However, these results were obtained in the range12Ty2 = 10 to 100 m2eV32 where other processes keep r,ifeclamped near 1 ms. Note that data points in Fig. 6 at high?Ta begin to deviate below the empirical fit. Recently,Wysocki et a1.35have shown that careful design of the CTXflux conserver has reduced field errors and reduced edge fluxso that CTX spheromak decay time increases with T,.We suggested earlier (Sec. II A) that the edge helicitydecay mechanism may play a role in determining rTlife f ourspheromak. A non-negligible component of unionized neu-tral gas is unavoidable in the spheromak formation process.Several hundred mTorr of hydrogen must be deposited in

_ x8 vs. r2Te30 for Cold Spheromaks (T, < 50eV) //1000

caF SCALING0 BETA (1983)

100

0 Ps.1 (1983)I/@CALTECH (1989),I

10 $ I I111111 1 I,,,, ,, I 1,111~.l 1 10 0

FIG. 6. Plot of T, ,~~ s iT for representative small, cold spheromaks.Expected empirical scaling and the Spitzer prediction are also plotted. Notethat the measured lifetimes fall below the Spitzer prediction and that data atlarger ?T fall below the empirical prediction.

Brown, Bailey III, and Bellan 6308

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the gun breech (see discussion in Appendix B) some ofwhich is not ionized. In addition, since the spheromak plas-ma is relatively cool and dense, significant recombinationmight be expected in the edge. Finally, recent studies haveshownJ4 that a large concentration of neutrals can existwithin the spheromak far from the edge due to multiplegeneration charge exchange. This effectively increases thethickness of the edge (since neutrals are present far fromthe wall) as well as increasing the energy lost due to chargeexchange with the neutrals. Based on the simple estimatepresented in Sec. II A, edge helicity dissipation may be animportant loss mechanism in our spheromak discharge.

APPENDICES: SPHEROMAK GUNCHARACTERIZATION AND OPERATION(b)

APPENDIX A: ELECTROMAGNETIC PROPERTIES I IIn addition to the spectroscopic measurements de-scribed in Sec. V, a number of auxiliary diagnostics havebeen used to characterize the spheromak gun and equilibri-um. Various arrays of magnetic probes have been used tomeasure the magnetic structure of the spheromaks and todetermine the magnetic lifetime.17 A typical loop in thesearrays is 0.5 cm in diameter and is electrostatically shieldedwith a slit copper foil. Both acti ve and passive integratorshave been used. Double tipped and single tipped Langmuirprobes calibrated with a 3 mm interferometer are used tomonitor plasma density. Calibrated Rogowski loops havebeen used to monitor the spheromak gun current and preci-sion voltage dividers monitor the voltage that appears be-tween the inner and outer electrodes of the gun.In Fig. 7, we present typical electromagnetic character-

istics of the gun (treating it as simple circuit). We presentdata of the gun current [I,, Fig. 7(a) 1, the gun voltage ( thevoltage that develops between the inner and outer electrodesduring formation, [ I,, Fig. 7(b) 1, a typical signal from amagnetic pickup loop [ Bsph Fig. 7 (c) 1, and a typical signalfrom the saturated double Langmuir probe [n,, Fig. 7(d) 1.The capacitor voltage was 4.2 kV and the stuffing flux was0.3 mWb for this sequence. Note that V, is determined bydynamic gun impedance and is usually significantly lowerthan the capacitor voltage. We can determine the point atwhich the spheromak breaks away from the gun by the char-acteristic signatures in the 1, and V, traces at about 4,~s. Asthe gun plasma distends the stuffing flux, the current path isextended thereby rapidly increasing the gun inductance.Since I, = (d /dt) (LgUnIg ), there is a sharp increase in] V, 1.When the spheromak tears away from the gun, the gundischarge restrikes at the back of the gun, rapidly decreasingthe gun inductance. At this point there is a drop in ] V, 1.Wecan also measure the spheromak velocity by noting thatthere is a 7 ,us delay between spheromak formation and de-tection of spheromak fields and density 30 cm away; thespheromak velocity is 4 cm/ps in this case. Finally, we areable to ascertain the gun stuffing threshold,36 jlgun = pOlg/Qp,, by noting that the spheromak breaks away from the gunwhen I, ~50 kA while a, = 0.3 mWb. We find that Rgun= 210 m - from this dynamic measurement.

b lb i0twFIG. 7. Typical electromagnetic characteristics of the magnetized plasmagun, (a) Z, ,,,, (b) V, ,,,, Cc) B,,,,, and Cd) n,., Z, ,,, and V,,, aremeasuredatthe gun electrodes, BIlrh and n, are measured in the tokamak vessel.

We have performed scans of rg (at fixed Cp, and mea-sured the spheromak magnetic field, density and resistanceof the gun plasma with both 2 and 12 external cables. Gunplasma resistance is defined as the ratio of I, at the peak ofgun current (to eliminate inductive effects) to the peak Ig.The fixed stuffing flux for this run was 0.4 mWb. The switchfrom 2 external cables to 12 reduced the total inductance ofour power supply and spheromak gun from 660 to 240 nHy.This reduced the rise time of the circuit from Q-,,~= 14 to 8.4,us and enabled us to make shorter, more localized sphero-mak plasmas. We were also able to operate at higher peakcurrent for the same capacitor voltage (since the capacitorcharge is switched faster). In Fig. 8 (a), note that we begin tosee small spheromak fields when I, E 60 kA (below this val-ue the gun is stuffed). From this measurement we find thestuffing threshold, Agun = ,~,l,/@, r 190 m - .Our measured gun threshold, Agun = 190-210 m - , is

6309 J. Appl. Phys., Vol. 69, No. 9, 1 May 1991 Brown, Bailey Ill, and Bellan 6309Downloaded 17 Jul 2003 to 130.58.92.72. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp


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We found that it was important to fire sufficiently lateinto the gas pulse so not to produce gas starved discharges.Material is typically sputtered from the cathode (the centerelectrode in most cases, ours included) due to high voltageion bombardment. However, material can also be sputteredfrom the outer anode in the case of a gas starved discharge.This occurs when there is not enough neutral fill gas (hydro-gen) to provide the ion flow that sustains the current in theradial current sheet between the inner and outer electrode. Alarge sheath develops and the material is electrostaticallypulled from the anode into the plasma.46 In order to preventthe metal electrode surface f rom becoming a source of ions, itmight be useful to make the anode a porous, high surfacearea material (such as plasma sprayed tungsten or titaniumloaded with hydrogen as proposed by Post and Turner25 ). Inthis case, gas adsorbed onto the surface of the anode couldsustain a gas starved discharge. In fact, the plot of n, increas-ing with 1, depicted in Fig. 8(b) (with fixed gas puff pres-sure) is suggestive of just such a process.

ACKNOWLEDGMENTSIt is a pleasure to acknowledge the technical assistanceof M & T Plating, Frank Cosso, and Larry Begay, as well asuseful discussions with Dr. Cris Barnes, Dr. Tom Jarboe,and Dr. Juan Fernlndez of Los Alamos National Laborato-ry and Dr. Charles Hartman and Dr. Jim Hammer of Law-rence Livermore National Laboratory. This work was per-formed under DOE Grant No. DE-FG03-86ER53232.

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