Chen, X.

Hokin, S.A.

Lane, B.G.

Post, R.S.

Smatlak, D.L.

DSpace@MIT

PFC/JA-87-6Experimental Observation of the Hot ElectronEquilibrium in a Minimum-B Mirror PlasmaD.L. Smatlak, X. Chen, B.G. Lane,S.A. Hokin, and R.S. PostFebruary, 1987Plasma Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139 USASubmitted for publication in: Physical Review LettersExperimental Observation of the Hot Electron Equilibrium in aMinimum-B Mirror PlasmaD.L. Smatlak, X. Chen, B.G. Lane, S.A. Hokin, R.S. PostPlasma Fusion Center, Massachusetts Institute of TechnologyCambridge, MA 02139Measurements of the hot electron (T-450 keV, n-2 x 1011cm-3 ) equilibrium in the Constance B minimum-B magneticmirror show that the pressure profile is peaked off theaxis and is shaped like the seam on a baseball. Thiscurve is the drift surface of the deeply trappedelectrons and the location of the strongest microwaveheating. The configuration is stable and decaysquiescently on the hot electron collisional time scale(1-2 seconds) after the microwave power is turned off.According to 1-D pressure-weighted fdl/B analysis thisplasma configuration is expected to be unstable.1The equilibrium and stability of plasma configurations in magneticfields is of fundamental importance in the development and understanding ofplasma confinement devices. Experimental measurements of mirror equilibriahave been made in electron cyclotron resonance heated (ECRH) maximum-Bmirrors', 2 and bumpy tori3 . The data shows that for maximum-B hot electronplasmas, the plasma pressure is concentrated in a ring structure which islocated near the second harmonic ECRH resonance. In this Letter we reportthe observation of the hot electron equilibrium in a minimum-B mirror. Thehot electron pressure profile is found to be peaked off-axis and shapedlike the stitched seam on a baseball.In the Constance B mirror 4, high beta (beta is the ratio of plasmapressure to magnetic field pressure), hot electron plasmas are createdusing up to 4 kW of fundamental electron cyclotron resonance heating at10.5 GHz. Typical plasma parameters are T.h = 450 keV, n.h = 2 x 1011 cM-3 ,a = 30%, n, M 2 x 1011 cM-3 and T., < 100 eV. The ECRH resonance zone isa closed ellipsoidal surface (Fig. 1). The typical operating hydrogenneutral pressure is 10-6 torr although stable hot electron plasmas can beformed over the pressure range from 5 x 10-8 torr to 10-1 torr. Pulselengths are typically 1 to 2 seconds. The hot electron confinement isdominated by ECRH-induced diffusion5 when the rf is on, but when the ECRHis turned off the diamagnetic decay time is consistent with collisionalscattering loss of the hot electrons.Insight into the spatial distribution of the hot electrons is given bythe visible light images of the plasma taken with a CCD TV camera. Figure22 shows the photographs of the Constance plasma which are taken 30 ms afterthe ECRH is turned off. At this time, >95% of the cold electrons havescattered into the loss cone (Tcat = 50 ps) and only the hot electrons arewell-confined. These pictures suggest that in three dimensions the hotelectrons are concentrated along a baseball seam, i.e. the curve describedby the stitched seam on a baseball. An x-ray pinhole photograph (Fig. 3)taken for the same plasma conditions verifies that the hot electrons aredistributed as the visible light photographs suggest. The plasma iscontained within the resonant mod-B surface. Measurements of the H-alphaprofiles, the hard x-ray flux and the hot electron temperature profiles,and the hot and cold electron endloss profiles also corroborate the hollow,and in particular, the baseball seam nature of the hot electron profile6 .Another strong indication that the hot electrons are distributed along thebaseball seam is the observation that it is possible to insert a 1/4"diameter aluminum probe in to the plasma axis at the opening of the "C"(point A on Fig. 1) with a resulting decrease in stored energy of less than10%. Inserting the probe to the axis at other axial positions completelydestroys the plasma.This hot electron equilibrium has been observed over a wide range ofoperating conditions. The baseball seam shape is established within thefirst 30-60 ms of the discharge when beta is low (<< 1%). The plasmaprofile is initially peaked on axis and then changes to the baseball shapewithin 30 ms, which is the time resolution of the framing CCD camera. Whenthis transition occurs the hot electron temperature is measured to bebetween 30 and 50 keV. In high neutral pressure discharges with no hot3electrons, the baseball seam is not observed. The baseball equilibrium isseen in hydrogen, helium and argon plasmas. Finally, the hollow plasma isseen over the range of midplane magnetic fields from 2.8 to 3.4 kG(resonant radial mirror ratio from 1.33 to 1.1).Two plasma characteristics can be associated with the observed baseballseam curve. First, this shape corresponds to the drift surface of thedeeply trapped electrons at the resonance zone. Figure 4 shows thecalculated drift orbit of a 340 keV electron with very little parallelenergy which is started near the bottom of the well on a mod-B surface inthe Constance magnetic field. This figure clearly shows the baseball seamnature of the particle drift. Second, the ECRH absorption will bestrongest along the baseball seam curve. The largest heating rate occurson field lines which are tangent to the resonant mod-B surface, since onthese field lines the gradients in the field at the resonant surfacevanish'. Mapping this tangent point along the mod-B surface produces abaseball seam. It is the cold electrons, which are the source for the hotelectrons, that are strongly heated on the baseball seam curve. Therelativistic hot electrons (y-1.7) are resonant further out along the fieldline. Thus, the anisotropically-heated hot electrons seek an equilibriumrelated to their drift motion and to the heating of their low energy sourceelectrons.An interesting feature of this equilibrium is that it is very stable.Although the magnetic geometry is minimum-B, plasma stability is notnecessarily to be expected for pressure profiles which are peaked off-axis.4A detailed theoretical analysis is complicated by the geometry and by thewide parameter range of the ratio of the electron drift frequency to themagnetohydrodynamic (MHD) growth rates. This ratio varies from much lessthan unity at the beginning of the ECRH pulse to unity as the hot electrontemperature approaches 200-400 keV. Thus, we do not attempt in this Letterto give a detailed stability analysis but instead, use the adiabatic fluidenergy principle of Rosenbluth and LongmireO to suggest why the stabilityof the observed configuration is surprising. If we apply the Rosenbluthand Longmire stability criterion, neglecting compressibility effects, tothe plasma inside the pressure peak, we conclude that the plasma isunstable in this region because the magnetic field curvature is unfavorablewith respect to the pressure gradient. This is the familiar fdl/Bcriterion for ideal MHD stability. The plasma would thus be expected toflute radially inward and assume the most energetically-favorable profile -one which is peaked on axis - on the time scale of the MHD growth rate.For Constance parameters, the MHD growth time is -0.1 vs. Experimentally,however, we observe that the plasma is stable and relaxes on thesignificantly longer hot electron collisional time scale of seconds whenthe ECRH is turned off.When compressional effects are taken into account, profiles which arepeaked off-axis are theoretically stable provided they are not too hollow.The marginally stable profile is given by PVY = constant, where P is thepressure, V is the volume of a unit tube of flux (V - fdl/B) and Ye(N+2)/N, where N is the number of degrees of freedom. For the Constancemagnetic field, this profile is one which drops to 88% of its peak value on5axis. Figure 5 shows the midplane radial profile and line-integrated sideand end views of two model pressure profiles. Figure 5a is the theoreticalcompressibility stabilized profile and 5b is a more hollow profile wherethe pressure drops to 45% on axis. The line-integrated profiles can bedirectly compared to the visible light photographs. Since the hot electrontemperature profile deduced from x-rays is measured to be flat across theplasma the pressure profile is equivalent to the density profile. Thelight emission is proportional to the product of the hot electron densityand the neutral density and since the neutrals are uniformly distributed inthis low density plasma, the light also reflects the hot electron densityprofile. Better agreement is achieved with profile (b), a profile which ismore hollow than the compressibility-stabilized pressure profile.Moreover, magnetic probe measurements of the diamagnetic fields outside thehot plasma9 are in good agreement with the predictions of the profile whichdrops to 45% on axis.Stabilization methods other than compressibility have been considered,but none yet provide a satisfactory explanation. First, stability isobserved very early in the shot and for low ECRH power shots where the hotelectron beta is very low (<<1%). In these cases the hot electrondiamagnetism is not sufficient to modify the vacuum magnetic field.Second, stability is observed in the absence of cold plasma. Thiscontrasts with the experimentally observed lack of stability under similarconditions seen in the EBT experiment10 . Third, line-tying is not thoughtto be the stabilization mechanism because the plasma density outside themirror peaks is measured to be less than 1% of the peak density during ECRH6and 100 times lower in the afterglow. The vacuum chamber design causesplasma to hit the endwalls at low density and magnetic field so that endwall isolation can be achieved6 . Finally, the stability early in the shotwhen both beta and the hot electron temperature are low suggests thatdecoupling due to fast particle drifts is not responsible. For electronenergies of 50 keV the drift period is long compared to the MHD growthtime. Although decoupling or stabilization due to effects of high plasmabeta may be valid under some plasma conditions, they cannot be invoked inthe early part of the shot or in low a shots.We have presented the observations of the hot electron equilibrium in aquadrupole mirror. We have found that the pressure profile is shaped likethe seam on a baseball, a curve which coincides with the drifts of thedeeply trapped electrons at the ECRH resonance surface and the points wherethe heating of the cold electron source is strongest. The data indicatesthat the pressure profile is more hollow than the profile which can bestabilized by compressibility. Stabilization by cold plasma, decoupling,line-tying, and the digging of a diamagnetic well are unlikely. Theextreme degree of stability which is experimentally observed is thereforenot understood at this time. We note that this equilibrium has implicationsfor the successful use of quadrupole hot electron cells to provide MHDstability in tandem mirrors1" where a peaked pressure profile is desired tostabilize the central cell core plasma.The authors gratefully acknowledge helpful discussions with S. Hiroe,J. Kesner, M. Gerver, and D.K. Smith. This work was supported by U.S.7Department of Energy Contract No. DE-AC02-78ET51013.8References:1. R.A. Dandl, A.C. England, W.B. Ard, H.O. Eason, M.C. Becker, and G.M.Haas, Nucl. Fusion 4, 344 (1964).2. B.H. Quon, R.A. Dandl, W. DiVergilio, G.E. Guest, L.L. Lao, N.H. Lazar,T.K. Samec, and R.F. Wuerker, Phys. Fluids 28, 1503 (1985).3. H. Ikegami, H. Ikezi, M. Hosokawa, S. Tanaka, and K. Takayama, Phys.Rev. Lett. 19, 778 (1967).4. R.S. Post, et al., Plasma Phys. and Cont. Nuclear Fus. Res. 1984,IAEA-CN-44/C-I-4 (1984).5. S.A. Hokin, R.C. Garner, R.S. Post, and D.L. Smatlak, MIT Plasma FusionCenter Report PFC/JA-86-37 (1986).6. D.L. Smatlak, et al., MIT Plasma Fusion Center Report PFC/RR-86-15(1986).7. M.A. Lieberman and A.J. Lichtenberg, Plasma Physics 15, 125 (1973).8. M.N. Rosenbluth and C.L. Longmire, Annals of Physics 1, 120 (1957).9. X. Chen, D.L. Smatlak, B. Lane, R.S. Post, R.C. Garner, S. Hokin, D.L.Goodman, Bull. Am. Phys. Soc. 31, 1426 (1986).910. S. Hiroe, J.B. Wilgen, F.W. Baity, L.A. Berry, R.J. Colchin, W.A.Davis, A.M. El Nadi, G.R. Haste, D.L. Hillis, D.A. Spong, T. Uckan, andT.L. Owens, Phys. Fluids 27, 1019 (1984).11. J. Kesner, R.S. Post, D.K. Smith, D.E. Baldwin, and Y.C. Lee, Nucl.Fusion 22, 577 (1982).101.2 1.41.6 1.810 cmFig. 1. Constance B magnetic field geometry. Solid lines are field linesand the dotted lines are surfaces of constant magnetic field.11a)b)Fig. 2. Visible light photographs of the plasma 30 ms after ECRH turn-off.(a) Side view. The magnetic field is oriented as shown in Fig. 1.The vertical bars are an ion heating antenna centered on themidplane. The bars are 7.6 cm apart. (b) End view.12Fig. 3. X-ray pinhole photograph of the plasma. The dark vertical bar isthe shadow of the diamagnetic loop.13*I *.b *0* S *06.00 00% O:  0 *.e0So S *:00 o .00. 0 0 00.. ... 0@ 0 ** 0. 00. *. .x*1. 0. ** Og *g 00 0 *. 00 o 0 55i. *0 5 0* 0 16 0000*0 oFig. 4.Calculted drft orbt of a340 keelecton whc is strednathe00 botmlftetel14rFig. 5. Midplane radial pressure profile, line integral of pressure fromthe side, and end view of line-integrated pressure for pressuremodels where the on-axis pressure is (a) 88% and (b) 45% of thepeak pressure. The highest pressure contour is shaded.15

Experimental observation of the hot electron equilibrium in a minimum-B mirror plasma

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Experimental observation of the hot electron equilibrium in a minimum-B mirror plasma

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