Attempts at Ion Cyclotron Heating. In a Toroidal Octupole. Presented at the Los Angeles Meeting of the American Physical Society. November 12-15, 1969

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1 Attempts at n Cycltrn Heating n a Tridal Octuple by J. C. Sprtt Presented at the Ls Angeles Meeting f the American Physical Sciety Nvember 1215, 1969 PLP 321 These PLP Reprts are infnnal and preliminary and as such may cntain errrs nt yet eliminated. They are fr private circulatin nly and are nt t be further transmitted withut cnsent f the authrs and majr prfessr.

2 ABSTRACT A lookw, J1vlHz scillatr has been cnstructed t prduce 300vsec rf pulses fr in cycltrn heating in a tridal ctuple. Varius methds f cupling t the plasma have been tried. By driving the hps electrstatically with respect t the wall at 2 kv YmS, sme electric field ( lov/cm) is bserved in the interir f the plasma, but the large fields at the bundary result in severe plasma lss during heating. A three phase system has been develped t drive rf currents int the three supprts n each hp. The rf hp current f loo amps prduces a field mdulatin 6B/B lo 3, and electric fields f lv/cm. Fr tile plasma densities used, magnetic prbes indicate cmplete penetratin f the rf field int the plasma. Calculatins indicate an expected average heating rate f O. lev/vsec. n saturatin current t a prbe n the B=O axis shws a slight increase after heating, prviding sme experimental evidence fr in heating.

2 Electrn Cycltrn resnance heating has prved s successful in multiples that it is te)ting t try t extend the technique t lwer frequencies in an attempt t resnantly heat the ins in the plasma.

3 2 Electrn Cycltrn resnance heating has prved s successful in multiples that it is te)ting t try t extend the technique t lwer frequencies in an attempt t resnantly heat the ins in the plasma. This prgram is di ffi cu t fr tw reasns. The firs t is that high density plasmas tend t exclude lw frequency electric fields, and the secnd is that since the free space wave length at the in cycltrn frequency is much larger than the cavi ty dimensins, it is difficult t get a gd impedance match between the rf scillatr and the cavity. Nevertheless, a 100 kw, 1 MHz scillatr was cnstructed that culd be pulsed n fr up t 300 l1sec. Varius methds f cupling the rf t the plasma were tried. By mdulating the current in the primary f the transfrmer used t excite the hps, the magnetic field culd be varied by ne part in 104, prducing electric fields f abut.1 V/cm. The synchrtrn gap culd be driven directly, but the impedance is very lw because f the small leakage inductance f the transfrmer, and n imprvement was nted. Tle Be gap was tuned t resnance at 1 Mf1:z using a bank f mica capacitrs, but the gap was nt adequately insulated fr the rf vltage. This methd will be tried again in the future with better insulatin. The scillatr was used t amplitude mdulate a 10 cm magnetrn in the hpe that sme nnlinear behavir f the plasma wuld demdulate the mcrwaves and prduce the desired lw frequency fields in the plasma. Kuswa has reprted preliminary results using this methd. l

3 Tle tw methds that were studied in the mst detail are utlined in fig. 1. Tle simplest metild cnsists f driving the hps electrstatically with an rms vltage f 2 kv with respect t the cavity walls.

The three phase is prduced with delay lines, and the lad is made t lk resistive by adding capacitrs which tune the circuit t resnance.

4 3 Tle tw methds that were studied in the mst detail are utlined in fig. 1. Tle simplest metild cnsists f driving the hps electrstatically with an rms vltage f 2 kv with respect t the cavity walls. Tle ther methd cnsists f driving currents thrugh the hps by applying three phase rf t tile three supprts n each hp. The three phase is prduced with delay lines, and the lad is made t lk resistive by adding capacitrs which tune the circuit t resnance. This electrmagnetic drive system prduces rf hp currents f abut 100 amps and electric fields appraclling 1 V / Cill. Tle fundamental difference between the tw systems is that the electrstatic drive prduces electric fields by creating ptential gradients, while the electrmagnetic drive prduces electric fields by a time cllanging magnetic vectr ptential. 11le first methd prduces cnsiderably larger electric fields in the absence f plasma, but the secnd methd is mre effective in penetrating a plasma at high density. Figure 2 shws a plt f the anlitude f the flating ptential scillatin between the hp and the wall when the hp is driven electrstatically. Tle electric field is smallest where the density is highest and largest at the bundaries f the plasma. Tle ptential distributin is in qualitative agreement with a theretical mdel f a dielectric plasma in a nnunifnn magnetic field. 2 The electric field at ljj = a was measured as a functin f plasma dens i ty us ing a radi al daub e capacitance prbe, and the result is shwn in the lwer part f Figure 3. Tlere is a lt f scatter in the data pints, but the electric field is clearly attenuated at hi l densities.

5 4 A micrwave prduced plasma was used t btain these data since the gtm. injected plasma culd nly prduce densities up t abut 109 an3. The attenuatin is in agreement with a simple mdel that treats the plasma as a dielectric medium. The mdel predicts an electric field f the frm E E =..,...,., n/n ' c where n c is the density at which the lw frequency dielectric cnstant, nm = +... if is equal t 2 0. Fr the electrmagnetic drive, the rf magnetic field was measured at the same place using a small magnetic prbe. The nns field is abut 0.4 gauss, and shws nly a slight attenuatin at the highest density available. The bserved decrease is cnsistent with a simple mdel f the penetratin f an electrmagnetic wave int a plasma belw the plasma frequency. The wave damps accrding t E = where 0 is the penetratin depth. E ex/ The critical density n c ccurs when 0 (= clw ) is cmparable t the dimensins f the plasma. The p critical density fr the electrmagnetic case (1 x 1012 an3) is much greater than fr the electrstatic case (4 x 108 an3). The electric field calculated frm these data is abut 1 V/an, r tw rders f magnitude less than btained with the electrstatic drive at lw densities. The imprtant pint, hwever, is that rf electric fields can be prduced in lw density plasmas even when the frequency is well belw the plasma frequency. These data were btained at lw amplitude (5 watts) and linearly extraplated up t the high pwer case.

6 5 Figure 4 shws a flux plt f the ctuple field. At MHz, in cycltrn resnance ccurs at abut 7 kg, and if the heating fllws the pattern f electrn cycltrn heating, the heating shuld be maximum at places where the resnant B surface is tangent t a flux surface. The fields in the previus slide were measured at the resnance zne in the midplane near the inner wall. An in saturatin current prbe was placed n the B = 0 axis, and Fig. 5 shws the result. Fr the electrstatic drive, the current drps alm::st t zer when the heating pulse in applied. This result suggests that mst f the plasma is swept ut f the field by the large electric fields. Micrwave diagnstics 3 cnfirm this fact. Optimistically, ne culd say that the heating was s effective that the magnetic field culd nt cnfine the energetic ins. 1be large negative flating ptential during heating indicates that the ins are indeed preferentially lst. With the electrmagnetic drive, the in saturatin current is nearly cnstant after heating. f the prbe is mved ut t the resnance zne and if the plasma is injected earlier t give it mre time t cl, there is a substantial rise ln in saturatin current. Since in saturatin current is prprtinal t density times the square rt f in temperature, ne interpretatin f this increase is that the ins are heated. The percentage rise f in saturatin current was measured vs psitin acrss the llidplane and the result is shwn in Fig. 6. The rise is maximum near the walls at apprximately the places where in cycltrn resnance shuld ccur. There is an uncertainty f several em in the exact lcatin f the resnances. This lcalized increase prvides further evidence that SOre in cycltrn heating is present. A simple thery has been used t estimate the in cycltrn heating 2 rate. The heating rate at a pint is expressed in terms f the density n,

7 6 perpendicular electric field E..L.' and cnductivity by 2 J. E J. n The cnductivity can be written in terms f a cllisin frequency v as = E: w v.j.. 0 p [ 2 2 w + W c and expanded in a Taylr series abut the resnance at w = w. c Fr n cnstant everywhere within the cavity, the heating rate can be integrated ver the vlume f the machine t get an average in heating rate: Fr an electric field f V/cm, the heating rate is abut 0.1 ev/vsec. Since the electric fields btained with the electrmagnetic drive apprach this value, we expect a small but definite heating. f the bserved increase in in saturatin current is a result f in heating, the heating rate is in apprximate agreement with the theretical predictin. ACKNOWLED(}1ENTS Sne f the heating apparatus and diagnstics were cnstructed by Rn Parker. Glenn Kuswa prvided helpful discussin, and made an attempt t measure the heating rate with an electrstatic analyzer. Wrk supprted by U.S. Atmic Energy Cmmissin

8 7 REFERENCES 1. G.W. Kuswa, Bull. Am. Phys. Sc. 14, 1033 (1969). 2. J.C. Sprtt, Univ. f Wisc. Ph.D. Thesis (1969). 3. J.W. Rudmin, private cmmunicatin. Figure Captins 1. Tw methds fr prducing lw frequency electric fields in the plasma. 2. RF ptential acrss plasma fr electrstatic drive. 3. Attenuatin f rf field with increasing density fr the tw drive methds. 4. Flux plt shwing cnstant B surfaces in the tridal ctuple 5. Oscillscpe traces shwing the effect f rf heating as measured with Langnrui r prbes. 6. Fractinal increase in in saturatin current vs distance acrss midplane fr electrmagnetic drive.

9 100kW " MHz 50!), ELECTROSTATC DRVE.67 JLsec delay line 200V rms 100kW MHz.33 JLsec delay line t t.01 JLF ELECTROMAGNETC DRVE Figure 1

10 .4.3 t9.2 "' t8t > 0:: <{ f!:. c 0:: <{ 5. 0 H / Figure 2

11 TO AXS CONSTANT B SURFACES N THE WSCONSN TORODAL OCTUPOLE Figure 4

12 ...v" 0 " 0. '3 " 101 '3 H> 101 rtl to JO..f 104_ 0 N CD C 0 Q. "C. E. 3 " ' K>f K> Ot r, 101 <r tot U) rn 0 ' \0 e " r.r... E ", d V'

$ELECTROSTATC DRVE 50, " x en r " 1\ _.$

13 . e il, ;; 0.2 0' m <3 0.1' ' ELECTROMAGNETC t " Xx x e./nln with n = x 1012 em ' DRVE ' ' ' xxw J x ELECTROSTATC DRVE 50, " x en r " 1\ _..'&'ft'" nc :: 4x10 ' em' E 20 e l> 10 x x x x x 10 ' 10 ' n (em') Figure 3

$.. ;;; ==. iht \fwr 1.$ . 1 1 rt' r rt' (') :c en

14 ft!.i r ft (') :c 3: l> G) Z ft :j (') C :c <: ft = i T...,... ;;; ==. iht \fwr 1... i 11:' 0= rt' r rt' (') :c en :::t (') c :c < rt' S iliiiii; iii_ T w r L 'e>!o r

Measurement of Radial Loss and Lifetime. of Microwave Plasma in the Octupo1e. J. C. Sprott PLP 165. Plasma Studies. University of Wisconsin DEC 1967

Measurement of Radial Loss and Lifetime. of Microwave Plasma in the Octupo1e. J. C. Sprott PLP 165. Plasma Studies. University of Wisconsin DEC 1967 Measurement f Radial Lss and Lifetime f Micrwave Plasma in the Octup1e J. C. Sprtt PLP 165 Plasma Studies University f Wiscnsin DEC 1967 1 The number f particles in the tridal ctuple was measured as a