J. R. Patau and J. C. Sprott

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1 NUMERCAL SMULATON OF MULT POLE CONFNEMENT (Examples) by J. R. Patau and J. C. Sprtt April 1974 PLP 557 Plasma Studies University f iscnsin These PLP reprts are preliminary and infrmal 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 authr and maj r prfessr.

2 ABSTRACT Sme examples f numerical simulatins f multiple cnfinement, generated by prgram SMULT, l are presented and discussed. pssible, cmparisns with experimental results are made. here The agreement between the calculatins and the plasma parameters frm experiments, is surprisingly gd in spite f the apprximatins inherent in a zer-dimensinal calculatin. l "Numerical Simulatin f r..1ul tiple Cnfinement, " J. R. Patau and J. C. Sprtt, PLP 556. This PLP is an expanded versin f the examples prtin f a talk given at the Philadelphia APS meeting n 2 Nv. 73. See PLP 556 fr the first part f that talk.

3 This PLP demnstrates usage f prgram SMULT discussed in detail in PLP 556. Examples la, 2, 4 and 5 were shwn at the Philadelphia APS meeting in Nvember All cases are fr neutral H 2 backgrund. The excitatin energy lss term (PE3 in SMULT) these results is different frm the ne in PLP 556. used in calculating PE3 was changed t the new versin after the calculatins discussed here were dne; in this paper, PE3 is given by PE3 = 1.44T 85 [exp(5.9l2t 1.8 ) ] Hwever, the new PE3 wuld make little difference in these results. The first tw examples simulate the PSL ctuple with supprts, and shw results f tw simulatins differing nly in the micrwave -6 input pwer. Fr bth examples, backgrund pressure is 1 Trr, magnetic field is 1 Kgauss maximum and plasma is an ECRH plasma, frmed by 2.45 GHz C micrwaves. Example la is fr 1 micrwaves, while lb is fr. 5. Fr la, the 1 input pwer initially all ges int heating the lw density (U)8/cm 3 ) electrns, which get quite ht (8 ev) and becme quite efficient at inizing the neutrals. This inizatin raises the charged particle density and thus lwers the heating rate per particle, shwn by the rapidly decreasing electrn temperature. Until just after peak field, particle lss is mainly t bstacles. Then, when the field starts t decay, field decay becmes the dminant particle lss mechanism, and the density drps. Fr mst f the run, the main electrn energy lss is t neutral excitatin.

4 Z n temperature rises like the density as the ins are heated by electrn-in cllisins. At late times, field decay particle lss is the dminant in energy lss. The high T i spike at very late times in bth ex lesnillaland lb are nt physical - they result frm failure f the numerical methd when the magnetic field gets t lw. n example lb, the pwer input is lwered t.5. The resmlting density and temperature prfiles change nticeably. Again, we see the electrn temperature spike - but this time it is much lwer, indicating that mst electrns are cbler than the neutral inizatin threshhld energy, s that little inizatin ccurs. As a result, the density builds steadily t a maximum at late times, when field decay again dminates the particle lss. The T e spike at early times has been experimentally bserved. Example Z is an extensin f examples la and lb. mere we plt in saturatin current t a.5 cm Z Langmuir prbe versus C micrwave pwer, fr the PSL ctuple perated supprted. Backgrund pressure -6 is 1 Trr H Z ' The lwer slid curve is cmputer predictin; the individual pints are the crrespnding experimental results. 2 The upper curve is fr the levitated case. Jg eem Rt srvery gd between experiment and simulatin. This graph can be understd in terms f examples la and lb. Fr the cnditins described here, in satmratin current measured primarily the density. Fr high pwers, the density peaks near max field is t lw t cause much iniza and is quite large; fr lw pwers T e tin and the density peaks very late, when the field decay starts t dminate particle lss. Neutral excitatin dminates the electrn

5 3 energy lsses; excitatin and bstacle lsses cmbine t almst cancel ut the electrn energy gain due t micrwaves. The upper curve fr the levitated case is in general agreement with bservatin. ith levitatin, a steady state is never reached and the density cntinues t build up until a large particle lss, due t field decay, results. Again the primary electrn energy lss is t neutral excitatin, and the knee arund 1 att reflects the strng temperature dependence f the inizatin rate. Example 3 gives the predicted maximum in saturatin current t a Langmuir prbe n the small ctuple versus C micrwave pwer fr -5 fur different neutral pressures: 1, 2, 5 and 1 x 1 Trr. This time the simulatins are carried ut t find the maximum pwer levels at which plasma is prduced. The cutff in each case is very shawp - -4 fr instance the 1 Trr case ges frm much plasma t n plasma by increasing pwer by 1. The same cmments fr case 2 apply t this graph. Hwever near the upper cutffs the density desn't rise as fast as the sa hlratin + current - the ht electrns determine the value f J. Abve the cutff pwer levels, runaway electrns ccur which cause breakdwn f the prgram methd. Example 4 shws experiment 3 (circles) and predictin (slid curve), fr the time evlutin f in saturatin current in a gun injected plasma in the small ctuple. J is in arbitrary units; thery was nrmalized t experiment at abut 75 sec after injectin. Cmputer predictin is that bstacle lss is the dminant lss fr bth particles and energy. The experimental initial fast drp is prbably frm turbulence left ver frm the injectin prcess. The experimental drp at late times cmes

6 4 frm densities being measured by a prbe n the separatrix, and as the field decays, the density peak mves twards the wall s that the measured density is lwer than the average density. Example 5 shws T e versus time fr the tw millisecnds after gun injectin fr the same case as example 4. There is a nticeable difference between the experimental pints 4 (x) and the slid curve predictin. Hwever, this discrepency prbably ccurs fr several reasns: 1. T can vary cnsiderably in space, e 2. mpurities aren't treated in ur prgram) 3. Treatment f lw energy excitatin lsses is still nt perfect. Again, ebstac1e lss dminates bth particle and electrn energy lss. Example 6 shws charges particle density as a functin f time, this time fr a pulsed ECRH plasma. Tfume is measured frm the start f the pulse. Experimental measurements 4 are by micrwave perturbatin (a's) and time integrated particle lss flux t hps, walls and bstac1es (x's). Again there is gd agreement between predictin and experiment. Particle lsses are dminated by bstacle lss until near the break arund 3 ms, when fmeld decay dminates. These prcesses als accunt fr energy lsses.

7 5 REFERENCES Fr a descriptin f the cmputer prgram used t generate these examples, see: 1 J. R. Patau and J. C. Sprtt, PLP J. C. Sprtt, Phys. Fluids 14, 1795 (1971). See Fig D. E. Lencini, J.. Pukey, J. A. Schmidt, J. C. Sprtt and C.. Ericksn, Phys. Fluids 11, 1115 (1968). 4 J. C. Sprtt, Phys. Fluids 13, 1626 (197). Example 5 - Fig. 7 - curve labeled GUN TORR. Example 6 - see see Fig. 6.

$.O-KGRlJ5S lledr:" f-tp (j) \ \ \ ::s: C) LLJ --..J 1 T L.. 5. >< 1. -2 1.! 1. r ---------- --- t _., en z: t- -.J Z. 1.. TME, 5. :r.1c-2 l1.$

8 2. MULTPBLt D[NS]TY-C** /CM.*3 TEM ERATURE-E::V SMULRTBN SAT CUR-MA/CM. 2 PCH";ER-ATTS M?G F EL..O-KGRlJ5S lledr:" f-tp (j) \ \ \ ::s: C) LLJ --..J 1 T L.. 5. >< ! 1. r t _., en z: t- -.J Z. 1.. TME, 5. :r.1c-2 l1. w 11 ;1 ' 5, hi U i i ' t-. 5. ><lo-'2 T 1 1 E

$-"3 " T'T t'-1 c 1, L_ 5. 1-2. (/),, - l =::) :z. 5.. 1-2 TME x.u r)_ 5. (D z: U ---1,. C-3 / bi. (." "- ----....J""- --! \\ l 5. 1. L.L.J - e 1-2 TME$

9 -- MULTPOLt TEMPfRrlTURE-EV SMULRTON SRT CUR-MA/CM)(2 PCL-i f R - AT TS '1PG r- fl,c-kgauss e n... J U n:::: :3: D-- ' = t----l ll. j 11 T L,,. -"3 " T'T t'-1 c 1, L_ (/),, - l =::) :z TME x.u r)_ 5. (D z: U ---1,. C-3 / bi. (." " J""- --! \\ l L.L.J - e 1-2 TME

$. ECRH PRODUCED PLASrvlA LARGE OCTUPOLE p :: 1-6 TORR = EPERMENT (\ TH SUPPORTS) Cmputer predictin - Levitated$

10 . ECRH PRODUCED PLASrvlA LARGE OCTUPOLE p :: 1-6 TORR = EPERMENT (\ TH SUPPORTS) Cmputer predictin - Levitated Cmputer predictin - Supprted - - '--...-l..u..u_-"'- _-'---'-d-..& MCROAVE KAV/PL E Z POlR (ATTS)

$... E R H - PRODUCED PLffsmR O'!.. SfYJHLL Ut ' OCTUPtJL PLAs-mll SUY1vt-rti /1\1 ONLt.( 3 ""2 u.1 1- :':) <:J :z a - 1- <t.$

11 ... E R H - PRODUCED PLffsmR O'!.. SfYJHLL Ut ' OCTUPtJL PLAs-mll SUY1vt-rti /1\1 ONLt.( 3 ""2 u.1 1- :':) <:J :z a - 1- <t.. 1- ' ::::>' <1::\ V)\ \ "'21 ' H \ -5 p;;. /. x 1 Turr -4 ( - /-5+., t, io. 1. i " ioy C.. mlcj<'oave POEi? (RTTS)

12 !( f,... VV u; - z :=) GUN NJECTON SMALL OCTUPOLE p ::: 1-6 TORR. CD CL <[ '--"" 1- Z w CL Lt:: :J U -7 L- a - t- <:( ::: :J -- <:( en z 1. COMPUTER PREDCTON 'ME.. A F,Ef(.NJ'EC-T.ON TME (msec) 1.5

$) ::> (J) - x LO -- U (]) (f) ::l --- l- a:: z O \ =>u -... -- :;!$

13 N :: ::: w O --.Jt- Z... - ::> f- t- _ U U Z --.J «11 (!) ::> (J) - x LO -- U (]) (f) ::l --- l- a:: z O \ =>u :;!@ :: ua.. LD 8,

14 ECRH - PRODUCED PLASMA '. SMALL OCTUPOLE MCROAVE PERTURBATON PARTCLE LOSS P = 1-4 TORR..-- -r- '--'" e l x TME (msec) [EAMPLE b/

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