Magnetic Fluctuation Induced Particle Transport and Parallel Ion Velocity Fluctuations on MST. Weixing Ding, D.L. Brower, T.Yates

Transcription

1 Magnetic Fluctuation Induced Paticle Tanspot and Paallel Ion Velocity Fluctuations on MST Weixing Ding, D.L. owe, T.Yates Univesity of Califonia, Los Angeles G. Fiksel, D. Den Hatog, S.C. Page, J.S. Saff Univesity of Wisconsin, Madison D. Caig Wheaton College, Wheaton, IL TTF Mach 27, 2008oulde, CO

2 Motivation Undestanding of density elaxation due to magnetic fluctuations (1) How does magnetic fluctuation cause electon (and ion) paticle tanspot? (2) What is ion paticle diffusivity in MHD appoximation?

3 Electon Density Relaxation Due to Stochastic Field MST n e () [10 19 m "3 ] DIII-D? Stochastic Magnetic Field L.Zeng (UCLA) et al DIII-D by eflectomety Diven by Teaing Instabilities in MST Diven by I-coil extenally in DIII-D

4 Stochastic Magnetic Fields Punctue Field Line Plot Punctue of Field Plot in MST DIII-D field with I-Coil Tooidal Angle / π /a Calculation(DES) +Exp R.Moye--Eo field wokshop 2007 Vacuum Field Calculation

5 Paticle Flux due to Stochastic Magnetic Fields " =< " // b e Paticle tanspot aises fom paticle steaming along stochastic field lines " // = " // + b = 0 + b " // Fluctuation-induced paticle flux " = < " // b 0 " // = n u // + n u // < n b " = u // + n < u // b 0 0

6 Outline Expeimental Measuement: (1) Stochastic Field Induced Paticle Tanspot and Electon Density Relaxation on MST; < n b " = u // + n < u // b 0 Fo both electon and ion 0 "n e "t (2) Discussion on oigin of ion velocity u //

7 Madison Symmetic Tous MST Revesed-Field Pinch (RFP) is tooidal configuation with elatively weak tooidal magnetic field T ( i.e., T ~ p) q() = T <1 R P R0 = 1.5 m, a = 0.51 m, Ip < 600 ka T ~ 3-4 kg, ne ~ 1019 m-3, Te0 < 1.3 kev τe ~ 10 ms, β =<p/2(a)=15%!

8 Effects of Fluctuations on Tanspot in the RFP Magnetic econnection events Geneation / manipulation of magnetic flux (dynamo) Paticle and enegy tanspot Ion heating Momentum tanspot

9 FIR Polaimete-Intefeomete System " ~ # ndl + # n dl # $ ~ n d l + # n b d l + # n d l MST Intefeomete Faaday otation density magnetic field 11 chods, space sepaation 8 cm

10 Measuement of magnetic fluctuation induced tanspot flux < n " e = u e b //,e + n < u //,eb V //,e, Lase Faaday otation J = " # V //,e " J // n e e b () Lase Faaday otation measues n e () Lase intefeomete ( ) " n e u i Ion Dopple Spectoscopy (IDS)

11 Density Gadient Measuement by Diffeential Intefeomete ω 1 ω 2 Lase1 (pobe) Lase 2 (pobe) δ plasma eam diamete ~1 cm Δx~ 1.2 mm Ref.mixe Δx z ω 3 Lase 3 (LO) " x Sig.mixe Phase (ω 1 ω 3 ) Phase (ω 1 ω 2 ) n e (x) = 1 L #n e (x) #x = 1 L $x =1 mm " n e()dz, 2 = x 2 + z 2 x " x #n e () # x dz

12 Localization of Density Fluctuations (1) Fo mean density "n e (x) "x = 1 L # "n e () " cos$dz x % "n e() " & (0.3 ' 0.5) fo x ( x=2 cm x=21 cm (2) Fo density fluctuations (m=1) Z (cm) 0 " = $ n e ()cos# dz Z " (x) # n e ()L $ (0.3 % 0.5) x & cos" = x 0.2 z cos(!) x

13 Measuement of tanspot by Faaday otation and intefeomete! J 0 [MA/m 2 ] n e0 [10 19 m -3 ] V e,// [10 6 m/s] Time [ms] Time [ms] Time [ms] V //,e = J 0 en e 0 " # = V //,e " < n eb! < n " = V e b //,e $ 2V //,e (a) /a b b! (< b % % n % e + < n e b ) %

14 80 Electon Paticle Flux and Ion Flux at /a<0.2 < n b " e = u //,e 0 + n < u //,eb 0 " < n b " i = u //,i 0 + n < u //,ib 0? (1) (2) (3) (4)! e [10 19 m -2 s -1 ] [10 19 m "2 s "1 ] n < u //,ib time [ms] Chage flux measuement " q = " i # " e = < j // b e $ 1 e R n ( k ) < 1 b % % b & $ 0 (1) Electon convective flux is significant (2) Ion convective flux is negligible and pinch flux is significant

15 Density Change is alanced by Paticle Tanspot [10 22 m -3 s -1 ] Time [ms] 2.0 " < n e "t " < n e "t # $ % + # $ % 0 n e (0) [10 13 cm -3 ] < n e " % # $ dt Time [ms] Flux includes multiple dominant mode contibution (n=6,7,8,9)!

16 Oigin of Paallel Ion Fluctuations Den Hatog et al, PoP 1999 u // u // ~ " #u // The advection of mean paallel velocity is a potential souce of paallel velocity fluctuations

17 Estimation of paallel velocity fluctuations! [cm] " = #n $n m/n=1/ time [ms] Estimated fluctuation amplitude is less than the measued 20km/s u // ~ u " // a ~ 3 [km /s] If u // " 0, u // " 0, # i = n < u // b " 0 0 Which is not consistent with density elaxation even if plasma has no otation

18 Othe souce of paallel ion velocity fluctuations? " # V #t + "( V $) V + µ$ 2 V = J % " # u // #t + µ $ % 2 u // = ( J & ) // + (J & ) // J = J // + J " = b // + b " + b (J " ) // = J # " b = $ %p f = " #p b b Fluctuating toque

19 Paallel Ion velocity fluctuations diven by fluctuating toque " # u // #t + µ $ % 2 u // = & %p "p = T"n + n"t = T(1+ L n L T )"n Estimate paallel ion velocity at cash phase b L n "1 = 1 n L T "1 = 1 T L n ~ L T, T = T i + T e " 700eV, #n "1$10 19 m %4 #n # #T # b =1.0 "10#2,$ = nm = 3.34 "10 #8 kg /m 3,%t =100µs " u // ~ 67 [km /s] Fo m=1,n=6 mode

20 Ion paticle flux in steady state Estimate flow fluctuations away sawtooth cash " # u // = 0 #t " # $ 2 u // = % $p & u // = " 1 Z eff b # ii %p ($ i k ) 2 $ b 2 $ " # ~ Z i eff % ii & 2 ~ k 2, If (" i k ) 2 ~ 1 k ~ 2" w u // ~ 5 [km /s]

21 Paticle Diffusivity due to Stochastic Field In steady state o away sawtooth cash u // = " " # u // #t = 0 # ii %p ($ i k ) 2 $ b " # $ 2 u // = % $p & b " # ~ $ 2 i % ii & 2 ~ k 2, " i = n < u // b = # $ ii (% i k ) (1+ L & n b ) ( 2 L T ' ) + * 2 c s 2,n = #D i,n 1 D i = (" i k ) (1+ L $ n b ' )# 2 m & ) L T % ( 2 " c b % s R-R theoy D ~ l c $ ' # & 2 v i

22 Compaison between Heat and Paticle Diffusivity 1 D i = (" i k # ) (1+ L % n b ( )$ 2 mfp ' * L T & ) $ 2c " RR e # l c s & % b ' ) ( 2 v e " e RR D i = M m e l c 1 ($ i k) 2 # mfp 1+ L n L T Recheste-Rosenbluth QL theoy RR " e " = M = 43 RR i m e " e ~ 300 [m 2 /s] D e ~ 137 [m 2 /s] Fom powe balance in a steady state " e ~ 5.50 #10 19 [m -2 s -1 ],$n ~ 4 #10 17 [m %4 ], D e = " e $n e Electon heat diffusivity is compaable to paticle diffusivity " e mst D e mst ~ 2

23 Fo typical MST paametes 1 D i = Z eff (" i k ) (1+ L $ n b ' )# 2 mfp & ) L T % ( 2 c s * (" i k ) 2 [m2 /s] D e [m 2 /s] D e = " e < n b, " e = u //,e #n e time [ms] D i = D e " i k ~ (0.5 #1) A few cm scale velocity fluctuation is needed to explain obseved ion paticle flux.

24 Summay (1) Convective electon paticle flux can account fo electon density elaxation; (2) Fluctuating toque can dive paallel ion velocity fluctuations and paticle flux " #p (3) The atio of heat tanspot to paticle tanspot can depend on magnetic fluctuations chaacteistics, not only mass atio. b