Magnetic Fluctuation-Induced Particle Transport. and Zonal Flow Generation in MST

Transcription

1 Magnetic Fluctuation-Induced Paticle Tanspot and Zonal Flow Geneation in MST D.L. Bowe Weixing Ding, B.H. Deng Univesity of Califonia, Los Angeles, USA D. Caig, G. Fiksel, V. Minov, S.C. Page, J. Saff Univesity of Wisconsin-Madison, Madison, Wisconsin, USA 4-7 Septembe 26 Maseille, Fance

2 Intoduction Magnetic and Cuent Density fluctuations play an impotant ole in plasma elaxation in the Revesed Field Pinch as well as tokamak configuations E T J // () δb, δj Hall Dynamo Momentum Tanspot < δj δb ne < δj δb Magnetic Reconnection All pocesses coupled though δj and nonlinea mode inteactions Paticle Tanspot - Maxwell Stess < δj // eb < 1 b b θ

3 q Pofile and Coe Magnetic Fluctuation Spectum.3.2 T e ~ T i ~ 5 ev t=-.25 ms 8 Teaing Modes standad 4ka ppcd 4ka q= RB T q.1 B P /6 1/7 1/8 1/9 (,1) P(f) [Gs 2 /khz] magnetic tubulence ρ (m) f [khz] 8 Teaing modes and boadband magnetic tubulence

4 Magnetic Fluctuation-Diven Paticle Flux Fluctuation-Induced flux Γ i,e = Γ es + Γ em = < n E e i,e i,e B ± < j // i,e eb Γ em i = < j // i eb Γ em e = < j // e eb Electostatic Magnetic non ambipola flux : Γ q = Γ i Γ e = Radial Chage Tanspot j = eγ q j eb

5 Fast polaimete measues coe mean and fluctuating B & J Faaday otation angle 11-chod FIR lase + Ψ ~ nb dl δψ = c F n δb d l + c F 32 magnetic coils tooidal aay δψ c F Faaday Rotation [deg.] δβ (a) n δb d l ~ δnb d l m=1 activity cash 25. Time [ms] δb = 33 [Gauss] x=-17 cm extenal magnetic coil 26.

6 Cuent Fluctuation Measuement Method Ampee's Law : L δb d l = µ δi Faaday Rotation Fluctuation: δψ = c F n δb d l c F n δb d l L δ B d l δb z dz µ δi φ = δψ 1 δψ 2 c F n dz [ ] [ δb ] z x1 x 2 Plasma δi X 1 X 2 Loop between polaimete chods is equivalent to a Rogowski coil measuement Ding, Bowe et al. PRL (23) z x

7 Measued Magnetic and Cuent Density Fluctuation Pofiles δj φ [A/cm 2 ] [Gs] 5 δj ϕ J ~ 6% Time [ms] δb B ~ 1% /a b θ.8 1. [ka/m 2 ] suges at sawtooth cash spatially localized in coe, peaks at esonant suface.4 /a = q(1,6) (m,n)=(1,6) teaing mode w=8 cm s =17 cm

8 Measued Chage Flux at sawtooth cash in MST Γ q = < j // eb whee = 1 eb δb = µ δj R nb ( k B ) < 1 and 1 < 1 µ b θ = 1 < j φ b µ b b θ = 1 eb 1. B T B (1- m nq() ) < j φ s s <<1 and... denotes flux suface aveage Γ q =<δ j // δ /eb 16 Maxwell Stess.5 N/m Γ q [1 2 /m 2 s] Γ Γ q 1% Paticle [m] [m].4.5 Chage flux is adially localized and changes sign acoss esonant suface

9 E = Chage Tanspot and Radial Electic Field ρ t + J =, E = ρ ε < j // dt ε B < j // B ε E t = e(γ i Γ e ) 1~4 [A/m 2 ] at the coe (FIR Faaday) Leads to a huge electic field, ~5 MV/m in coe Howeve, shielding occus due to ion polaization cuent ρ t + J =, E = ε ε E t = < j // B ρ ε ε ε =1+ ( c V A ) 2 E = 1 1+ c 2 V A 2 < j // dt V A ε B c 2 < j // dt ε B At econnection, a adial electic field is established due to non-ambipola tanspot, but electic field is educed by 1 4 due to shielding by the ion polaization dift.

10 Localized Radial Electic Field and ExB Flow 1 electic field pofile 1 ExB flow pofile 5 5 E [ kv/m] km/s [m] Chage flux geneates a local E with spatial scale ~5 cm that changes sign acoss esonant suface [m].4.5 (1) ExB geneates flow and flow shea (which may stongly damp the mean flow) (2) Flow is tooidally and poloidally symmetic (m=,n=) zonal flow diven by esistive teaing modes

11 Summay Measuements indicate the following coupled elaxations: Loentz foce <δjxδb Hall dynamo on electons Cuent elaxation (electon velocity) Maxwell Stess (mode coupling) Toque on ions Ion foce balance Momentum elaxation (ion velocity) Teaing mode J // ( ) δ B, δj Ion viscous damping Chage Tanspot <δj // Electic Field and Flow shea Zonal flow

12 Evidence of potential stuctue? Potential measuement by Heavy Ion Beam Pobe (HIBP) Lei,J, et al, PRL, 89,2751(22)

13 Possible Effect of Electical Field on Plasmas (Open Questions) φ φ [V] 2 1 A potential well is fomed nea the econnection laye -1-2 Questions not clea to me: -3. V id [m].4 V id.5 (1) Whee does electic field enegy come fom? (2) Do ions and electons gain enegy fom the field? V e V e (3) Whee does flow enegy go?

14 Momentum tanspot and nonlinea toque 1 <δjx δb // with k 3 (m=,n=1) without k 3 (m=,n=1) [N/m 3 ] 5 V φ [km/s] Time [ms] with k 3 (m=,n=1) without k 3 (m=,n=1) k 1 ± k 2 = k = Time [ms] <δjxδb and chage tanspot obseved when thee modes ae coupled.

15 Dynamics of Radial Electic Field ove Sawtooth E [kv/m] E ~ ( V A c )2 eγ q dt Electic Field Chage Flux eγ q [A/m 2 ] Time [ms] What dissipates the electic field o dissipates ExB flow afte the sawtooth cash??

16 Pependicula Momentum Balance Equation ρ V E B B t µ * B 2 V E B = < j // B ρ is mass density and µ is the classical viscosity coefficient ρ E B 2 t µ * B 2 E 2 = < j // B ion viscosity µ * = 3nkT i 1ω 2 ci τ i Γ x i Γ x e =< j z B x eb + c eb x P xys = 1 E x 4πe t + n i m i c 2 eb 2 E x t See: R. E.Waltz, Phys. Fluids, 25,1269(1982); ε (1+ ( c ) 2 ) E V A t ε ( c E ) 2 V A t = < j // B + µ * 2 V E B B

17 Electic Field Dynamics (with Collisional Dissipation) E [kv/m] Chage Flux Radial Electic Field Radial Electic Field w/o dissipation Time [ms] eγ q [A/m 2 ] E [kv/m] t=.1 ms t=1.65 ms t=3 ms /a.8 1.

18 (4)Effect of mode-mode inteaction on <δjxδb foce <δjxδb foce and chage tanspot esult fom nonlinea mode-mode inteaction.3.2 k 1 k 2 s k B = t=-.25 (esonant ms suface) q = R B T q.1 1/6 1/7 1/8 1/9 k 3 B P. (,1) ρ (m).3 k 1 ± k 2 = k 3.4.5

19 Madison Symmetic Tous (MST) (Madison, Wisconsin) MST Revesed-Field Pinch (RFP) is tooidal configuation with elatively weak tooidal magnetic field B T ( i.e., B T ~ B p ) q() = R B T B P <1 R = 1.5 m, a =.51 m, I p < 6 ka B T ~ 3-4 kg, n e ~ 1 19 m -3, T e < 1.3 kev τ E ~ 1 ms, β =<p/b 2 (a)=15%

20 Measued Coe Magnetic Fluctuations by Faaday otation Faaday Rotation [deg.] δβ (a) (1,6) mode 24.5 m=1 activity x=-17 cm cash 21 extenal magnetic coil Time [ms] Faaday Rotation : Ψ=c F nb d l Ψ=Ψ +δψ, B = B +δb, n=n +δn δψ=c F n δb d l +c F c F c F δnb d l n B z dz=c F n B θ cosθdz (µ J() 2 ) x n dz δψ c F µ =c J() F 2 x n dz n δb d l δb = 33 [Gauss]

21 (1) Measued Cuent Pofile Relaxation 2 At cash, cuent pofile flattens 15 ~ 1 µs J (,t) [A/cm 2 ] /a Time (ms) 2. 6 At cash, electic field inceases E T 4 E ϕ [V/m] 2 [V/m] E // E T () = V L 2πR a B P (,t)d t Time [ms] E // ηj // Bowe, Ding, et al PRL,88,1855(22)

22 Hall Dynamo is balanced by Inducted Electic Field η // <J // =<E // +<δ v δ B // <δ J δ B // /n e e Paallel Mean Field Ohm s Law fom 2-Fluid Theoy MHD dynamo Hall Dynamo < δj δb // n e e B p B T (1+ ( B T B p ) 2 ) < δj φ E // <δjxδb // /ne 1.7 V/m.5 V/m Time [ms] [V/m] < δjxδb // /n e e.4 /a.8 Ding, Bowe, et al PRL,93,452(24)

23 Ion Momentum (Toque) ove Sawtooth Cash 1 N/m <δjx δb // ρ< dv/dt // Huge Imbalance!! Time [ms] 2 V < ρ V t // +ρ < V V // = < δj δb // +µ * < 2 V // δv 1 km/s ~ 5 N/m 3 ~ 6 N/m 3 1 cm ρ < V V 3 N/m 3 µ V a 2 ~ 1 2 ~ 1-3 N/m 3 Classical dissipation

24 Ion Momentum Tanspot ove Sawtooth Cash V φ [km/s] Time [ms] At sawtooth cash ion momentum in the coe dops much faste than classical viscous time.

25 Fluctuation-Induced Radial Chage Flux Γ q = < j // eb = < j //,i eb < j //,e eb chage flux On MST fo a specified (m,n) mode < j // =< ( B j P θ B + B j T φ B ) b δb = µ δj = R nb ( k B ) < 1 k B = m s B θ + n R B φ b b θ = R nb ( k B ) < j φ s <<1 s At mode esonant suface chage flux is zeo, but can be non-zeo locally (nea the esonant suface) to fom chage filamentation * * R.E. Waltz, Phys.Fluid,25,1269(1982)

26 Phase between cuent and magnetic fluctuation < δj φ ( s )δ ( s ) = δj φ ( s ) δ ( s ) cos = ph _δj φ ( s ) ph _δ ( s ) = ph _δj φ ( s ) ph _δ (a) Pependicula global magnetic fluctuation has a constant phase Time [ms]

27 Magnetic Fluctuation Spectum 8 Teaing Modes standad 4ka ppcd 4ka P(f) [Gs 2 /khz] 6 4 magnetic tubulence noise f [khz] 6 8 Teaing modes and boadband magnetic tubulence

28 RFP Safety Facto Pofile.3 T e ~ T i ~ 5 ev t=-.25 ms.2 q = R B T q.1 1/6 1/7 1/8 1/9 B P. (,1) ρ (m).3.4.5

29 Chage Tanspot and Radial Electic Field ρ t + J =, E = ρ ε ε E t = e(γ i Γ e ) < j // B 1~(-12) [A/m 2 ] at the edge (pobe, Neal Cocke, 21) 1~4 [A/m 2 ] at the coe (FIR Faaday) If Chage flux induced only by magnetic fluctuation E = < j // dt ε B 56 [MV/m]~6.7 [GV/m] at the edge ( dt=.5ms) T e /a 56 ~224 [MV/m] at the coe (dt=.5ms) T e /a

30 Ion Polaization Dift ρ t + J =, E = ε ε E t = < j // B ρ ε ε See: R. E.Waltz, Phys. Fluids, 25,1269(1982); K.Itoh and S. Itoh, Plasma Phys. Contol Fusion,38,1(1996). ε =1+ ( c V A ) 2 E = 1 1+ c 2 V A 2 Due to ion polaization cuent < j // dt V A ε B c 2 < j // dt ε B At econnection, a adial electic field is established due to non-ambipola tanspot, but electic field is educed by 1 4 due to shielding by the ion polaization dift.

31 Motivation Magnetic fluctuations play an impotant ole in magnetic econnection in the laboatoy plasma and astophysical plasmas Magnetic Reconnection E T J // () δb, δj Paticle and Enegy Tanspot η // <J // =<E // +<δ v δ B // <δ J δ B // /n e e MHD dynamo Hall Dynamo

32 Outline (1) Hall Dynamo: (2) Ion Momentum Balance: < δj δb ne < δj δb (3) Magnetic Fluctuation-Induced Paticle Tanspot; - Maxwell Stess < 1 b b θ < δj // eb All thee pocesses ae coupled though cuent density fluctuations (4) Nonlinea mode-mode inteaction Identify the ole of magnetic and cuent density fluctuations in paticle and momentum tanspot