Density Fluctuation Induced Kinetic Dynamo and Nonlinear Tearing Mode Saturation in the MST Reversed Field Pinch

Transcription

1 Density Fluctuation Induced Kinetic Dynamo and Nonlinear Tearing Mode Saturation in the MST Reversed Field Pinch W.X.Ding, L. Lin, D.L. Brower, A. Almagri, B. Chapman, G. Fiksel, D.J. Den Hartog, J. Reusch, J.S. Sarff, V. Mirnov and the MST Group Department of Physics & Astronomy, University of California Los Angeles Department of Physics, University of Wisconsin, Madison Center for MagneMc Self- OrganizaMon in Laboratory and Astrophysical Plasmas, University of Wisconsin, Madison

2 Introduction 1. On MST reversed field pinch, plasma current is simultaneously self generated from fluctuating magnetic fields known as dynamo to sustain plasma discharge longer than the resistive decay time. 2. Kinetic dynamo is the correlated product of parallel pressure fluctuations and radial magnetic fluctuations, which is very attractive to future RFP devices where resistive MHD processes may not be effective to sustain magnetic field reversal configuration. 3. Density fluctuation induced kinetic dynamo is observed to account for, at least partially, the imbalance of Ohm s law on MST

3 Fluctua*on- Induced Current and Momentum Transport Hall Dynamo MHD Dynamo " $ <!! j!! b! > # %$ <! v!!! b! > Kinetic Dynamo '!! 2!b r $ ) skinl c # & " B % ( ) <! p //,e!b r > *) B 2 E T J // (r)" Free Energy!! B,!! V!n,!T " Current transport/ Ohm s law" " Momentum transport" "" MHD Effects! <!! b! b! > " # <!! v! v! > Kinetic Effects ) + * +, + l c # % $ "b r B & ( ' 2 < "p // "b r > B

4 Madison Symmetric Torus - MST MST Reversed- Field Pinch (RFP) is toroidal configura;on with rela;vely weak toroidal magne;c field BT ( i.e., BT ~ Bp) "" " # 6% For plasma w/o current profile control " " R0 = 1.5 m, a = 0.51 m, Ip ~400 ka "! " ne ~ 1019 m-3,te~ti~400ev" " "

5 Broadband Radial Magne*c Fluctua*on Spectrum 0.30 P(f) [Gs /khz] Tearing Modes # "b r dl standard 400ka ppcd 400ka magnetic turbulence /6 q=rb T /RB P 1/7 1/8 1/9 t=-0.25 ms (0,1) f [khz] 80 noise ! (m) Overlapping of magne/c islands lead to stochas/c magne/c field!!

6 Density fluctuation evolution correlates with magnetic fluctuations in MST Standard Discharge I=400 ka, n e =1 Magnetic mode 1/6 p13 p [Gs] [cm -2 ] [ms] Density fluctuation change across (1,6) magnetic island increases when the tearing mode saturates just prior to a sawtooth crash.

7 Measurement of Electron and ion current profile electrons V // [km/s] ions r/a r/a Imbalance between applied inductive electric field and measured electric current Imbalance between momentum input (zero) and measured ion flow plasma self- generates both electron current and ion current

8 Coupling between Current and Momentum Transport due to Magne*c Fluctua*ons in a torus Parallel Ohm s law can be obtained by mean field theory "!J //! E // =< " v! "" B! > //! < " J! "" B! > // +# < " p e,// "b r > /enb 0! µ T e.// # " # " J // +... MHD dynamo Hall dynamo Kinetic dynamo! Electron viscosity! Parallel momentum equation can be obtained by mean field theory "! " "t < V // >=< #! J!#! B > // "! < #! V ##! V > // "# < # p // #b r > /B + µ T # 2 < V // > +... Kinetic stress! Flow Change! Maxwell Stress! Reynolds Stress! Flow dissipation!

9 Kinetic dynamo-electron momentum transport in a stochastic magnetic field (non-fluid effect) Parallel pressure (or electron momentum flux) projected to the radial direc;on in a fluctua;ng magne;c field! = < p! e,// B e! r > B! p e,// = T e,.//!n + n e!t e,// A.R.Jacobson, R.W. Moses PR E (1984) S. Prager, PPCF (1995)! r = <! p e,//!b r > <!n = T e!b r > <!T e,.// + n e,//!b r > e B B B Radial electron Density fluctuamons! N! T momentum flux Fluid CGL derivation gives additional dynamo contribution from perpendicular pressure fluctuations (! p! ). See Poster PP , Den Hartog]

10 Mul*ple Diagnos*cs Enable Measurement of Flow, Kine*c Stress and Stochas*c magne*c field InvesMgate relamons between flow and fluctuamon- induced forces " # #t < V // > $ % ' ) T // ( < &n&b r > B 0 *, e! r D RR '&b ~ l r c + ( ) B * +, 2 V // B 0 Rutherford ScaNering, mode velocity, ion Doppler spectroscopy Mo;onal Stark effect+faraday rota;on "b r (r) Laser Faraday rota;on n "n!!n T //,i T //,e Laser (differen;al) interferometer ( ) Rutherford ScaNering (bulk deuterium ions), CHERS (impurity) Thomson scanering

11 FIR Laser Polarimeter- Interferometer System MST " ~ # ndl + # $ndl Interferometer # % ~ n r B d r l + # density fluctuamons n$ r b d r l + # $nb r d r l Faraday rotamon magnemc field fluctuamons 11 chords, Δx=8 cm, phase~ 1 degree, ;me response ~ 1 µs 32+8 magne;c coils toroidal- poloidal array (m,n) Ding, Brower, et al., PRL(2003),(2004),(2009), RSI(2004),(2008)

12 Space- Time Evolu*on of Fluctua*ons using combined interferometry and Faraday polarimetry "# $ % "n dl "# $ % "n B r o d r l + % n o " b r d r l m=1,n=6 2πR!" # n = $ <!n!b!" T r > ' & // ) % ( B 0

13 Typical Core Mode Density and Magne*c Fluctua*on Spa*al Profile (from fluctua*on fijng)!n [ m -2 ] [deg.] Exp fit [m] [m] Exp fit [m -3 ] Density fluctuamons profile Radial magnemc fluctuamons profile [G] Correlated product of fluctuamons is obtained from flux surface average m/n=1/6 m/n=1/ r/a r/a br (m/n=1/6) br (m/n=1/7) 1.0

14 Imbalance between electric field (E) and current (J) Ennis, PoP 2008!J //! E // =< " v! "" B! > //! < " J! "" B! > // +# < " p e,// "b r > /enb 0! µ T e.// # " # " J // +... Density fluctuation induced dynamo T e,// <!n!b r > neb + <!T e,//!b r > eb

15 Spatial profile of kinetic dynamo [V/m] E //! J // Kinetic dynamo sign and spatial profile is consistent with electric current direction [V/m] r/a Partial kinetic dynamo r/a 0.8 Dynamo < 0, Suppressing current Dynamo > 0 Driving current Measured kinetic dynamo in RFP plasmas implies that field reversal may arise from kinetic dynamo effect.! " N! N = T e,// <!n!b r > neb 0

16 Kinetic Dynamo and Ohm law r/a Kinetic Dynamo (V/m) E // -ηj // (V/m) Density fluctuation induced kinetic dynamo partially accounts for the imbalance between electric field and plasma current (assuming Z eff =4).

17 Parallel Electric Field vs Kinetic Dynamo Scaling I N! discharge current(ka) line density(10 13 cm "3 ) E // Kinetic dynamo! N = T e,// <!n!b r > neb 0 r / a! 4 Parallel electric field decreases with increasing kinetic dynamo (in the core) for different I/N, implies the reduction of current in the core. (c1 is approximately constant).

18 Magnetic Fluctuation Energy vs kinetic dynamo δb 2 I N! discharge current(ka) line density(10 13 cm "3 )! N = T e,// <!n!b r > neb 0 r / a! 4 Magnetic fluctuation energy (!! b p ) at wall decreases with n increasing kinetic dynamo, consistent with the reduction of electric field. Kinetic dynamo

19 Coupling between plasma flow and dynamo Kinetic effect acts on electron and ion due to finite plasma temperature Electron momentum E // ~!J // +! " n Ion momentum! " < V // > "t ~!" # n +!D ST " 2 < V // > Self-generated current and plasma flow are coupled through finite pressure effect. Flow increases with kinetic stress [PRL 2014,d Ding, et al.]

20 kinetic dynamo increases in NBI plasmas It is measured that anti-kinetic dynamo significantly increases from -3 V/m to V/m prior to EP mode burst, consistent with reduction of n=5 tearing. [Minus sign means the reduction of current in the plasma core.] See Poster PP for measurements by L. Lin in this meeting

21 Conclusion Kinetic dynamo (density fluctuation induced) plays an important role in the reversed field pinch, providing an attractive mechanism for future RFP devices to sustain current and transport particles. Kinetic dynamo (density fluctuation induced) plays a role in the reduction (saturation) of tearing mode. Electron temperature fluctuations may also play the role in the kinetic dynamo. [ see poster PP by D. Den Hartog]