Current Profile Control by ac Helicity Injection

Transcription

1 Current Profile Control by ac Helicity Injection Fatima Ebrahimi and S. C. Prager University of Wisconsin- Madison APS 2003

2 Motivations Helicity injection is a method to drive current in plasmas in which the current distribution relaxes by internal processes. dc and ac helicity injection can be used for steady-state current sustainment using 3-D MHD computations two key questions can be addressed what is the effectiveness of current drive by ac helicity injection? Can current be sustained? what is the effect of ac helicity injection on plasma fluctuations? controlling the current profile to suppress fluctuation amplitudes UW-Madison Slide 2

3 Magnetic helicity injection Magnetic helicity, K = A Bdv φ z φ p a measure of the knottedness of the magnetic field lines The rate of change of magnetic helicity is K t = 2φ zv {z z } 2 Z ΦB ds {z } 2 Z ηj Bdv {z } inductive injection electrostatic injection dissipation or ac injection UW-Madison Slide 3

4 Helicity is injected steadily by oscillating toroidal and poloidal surface voltages ac helicity injection In steady state = φ z v z = η J. Bdv Helicity injection rate = φ z0 v }{{ z0 } + ˆv zˆv θ sin(δ) } 2ω {{} ohmic ac injection ω φ (ω +π/2) θ Bevir and Gray (1981) UW-Madison Slide 4

5 Low power experiments A small amount of current was driven in ZT40-M RFP F Θ pumping (OFCD) [Schoenberg et al.(1988)] 450 Drive Off Anti-drive 400 Blair, McCollam and Sarff I p (ka) 350 = MST Time (ms) UW-Madison Slide 5

6 Ac helicity injection relies on current relaxation by magnetic fluctuations E + < Ṽmn B mn > + (V 00 B 00 ) = ηj = [E 00 B]/B 2 unstable edge-driven current = (V 00 B 00 ) from the axisymmetric oscillations generates fluctuations MHD fluctuations relax the current in the plasma core = < Ṽ B > The dynamo term from the non-axisymmetric fluctuations UW-Madison Slide 6

7 Magnetic fluctuations distribute the current < e V e B > +E = ηj tearing dynamo The tearing modes transfer current from the core to the edge. UW-Madison Slide 7

8 ac helicity injection sustains the current and helicity (S = 10 5 ) To replace ohmic helicity with ac helicity, oscillating fields are imposed on the relaxed plasma in the absence of time-independent axial electric field (E Z (a) = 0 ). E(a) = 0 z τ ω = τ A UW-Madison Slide 8

9 The current oscillations are reduced at higher S Axial current (S = ) The current oscillation decreases to about 50% at S = Assuming a relaxed state plasma with a stationary J /B profile, bi z /I z S 1/4 ω 1/2 H ξ1/2 (R/a) 1/2 F. Ebrahimi, S. C. Prager, J. S. Sarff, and J. C. Wright, Phys. Plasmas , 2003 UW-Madison Slide 9

10 The tearing fluctuations transfer current from the edge to the core < e V e B > (V 00 B 00 ) The core current is sustained by the tearing dynamo. The (V 00 B 00 ) term from symmetric oscillations drives only an edge current. UW-Madison Slide 10

11 Edge-resonant modes are excited. core-resonant m=1, n=-3 The edge-resonant modes (resonant outside reversal surface) are excited as the reversal deepens through a cycle. edge-resonant m=1, n=2 UW-Madison Slide 11

12 Fluctuations increase mainly because of the growth of the edge-resonant mode Modal magnetic energy W m,n = 1/2 R B 2 r(m,n)d 3 r The global m=1, n=+2 edge-resonant mode has the largest amplitude. The core-resonant tearing modes are not increased significantly. UW-Madison Slide 12

13 The growth of edge mode is a linear instability linear growth m = 1, n = +2 (linear terms) During the sudden growth phase, the volume integral of the LHS and RHS are equal. 1 2 B 2 1 t = SB 1[(B 0 )V 1 (V 1 )B 0 ] +nonlinear terms }{{} linear terms UW-Madison Slide 13

14 Current profile control via ac helicity injection -combining standard RFP with partial OFCD- UW-Madison Slide 14

15 Motivations In conventional RFP Current is driven by toroidal inductive electric field Edge magnetic field is dominantly poloidal ==> large gradient in ll E To control current profile and suppress magnetic fluctuations PPCD parallel inductive electric field Non inductive RF current drive Free energy from current gradient ==> tearing fluctuations AC helicity injection UW-Madison Slide 15

16 Oscillating poloidal electric field (OPCD) does not lead to a reduction in the time-averaged fluctuation level. regular sawtooth oscillations with the OPCD period standard OPCD (1,-4) (1,-3) (0,1) Modal magnetic energies are reduced during part of the cycle and are enhanced during the other part. No reduction of B/B in both OPCD and OTCD. UW-Madison Slide 16

17 OPCD does affect the radial profiles during a cycle. edge-drive anti-edge drive during edge drive during anti-edge drive E modify the current density toward a more stable profile (E > 0), and a more unstable profile (when E < 0) UW-Madison Slide 17

18 Partial sustainment by ac helicity injection suppresses the total magnetic fluctuation level. The total magnetic fluctuation level (rms( e B/B)) is reduced by a factor of UW-Madison Slide 18

19 Current driven by axisymmetric oscillations modifies the current density profile. E + S(V 00 B 00 ) {z } + S < e V e B > = ηj (E 00 B 00 )/B ωτ H < 1 In OFCD, a more favorable parallel electric field results which causes the reduction of magnetic fluctuations for most part of the cycle. UW-Madison Slide 19

20 Tearing mode amplitudes become zero in OFCD Standard OFCD UW-Madison Slide 20

21 OFCD flattens the current density profile in the core. at the highest fluctuations dynamo free E < 0 E > 0 The dynamo relaxes current from the core to the edge in the ejection phase similar to standard case. Current is mainly sustained by E during the injection phase. UW-Madison Slide 21

22 Stochasticity of the magnetic field lines t1 - stochastic UW-Madison t2 - ordered t3 - single helicity Slide 22

23 High-S standard RFP computation Motivation the effect of high Lundquist numbers study the dynamics of sawtooth oscillations and m=0 modes provide a benchmark with OFCD plasmas UW-Madison Slide 23

24 The dynamo relaxation occurs during the sawtooth crash. m=1, n= 6 m=1, n= 7 m=0, n=1 the growth of low-n core m=1 modes (resistive diffusion phase) the transfer of energy to high-n m=1 modes and m=0 modes (the sawtooth crash) UW-Madison Slide 24

25 The sawtooth oscillations are not observed without m=0 modes. field reversal total magnetic fluctuation without m=0 without m=0 with m=0 with m=0 the plasma settles into a steady-state with a weak reversal. the transfer of energy from m=1 to m=0 modes can not occur (no crash phase). UW-Madison Slide 25

26 Conclusions Plasma current is sustained steadily through ac helicity injection in the absence of a dc electric field. Plasma fluctuations increase with ac helicity injection; however the increase is concentrated mainly in a global mode that is nearly ideal. This instability is suppressed in high S plasma where q oscillations near the plasma edge are reduced. Partial sustainment by ac helicity injection suppresses the total magnetic fluctuation level. The future work would be the optimization of the time dependency of the oscillating fields. UW-Madison Slide 26