1. Control of Magnetic Chaos & Self-Organization John Sarff for MST Group CMSO General Meeting Madison, WI August 4-6, 2004

2. Plasma control permits adjustment of magnetic reconnection and self-organization processes in the RFP. r / ar / a Toroidal, r / ar / a Adjust Current Drive Example: Reduce tearing fluctuations and magnetic chaos by current profile control.

3. Outline. Control MHD tearing and consequent relaxation processes by: Adjustments to inductive current drive –Reduce tearing by matching E(r) to more stable J(r) –AC helicity injection (oscillating loop voltages) Adjustment of mean-field B(r) to include/exclude resonant surfaces Tuning for empirically different resonant mode spectra, e.g., quasi-single-helicity (QSH) Other control techniques used previously: – electrostatic probe biasing (edge current drive & rotation control) – helical magnetic perturbations from external coils

4. Outline. Control MHD tearing and consequent relaxation processes by: Adjustments to inductive current drive –Reduce tearing by matching E(r) to more stable J(r) –AC helicity injection (oscillating loop voltages) Adjustment of mean-field B(r) to include/exclude resonant surfaces Tuning for empirically different resonant mode spectra, e.g., quasi-single-helicity (QSH) Other control techniques used previously: – electrostatic probe biasing (edge current drive & rotation control) – helical magnetic perturbations from external coils

5. Magnetic reconnection (resonant tearing) occurs at many radii in the RFPs sheared magnetic field. RFP Magnetic Geometry Tearing resonance:

6. Standard induction produces a peaked current profile, unstable to MHD tearing (free energy r J || /B ). Standard RFP Ohms law imbalance characteristic of steady induction in the RFP

7. Standard induction produces a peaked current profile, unstable to MHD tearing (free energy r J || /B ). Standard RFP Ohms law imbalance characteristic of steady induction in the RFP multiple dynamo-like effects possible (several observed)

8. Poloidal inductive current drive targeted to outer region reduces MHD tearing instability. Measured E(r) Profiles Pulsed Poloidal Current Drive (PPCD) @15 ms

9. Magnetic fluctuations reduced at all scales & frequencies. Long wavelength amplitude spectrum Frequency (kHz) (T 2 /Hz) Frequency power spectrum PPCD Standard Toroidal Mode, n

10. Dynamo essentially absent with PPCD. PPCDStandard RFP Simple Ohms law satisfied strong dynamoweak dynamo (simple Ohms law satisfied)

11. Electron T e and energy confinement increase. PPCD

12. Stochastic magnetic diffusivity and heat transport reduced 30-fold in core. (m 2 /s) r/a field line tracing where magnetic chaos is strong (several overlapping islands) measured predicted Rechester-Rosenbluth PPCD Standard R-R

13. Anomalous ion heating probably reduced. T i (r) Profiles Standard: P e-i < P CX and T i / T e ~ 1 anomalous ion heating must occur PPCD: P e-i P CX and T i / T e ~ 0.5 collisional ion heating only?? PPCD

14. Anomalous ion heating probably reduced. T i (r) Profiles Standard: P e-i < P CX and T i / T e ~ 1 anomalous ion heating must occur PPCD: P e-i P CX and T i / T e ~ 0.5 collisional ion heating only?? PPCD

15. Outline. Control MHD tearing and consequent relaxation processes by: Adjustments to inductive current drive –Reduce tearing by matching E(r) to more stable J(r) –AC helicity injection (oscillating loop voltages) Adjustment of mean-field B(r) to include/exclude resonant surfaces Tuning for empirically different resonant mode spectra, e.g., quasi-single-helicity (QSH) Other control techniques used previously: – electrostatic probe biasing (edge current drive & rotation control) – helical magnetic perturbations from external coils

16. Nonlinear mode coupling appears important for anomalous momentum transport. Nonlinear torque: force on n=6 (plasma rotation)

17. Adjusting B(r) to exclude m = 0 resonance greatly reduces momentum loss & ion heating during relaxation events. Shift q > 0 to remove m = 0 resonance

18. Adjusting B(r) to exclude m = 0 resonance greatly reduces momentum loss & ion heating during relaxation events. No sudden rotation loss with small m = 0

19. Outline. Control MHD tearing and consequent relaxation processes by: Adjustments to inductive current drive –Reduce tearing by matching E(r) to more stable J(r) –AC helicity injection (oscillating loop voltages) Adjustment of mean-field B(r) to include/exclude resonant surfaces Tuning for empirically different resonant mode spectra, e.g., quasi-single-helicity (QSH) Other control techniques used previously: – electrostatic probe biasing (edge current drive & rotation control) – helical magnetic perturbations from external coils

20. Under come conditions, the tearing spectrum is dominated by one mode. MST RFX Soft x-ray image Spontaneous Quasi-Single Helicity (QSH)

21. Magnetic & velocity fluctuations are single-mode dominated. (mT) (km/s) QSHStandard QSHStandard

22. MHD dynamo is single-mode dominated in QSH. (V/m) QSH Standard

23. Outline. Control MHD tearing and consequent relaxation processes by: Adjustments to inductive current drive –Reduce tearing by matching E(r) to more stable J(r) –AC helicity injection (oscillating loop voltages) Adjustment of mean-field B(r) to include/exclude resonant surfaces Tuning for empirically different resonant mode spectra, e.g., quasi-single-helicity (QSH) Other control techniques used previously: – electrostatic probe biasing (edge current drive & rotation control) – helical magnetic perturbations from external coils

24. AC helicity injection using oscillating loop voltages. apply oscillating V Magnetic helicity balance evolution: (Standard RFP: V, = constant)

25. AC helicity injection using oscillating loop voltages. apply oscillating V Magnetic helicity balance evolution: (Standard RFP: V, = constant)

26. MHD behavior is altered when AC loop voltage applied. Time (ms) AC volts on relaxation events entrained (V) (G) m = 0 m = 1 increase between crash

27. Between-crash heating should help identify anomalous ion heating mechanism. sawtooth crash smaller heating at applied frequency

28. Summary. Several methods to control and adjust MHD tearing-reconnection have been developed for the RFP. Characteristics and strength of consequent relaxation processes are adjustable. MSTs CMSO plans systematically include PPCD, q > 0, OFCD, etc. as tools to expose underlying physics.

29. Tearing occurs spontaneously, both from linear instability and nonlinear mode coupling. Core-resonant m=1 modes are largest, calculated to be linearly unstable from. Edge-resonant m=0 modes grow from nonlinear coupling to the unstable m=1 modes.