1. Statistical Properties of Broadband Magnetic Turbulence in the Reversed Field Pinch John Sarff D. Craig, L. Frassinetti 1, L. Marrelli 1, P. Martin 1, P. Piovesan 1 1 Conzorzio RFX, Italy CMSO Workshop on Magnetic Turbulence Madison, WI June 20-21, 2005

2. Spectral structure and intermittency in RFP turbulence. 10 –4 10 –8 10 –12 P( n ) (T 2 ) 1 10100 Toroidal Mode, n ~ n –3/2 ~ n –5/3 Standard Reduced-Tearing Standard Reduced Tearing Marrelli et al., PoP 12, 2005

3. Outline. RFP basics and controllable conditions: –Standard RFP (strong relaxation) –Reduced-tearing RFP (weaker relaxation) Spectral structure: nonlinear cascade origin for high- k turbulence? Intermittency revealed in non-Gaussian and non-self similar statistics

4. Reversed Field Pinch (RFP). Toroidal, current-carrying Density, n ~ 10 13 cm –3 Temperature, T e,i ~ 1 keV B / B ~ 2% ( B 0.5 T) ~ MST

5. Standard RFP is self-organized, with a strong dynamo. Pronounced sawtooth events strong dynamo 0 0.20.40.6 0.8 1 r/a 2.0 1.5 1.0 0.5 0 –0.5 V/m E || neo J || 10 20 30 40 Time (ms) –10 0 10 (G) 0 600 (G) Toroidal Flux B ~

6. MHD tearing instability produces largest fluctuations. Tearing resonance: Toroidal Mode, n inner-most resonant mode m = 1, n = 6

7. Origin of fluctuations at high frequency, short wavelengths is not understood. 1 101001000 Frequency (kHz) 10 –4 10 –8 10 –12 P( f ) (T 2 /Hz) Frequency Power Spectrum tearing (plasma rotation)

8. Reduced tearing RFP is more stable (and less reliant on magnetic self organization). Controlled inductive current drive. 0 0.20.40.6 0.8 1 r/a 2.0 1.5 1.0 0.5 0 –0.5 V/m E || neo J || Toroidal Mode, n Reduced Tearing weak dynamo

9. Simultaneous reduction at all frequencies suggests high- k origin is connected to low- k tearing. 1 101001000 Frequency (kHz) 10 –4 10 –8 10 –12 P( f ) (T 2 /Hz) Standard Reduced Tearing Frequency Power Spectrum

10. Puzzling structure in the high- n toroidal mode spectrum. 10 –4 10 –8 10 –12 P( n ) (T 2 ) 1 10100 Toroidal Mode, n ~ n –3/2 ~ n –5/3 Inertial cascade? 2-pt spectrum: Wavenumber Power Spectra

11. Puzzling structure in the high- n toroidal mode spectrum. 10 –4 10 –8 10 –12 1 10100 0 300200 logsemi-log ~ n –3/2 ~ n –5/3 exponential Toroidal Mode, n Wavenumber Power Spectra P( n ) (T 2 )

12. Puzzling structure in the high- n toroidal mode spectrum. 10 –4 10 –8 10 –12 1 10100 0 300200 logsemi-log ~ n –3/2 ~ n –5/3 exponential Toroidal Mode, n Wavenumber Power Spectra P( n ) (T 2 ) Two possibilities: (1) Narrow inertial band, n ~ 10-70 (but note excess power n >100) (2) Dissipation scale, n 30 (but note R / i ~ 150)

13. Left and right propagating waves separated in 2-pt analysis. Issues: – radial correlation length – sheared rotation 10 –4 10 –8 10 –12 P( n ) (T 2 ) 0 300 Toroidal Mode, n –300 ion diamagnetic drift direction 1 10100 Toroidal Mode, n 10 –4 10 –8 10 –12 P( n ) (T 2 ) Spectral structure not left-right symmetric.

14. Turbulence exhibits temporal intermittency, partly associated with sawtooth cycle. 10 20 30 40 0 Time (ms) dB dt Reduced Tearing Period Standard Period

15. PDF of signal differences reveals non-Gaussian turbulence in standard RFP. Standard Signal differences: Probability Distributions

16. PDF of signal differences reveals non-Gaussian turbulence in standard RFP. Standard Reduced Tearing Signal differences: In contrast, turbulence in reduced-tearing RFP more nearly Gaussian Probability Distributions

17. Turbulence in not self-similar at different time scales. PDFs fit to stretched exponentials, characterized by shape parameter. Standard

18. But in the reduced tearing RFP, it is nearly self-similar. Standard Reduced Tearing

19. Analogous behavior observed in the electrostatic particle transport of standard RFP. V. Antonni et al., PRL 87, 045001 (2001) Particle flux is intermittent, correlated with flux-regeneration events. RFX reversed field pinch

20. Summary. Origin of high frequency, short wavelength magnetic turbulence appears connected to dominant MHD tearing instability. Spectral structure indicates two possibilites: 1)Narrow inertial range, probably requiring independent source at high- k 2) Dissipation scale near to unstable tearing enhancement of anomalous ion heating power density? (via cascade) Plasmas with large tearing exhibit non-Gaussian, non-self-similar turbulence. –Effects diminished when tearing is reduced. –Similar to electrostatic turbulence