1. Momentum Transport During Reconnection Events in the MST Reversed Field Pinch Alexey Kuritsyn In collaboration with A.F. Almagri, D.L. Brower, W.X. Ding, F. Ebrahimi, G. Fiksel, M.C. Miller, V.V. Mirnov, S.C. Prager, J.S. Sarff, and MST Team 13 th RFP Workshop Stockholm, Sweden October 9-11, 2008 TexPoint fonts used in EMF: AAA A A A A AAA A

2. Motivation Accretion Disks How is toroidal angular momentum transported? What drives spontaneous rotation in RFPs and tokamaks? MST experiment Sudden changes of momentum can not be explained by classical processes Reconnection (relaxation) events

3. Outline Introduction: Tearing magnetic fluctuations and current profile relaxation in the MST RFP & Theory Bulk flow measurement techniques Relaxation of parallel plasma momentum during reconnection events Measurements of non-linear Maxwell and Reynolds stresses Importance of multiple reconnections Summary

4. Tearing modes govern RFP performance Explore regimes with large magnetic fluctuations. Main contribution - from current gradient driven resistive tearing modes that become unstable over the entire plasma volume. m=0 n=-1,-2,-3,.. q m=1 n=6,7,8,..

5. Fluctuations mediate current profile relaxation Parallel current profile 2.0x10 6 1.5 1.0 0.5 0.0 J || (A/m 2 ) 0.50.40.30.20.10.0 r (m) 0.25ms after -0.25 ms before After reconnection Before reconnection Brower, Ding, PRL (2002) Fast growing multiple tearing relax the current profile via current transport, and reduce the instability drive. Taylor relaxation (single fluid). Current profile relaxes to the minimum energy state while conserving the global helicity. Two-fluid (Steinhauer, Ishida, 1997; Hegna, 1998). Current and momentum profile relax to the minimum energy state while conserving the helicities for both species.

6. Flow profile flattening also observed in MHD simulations Non-linear resistive MHD (DEBS) Multiple tearing modes Periodic relaxation events - similar to experiment F. Ebrahimi et al., PRL (2007) Flow profile flattens at the peak of the reconnection Driven by both Maxwell and Reynolds stresses Multiple reconnections are important – effect is much weaker when only single mode is present Key observations: Next slides demonstrate experimental verification of these points

7. Core flow measurements Rutherford scattering – poloidal flow. −local measurement; utilizes scattering of mono-energetic He beam (16 keV) from bulk plasma ions (D). Mode rotation of core resonant tearing modes - toroidal flow. −from the edge toroidal array of 64 magnetic pick-up coils. Passive Doppler spectroscopy (CV line) - toroidal flow. Edge flow measurements Mach and optical probes. Measurements of bulk flow velocity

8. Parallel momentum profile flattens at the reconnection event After Before During While the core parallel flow slows down the edge speeds up Can not be explained by classical processes Radial Profile Time Evolution V || (km/s)

9. Maxwell stress is large and opposite to the flow change in the core Measured using FIR laser faraday rotation diagnostic by W.X. Ding et al. (UCLA) inertiaReynolds Maxwell Reconnection ? Near (1,6) R.S.

10. B r coil Boron Nitride 2.5 cm 2 cm B φ coil Maxwell and Reynolds stresses measured by the probes in the edge Maxwell stressReynolds stress B coil

11. Maxwell and Reynolds stresses balance in the edge N/m 3 Near (0,1) R.S.

12. Flow dynamics is coupled to the current dynamics Change in current is small – Electric Field is balanced by Hall dynamo! Current and momentum equations are coupled. Current relaxation - large MHD and Hall terms. In order to maintain a momentum balance a large ṽ∇ṽ force (Reynolds stress) is required. Large MaxwellReynolds Near reversal surface Hall

13. Both core and edge modes (multiple reconnections) are important for momentum transport Edge modes are large Core modes are large Large momentum transport Edge modes are small Core modes are large No momentum transport Both core and edge resonant modes must be present. No momentum transport without edge modes. Agrees with numerical modeling - multiple modes with nonlinear coupling result in a greater momentum transport.

14. Summary Relaxation of the parallel momentum carried by the bulk ions is measured in the core and in the edge of the MST RFP plasma through the reconnection (relaxation) event. The parallel flow profile flattens in the core similar to the electrical current. Maxwell stress is about 10 times larger than the inertial term in the edge and in the core. Edge probe measurements indicate that Maxwell and Reynolds stresses are approximately equal and opposite to each other, thus providing the momentum balance. Multiple reconnections (m=0,1) are necessary for large momentum transport. By transiently applying edge biasing it is demonstrated that improved confinement (PPCD) leads to six-fold increase of the momentum confinement. (not presented in this talk)

15. The End