1. Dynamo and Magnetic Helicity Flux Hantao Ji CMSO & PPPL CMSO General Meeting Princeton, October 5-7, 2005 Contributors: Eric Blackman (Rochester) Stewart Prager (Wisconsin)

2. Outline Introduction to magnetic relaxation Magnetic helicity transport The -effect Relation between the -effect and helicity transport Summary

3. Reversed Field Pinch (RFP) Plasmas Sustained by a Toroidal Electric Field Donut-shaped plasmas is enclosed by electrically conducting shells –Cuts in both toroidal and poloidal directions allow flux penetration. –Rate of flux change corresponds to finite loop voltages.

4. Determining Integrated Quantities Directly measured –Total toroidal current (plasma current) –Total toroidal flux –Toroidal and poloidal loop voltages Inferred from equilibrium –Total internal poloidal flux –Total magnetic helicity –Total magnetic energy Periodic relaxations Toroidal flux in MST

5. Balance of Integrated Quantities Between relaxations: dissipation injection During relaxations: dissipation rate of change ensemble average: injection dissipation

6. Balance of Mean Profiles: Transport K is transported outward W is dissipated in the core

7. Helicity in a Sub-volume of a Torus Total helicity K can be split into three parts:

8. Transport of Magnetic Helicity The required magnetic helicity flux at r=b can be determined. outward helicity transport

9. Fluctuation-driven Flux Explains Helicity Transport

10. Balance of Mean Electric Field Profile: the -Effect Requires nonzero

11. The -effect in MHD Ohms law: The mean and turbulent parts: The -effect:

12. Measured -effect Satisfies Mean Ohms Law

13. Experiment (plasma edge): Electric Field is Mainly Electrostatic Simulation: Bonfiglio, Cappello & Escande (2005)

14. Averaging over periodic (toroidal & poloidal) directions: -effect Closely Related to Helicity Flux The -effect is propotional to the convergence of helicity flux.

15. Summary Magnetic relaxation is accompanied by -effect and magnetic helicity transport. and helicity flux are related by –where averaging is taken in the periodic direction(s), and –helicity flux points towards the un-averaged direction(s). Astrophysical implications –Averaging directions important