1. General Meeting Madison, August 4-6, 2004 Plans and Progress of Magnetic Helicity Conservation and Transport H. Ji for participants of the Center for Magnetic Self-organization

2. Outline Introduction –Magnetic helicity –Physics issues Goals, plans and progress –The basics –The role –The applicabilities Summary: relations to other topics

3. Introduction: Magnetic Helicity Magnetic helicity is a global topological quantity which measures linkage (knottedness and twistedness) of magnetic field lines. Gauge invariant when B is tangential to the surface of V, which is simply-connected. K is conserved in ideal MHD plasmas.

4. Physics Issues Ambiguities in gauge-invariant definitions and their physical interpretations still exist in realistic geometries. –Non-uniqueness of gauge-invariant definitions –Practical formulation Are they really conserved in reality? How does the helicity conservation regulate dynamo process? –The helicity conservation is a fundamental assumption in the theories of magnetic self-organization (relaxation).

5. Physics Issues (Contd) Can the concept for helicity and relaxation be extended to 2- fluid plasmas? –Other helicities and possible new relaxed states? How does the helicity related to solar dynamo, flares, and CMEs (coronal mass ejections)? –Reversed S tends to appear in the northern hemisphere while S tends to appear in the southern hemisphere.

7. Major Goals I.Study basic properties of magnetic helicity in realistic geometries and its extensions to 2-fluid plasmas. II.Determine role of conservation and transport of magnetic and kinetic helicities during magnetic self-organization processes. III.Assess applicabilities of physics understandings gained in achieving Goals I&II to astrophysical circumstances, such as solar dynamo activity and accretion disk dynamics.

8. Tasks for Goal I - The Basics Revisit the concept of relative helicity (short) Consider helicity concept in 2-fluid plasmas (short-mid) Evaluate conservation of magnetic and kinetic helicities during 2-fluid dynamo simulations (short-mid) Evaluate conservation (and transport) of magnetic and kinetic helicities during self-organization events in MST (short-mid) Evaluate conservation of magnetic and kinetic helicities during merging processes in MRX and SSX (short-mid)

9. Gauge-invariant Definition Gauge-invariant definition when magnetic field intercepts with boundary and/or the volume is doubly-connected –Concept of relative helicity which subtracts off unknown linkage outside of V (Berger & Field 84, Finn & Anderson 84) –Non-uniqueness of gauge-invariant definitions identified (Blackman & Ji, 03). Practical formulation exist for spherical shell or slab geometry (Berger 85), but not for toroidal/cylinderical shell –Important for a sub-volume of a torus, accretion disks

10. Helicities in 2-fluid Plasmas Self-helicities (e.g. Steinhauer & Ishida 98): Electron-helicity reduces to magnetic helicity when size is larger than electron skin depth (c/w pe ). Ion-helicity is equivalent to helicity of the generalized vorticity (e.g. Mahajan & Yoshida 98): Discussions by C. Hegna (98) canonical momentum: =e,i:

11. Helicity change: Energy change: Ratio of changes: In reality, is small in large systems a: plasma size Magnetic Helicity Change Relative to Energy: an Estimate due to Reconnection

12. Test Helicity Conservation in Simulation (Horiuchi & Sato, 88) MHD simulation: –Tested for magnetic helicity in some cases 2-fluid simulations : –NIMROD ready in a few months –DEBS later

13. Test Helicity Conservation in MST External info only (MST 95) Internal + external info (MST 03) Magnetic helicity: Progress in measuring velocity profiles (CHERS) Neutral beam injection to drive flow

14. Test Helicity Conservation during Merging Data from TS-3 (Ono et al., 96)

15. Test Helicity Conservation in SSX and MRX SSX: –Data available for evaluation of magnetic helicity –New velocity measurements in progress MRX: –Machine upgraded for merging –Plan to drive flow by biasing and/or neutral beam injection

16. Tasks for Goal II - The Role Investigate role of helicity flux for large -effect in RFP and compare with computations (short-mid) Evaluate 2-fluid relaxation theories and explore new relaxation phenomena experimentally (mid-long) Evaluate role of helicity conservation in cascades where wave anisotropy supercedes invariant constraints on cascades (mid) –P. Terrys talk –E. Blackmans talk

17. Quenching of the Dynamo Effect The -effect is a key ingredient of dynamo action. Recent theories and simulations using periodic or closed boundaries predict the quenching of -effect due to large R m or B 0. (Cattaneo & Hughes 96)

18. Large -effect accompanies an large outward helicity flux. Importance of open boundaries? smalllarge The Dynamo Effect is Large in the Lab largesmall

19. Magnetic field generated in the convection zone –Polarity reverses every 11 years Has open boundaries, with helicity flux outward to corona –S and reversed S loops Anything common between lab and sun? The Dynamo Effect is Also Large in the Sun

20. Flow of magnetic energy –Generated in the convection zone –Transported to the corona, reversing polarity every 11 years –Effectively dissipated by flares Flow of magnetic helicity –Generated in the convection zone, with opposite signs each hemisphere –Transported to the corona, with no polarity reversal –Almost no dissipation by flares –Removed effectively only by CME ==> Inevitability of CME Magnetic Helicity and CME (Flux Rope) (Zhang & Low 04)

21. 2-fluid Self-organization or Relaxation New relaxed states can be readily found using additional conserved quantities in 2-fluid. An example is given below. Energy Magnetic helicity Generalized (or ion) helicity Minimizing W while keeping K and G constant: (Mahajan & Yoshida 98)

22. 2-fluid Relaxation (Contd) When 2 0, then V 0 and When 1 0 and 2 large, then V is large: Taylor solution; paramagnetic Scale arbitrary, decided by 1 Scale on order of c/ pi diamagnetic Shock front, diamagnetic cavity, small s FRC, etc

23. Preliminary Indications From TS-3 Plan to drive large flows by biasing and/or NBI to explore new relaxation phenomena in MRX/MST

24. Tasks for Goal III - Application to Astrophysics Investigate solar dynamo using a comprehensive computational model (long) –F. Cattaneos dynamo talk Relate above helicity concepts to solar dynamo and to computation (long) –E. Blackmans talk Understand helicity/poynting flux injection in disk- jet system –Related to coronal MRI

25. Summary: Relations to Other Topics Dynamo: –Conservation and transport of helicity may regulate dynamo Reconnection: –Helicity is dissipated at the reconnection region Magnetic turbulence: –Conservation of helicity is linked to the inverse cascade Angular momentum transport: –Properties of kinetic helicity and cross helicity could be related to (angular) momentum transport?

26. Links with Astrophysical Plasmas Physics of fast solar/disk dynamo: –Role of helicity conservation and transport Magnetic turbulence: –Inverse cascade due to helicity constraint High-beta magnetic structures (cavity, hole) –A relaxed state of 2-fluid plasma with significant flow