1. NSF Site Visit Madison, May 1-2, 2006 Magnetic Helicity Conservation and Transport R. Kulsrud and H. Ji for participants of the Center for Magnetic Self-organization

2. Major Goals I.Study basic properties of magnetic helicity. II.Determine role of helicity conservation and transport during magnetic self-organization. III.Assess applicabilities of the helicity concept to astrophysical circumstances. Is magnetic helicity really conserved in reality? Can the concept of helicity be extended to 2-fluid plasmas? Can the helicity conservation illuminate dynamo process? How is the helicity related to solar dynamo, flares, and CMEs (coronal mass ejections)?

3. Introduction: Magnetic Helicity There are many flux conserving quantities (e.g. the flux point mappings for the coronal field). Only one can be expressed simply: magnetic helicity, where A is the vector potential: A=B. Conservation of magnetic helicity is a key element of the concept of magnetic self-organization.

4. Physical Interpretation of Helicity Helicity represents the amount of flux linkages between pairs of lines. Consider two flux tubes 1 and 2. In first volume since the integral is the flux in the second tube by Stokes theorem. Similarly for the second volume so the total helicity is simply If the loops were not linked, K=0. Gauge invariant definitions exist.

5. Major Goals I.Study basic properties of magnetic helicity. II.Determine role of helicity conservation and transport during magnetic self-organization. III.Assess applicabilities of the helicity concept to astrophysical circumstances. Is magnetic helicity really conserved in reality? Can the concept of helicity be extended to 2-fluid plasmas? Can the helicity conservation illuminate dynamo process? How is the helicity related to solar dynamo, flares, and CMEs (coronal mass ejections)?

6. Test Helicity Conservation in Simulation and MST (Horiuchi & Sato, 88) MHD simulation: MST experiment: Internal + external measurements

7. Helicities in 2-fluid Plasmas Self-helicities: Electron-helicity reduces to magnetic helicity when size is larger than electron skin depth (c/w pe ). Ion-helicity will be significantly different from magnetic helicity if ion flow is large (e.g. Alfvenic) Different relaxed states under conservation of these helicities canonical momentum: =e,i: ( Steinhauer & Ishida, 1998; Mahajan &Yoshida, 1998; Hegna, 1998)

8. Parallel Flow Profile Appears to Become More Uniform During Relaxation in MST Will be studied also numerically using 2-fluid code and PIC code

9. Major Goals I.Study basic properties of magnetic helicity. II.Determine role of helicity conservation and transport during magnetic self-organization. III.Assess applicabilities of the helicity concept to astrophysical circumstances. Is magnetic helicity really conserved in reality? Can the concept of helicity be extended to 2-fluid plasmas? Can the helicity conservation illuminate dynamo process? How is the helicity related to solar dynamo, flares, and CMEs (coronal mass ejections)?

10. Helicity Conservation and Dynamo Large-scale magnetic field is generated by the -effect. Most such large-scale magnetic field contains helicity (e.g. solar magnetic field). However, the total helicity should be conserved for timescales shorter than the resistive time. Two possibilities: –Transport helicity across scales. –Transport helicity across space. Lab

11. K Transported Outward While W Dissipated Locally during Relaxation in MST

12. Helicity Transport Driven by Fluctuations The required helicity flux across the r = b surface can be quantified by evaluating each of three parts: Helicity flux due to fluctuations: outward helicity transport

13. Fluctuations Also Drive a Nonzero - Effect in Mean Ohms Law Electric field mostly electrostatic

14. -effect Closely Related to Helicity Flux Averaging is taken in the periodic direction(s) Helicity flux points towards the un-averaged direction(s). Thus, limiting helicity transport can affect -effect

15. Major Goals I.Study basic properties of magnetic helicity. II.Determine role of helicity conservation and transport during magnetic self-organization. III.Assess applicabilities of the helicity concept to astrophysical circumstances. Is magnetic helicity really conserved in reality? Can the concept of helicity be extended to 2-fluid plasmas? Can the helicity conservation illuminate dynamo process? How is the helicity related to solar dynamo, flares, and CMEs (coronal mass ejections)?

16. Motivations to Study Helicity in Solar Physics Most large-scale magnetic field contains helicity (e.g. S and reversed S loops). Why solar flares are sporadic in space and intermittent in time with constant shearing motion of magnetic field on the surface? – Related to helicity flux? Helicity piling up is a reason for CME? Closely related to the solar dynamo process Correlations found between helicity flux and X-ray flux (Kusano et al.)

17. Major Goals : Summary and Plans I.Study basic properties of magnetic helicity. II.Determine role of helicity conservation and transport during magnetic self-organization. III.Assess applicabilities of the helicity concept to astrophysical circumstances. Assessments of helicity concept, its conservation, and its extensions to 2-fluid plasmas. More data expected from experiments and simulations Experimental verification of relation between magnetic helicity transport and -effect. Further study by AC helicity injection experiments Evaluation of role of magnetic energy and helicity during solar flares and CMEs.

18. END