1. G. Li(1), ‏Y. Yan(2), B. Miao (3)‏, G. Qin (4)‏ 1) Dept. of Physics and CSPAR, University of Alabama in Huntsville, AL 35899 2) Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Science, Beijing 100012, China 3) School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, China 4) Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Science, Beijing 100012, China Magnetic networks on the photosphere and fluxtubes in the solar wind and their effects on the transport of SEPs

2. magnetic network on the solar surface Hinode/SOT vector magnetogram Ca II image

3. MDI 2004 and 2005 within 15 degrees of the solar ecliptic. We use the middle part of the MDI plot for a period of Carrington Rotation (27.2753 days)‏ Example of MDI for a Carrington Rotation.

4. 2005-0104 2005-0704 Threshold=30 No dilation Threshold=15 Dilate 2X4 Ca II imageOriginal Threshold=30 No dilation Threshold=15 Dilate 2X4 Ca II imageOriginal

5. Counting the Supergranules

6. R sun ~ 0.75 * 10^6 km size of super granule l ~ 3*10^4 km one solar rotation ~ 27 days => (2 pi Rsun/l) / (27 days *24 hours) ~ 5 / day Fix at a point in space, counting boundaries: Rotation of the Sun changes longitudinal structures to radial structures Interplanetary imprint of Supergranule

7. What could be these structures? Bruno et al, 2001Borovsky, SHINE 2006 Flux tubes in the solar wind can be originated from the Sun! Current sheets are the boundaries!

8. Complications from MHD turbulence Numerical simulations suggest that coherent structures such as “current sheets” can be generated as the results of the non-linear interaction term in “NS” equation. Zhou et al 2004 Chang et al 2004

9. f ~ (  /  ) / [(T-  )/  ] f: frequency of large angle changes between B(t) and B(t+  T: total measurement interval  : measurement interval f scale with   : measurement resolution t Finding a current sheet T 2   Current sheets Li 2008

10. Ulysses Observations McComas et al 1998

11. They are everywhere 1997 A B Miao et al. 2010

12. Current-sheet example – class A Miao et al. 2011 Gradual change of angle Perhaps reconnection

13. Current-sheet example – class B One-peak eventTwo-peak event Sharp change of angle

14. One-peak event -- Flux tube crossing

15. Two-peak event -- Flux tube dangling

16. As the lag increases, the two peaks get closer, till they touch, and then separate again

17. The history of magnetic field Similar to magnetic holes identified previously Tsurutani et al. (2005)‏

18. A hedogram movie

19. Do the numbers match? If sharp change, one-peak events ==> boundaries of flux tubes, and are rooted at the solar surface, We expect to see approximately equal number of supergranules and one-peak C/S event. For the month of 2004 – 01, we find ~ 100 one-peak event, fewer than 10 two-peak events.

20. Daily number of Supergranules in 2004

23. Daily number of Supergranules in 2005

26. N15 0 S15 2004 1196 1010 1123 2005 1156 943 1097 The Results Match nicely with the C/S data!

27. So current sheets are copious in the solar wind... Will they affect the transport of energetic particles?

28. Parker's transport equation Gleeson & Axford 1967 In conservation form:‏ S: current in r space J: current in p space Diffusion coefficient  No explicit magnetic field dependence.  Effect of (turbulent) magnetic field comes through diffusion coefficient. Diffusion is assumed implicitly in all directions, therefore both the parallel and the perpendicular directions.

29. Diffusion, sub-diffusion and super-diffusion z Diffusion: r diff (t)=(x 2 +y 2 +z 2 ) 1/2 ~ t 1/2 Super-diffusion r(t) > r diff Diffusion is widely used in astrophysics and space physics! x y Sub-diffusion r(t) < r diff The sum of a series random variables is itself a random variable with a Gaussian distribution, irrespective of the shape of the original distribution, if the following is satisfied: If the individual R.V. has finite expectation µ and variance σ > 0. Why Diffusion: Central Limit Theorem

30. Is diffusion a good approximation? Depends on turbulence geometry 2D turbulence is proposed to account for discrepancy between QLT and observed mean free path of cosmic ray. Slab geometry: Slab geometry: wave vector parallel to the mean magnetic field 2D geometry: 2D geometry: wave vector perpendicular to the mean magnetic field Belcher, 1971 Bieber et al., 1994 Alfven waves Competing view: Do we need significant 2D turbulence or is Alfven wave turbulence enough?

31. Sub (compound) diffusion for a slab turbulence If slab geometry only, then only gets sub-diffusion

32. Compound diffusion What happened: Having ptcls tightly tie to field lines violate the “randomness” assumption of “CLT”. == > Compound diffusion If slab turbulence gives sub-diffusion, then 2D turbulence must be introduced if Parker's transport equation is correct. Is there an alternative?

33. Effects of current sheets on the transport of energetic particles Toy model: a cellular solar wind. If plasmas come in as many parcels with local magnetic field orientated different from the background magnetic field, and having a local turbulence, how energetic particle will respond to it? Local magnetic field Qin and Li ApJL, (2008)‏ What is the effect of having flux tubes in the solar wind on energetic particle transport?

34. Running Diffusion Coefficient --- Kubo's formula Perpendicular direction Parallel direction is the ensemble average

35. current sheet:   from sub- diffusion to diffusion Pure slab turbulence in individual cell. == > large scale perpendicular diffusion is recovered. As long as magnetic wall exists (whatever its origin), 2D turbulence is not necessary for having a perpendicular diffusion. Diffusion Sub-diffusion

36. What is next? Sectors in the heliosheath Work in progress Florinski et al 2011 Question: what is the response of energetic particles to these ordered current sheets?