Turbulent Reconnection: Particle Acceleration and Coronal Heating

1. Today’s Talk • Report on “Priest 60 Years Old Conference” • Report on “Magnetic Reconnection 2003” • Turbulent reconnection (Tanuma et al.; Vishiniac & Lazarian; Cho et al….) • Particle acceleration in turbulence (Dmitruk et al. 2003, ApJ, 597, L81) • Particle simulations (Tanuma et al.)

2. Priest 60 Years Old Conference • http://www-solar.mcs.st-and.ac.uk/~mhd03/ • Magnetic Reconnection and the Dynamic Sun • 8-10 September 2003 • Institute of Mathematics, University of St. Andrews, Scotland. • Linton’ talk

3. Programme • Reconnection Theory and Applications (Forbes, Drake, Fujimoto, Linton, Birn, etc.) • The Dynamic Sun (Proctor, Weiss, Asai, Klimchuk, Longcope, Galsgaard, Neukirch, Kusano, etc.) • The Dynamic Sun and Astrophysics (Dahlburg, Antiochos, Roussev, Heyvaerts, Casse, Baty, etc.) • Poster (Chen,Yokoyama, Miyagoshi, Suzuki, Tanuma etc.) • Annual PLATON Network Meeting follows the meeting.

4. MR2003 • http://www.aph.caltech.edu/mr2003/ • Fifth US-Japan Workshop on Magnetic Reconnection, Plasma Merging, and Magnetic Jets • November 3-5, 2003 • Catalina Canyon Resort, Catalina Island, California • Ono-san’s talk • Tanuma’s talk

5. Program • Particle heating during reconnection (Lin, Hoshino, Oieroset, Birn, Ono) • Jets, dynamo, & reconnection (Hirose, Kudoh, Bellan, Li) • Turbulent versus Laminar reconnection (Wygant, Ji, Diamond, Bale, Horiuchi, Lazarian) • Macroscale structure (Kawamori, Tanuma) • Structure and scaling of reconnection (Egedal, Terry, Shay, Cowley, Fujimoto, Kusano) • Guide versus null field reconnection (Prager, Porcelli, Cothran, Fuselier, Hesse, Swisdak) • Poster (Colgate, Furno, Uzdensky, T.Nakamura, Phan, M.Nakamura, Tanaka, Yamada, Tripathi, Jorne, Vou, Romero-Talamas, Izzo)

6. My Recent Study about Turbulent Reconnection • Talk at MR2003 • Internal shocks created by some instabilities and Turbulence in the reconnection jet

7. Turbulent Reconnection • Matthaeus & Lamkin 1985, Phys. Fluids, 28, 303, ‘Rapid magnetic reconnection caused byu finite amplitude fluctuations’ • Matthaeus & Lamkin 1986, Phys. Fluids, 29, 2513, ‘Turbulent magnetic reconnection’ • Enhanced viscous and resistive dissipation

8. Turbulent Reconnection

9. Coronal Heating by Turbulence • Matthaeus et al. 1999, ApJ, 523, L93, ‘Coronal heating by magnetohydrodynamic turbulence driven by reflected low-frequency waves’

10. Reconnection Rate Enhanced by Turbulence • Vishniac & Lazarian 1999, ApJ, 511, 193, ‘Reconnection in the interstellar medium’ • Lazarian & Bishniac, 1999, ApJ, 517, 700, ‘Reconnection in a weakly stochastic field’

11. Reconnection Rate Enhanced by Neutral Gas • Cho, Lazarian, & Vishniac 2002, ApJ, 564, 291, ‘Simulations of magnetohydrodynamic turbulence in a strongly magnetized medium’ • Yan & Lazarian 2003, ApJ, 592, L33, ‘Grain acceleration by magnetohydrodynamic turbulence: Gyroresonance mechanism’ • Cho, Lazarian, & Vishniac 2003, ApJ, 595, 812, ‘Ordinary and viscousity-damped magnetohydrodynamic turbulence’ • Many papers are posted in astro-ph.

12. MHD Simulations of Turbulent Reconnection • In Yokoyama-san’s results, the reconnection rate is not enhanced. • They are same with Tanuma’s results. • Much more simulation grids would be required.

14. Particle Acceleration in Analytic Reconnection Current Sheet • Craig & Henton’s analytic solution(Craig & Henton 1995, ApJ, 450, 280) • Hirose, Litvinenko, Shibata, Tanuma et al. (2003): MHD simulations of stability. • Heerikhuisen, Litvinenko, & Craig (2002), ApJ, 566, 512, ‘Proton acceleration in analytic reconnecting current sheets’: Test particle in Craig & Henton solution • Takasaki, Asai, et al.: Test particle in Craig & Henton solution

15. Craig & Henton(1995)’s Solution

16. Numerical Test of Stability • Hirose, Litvinenko, Shibata, Tanuma et al. (2003) examine stability of Craig & Henton solution by performing MHD simulations. • It is revealed that Craig & Henton solution is unstable to tearing instability or Kelvin-Helmholtz instability in some cases.

17. Particle Acceleration in Analytic Solution • Heerikhuisen, Litvinenko, & Craig (2002), ApJ, 566, 512, ‘Proton acceleration in analytic reconnecting current sheets’: Test particle in Craig & Henton solution

18. Trajectories of Test particles

19. Spectrum of Test Particles

20. Particle Acceleration in Turbulence • Dmitruk, Matthaeus, Seenu, & Brown 2002, ApJ, 597, L81, ‘Test particle acceleration in three-dimensional magnetohydrodynamic turbulence’

21. MHD Equations

22. Simulations • Mach number is 0.25. • Specific heat ratioγ=5/3 • The random fluctuation is assumed at 1<k<4. • R=Rm=1000 • Pseudospectral code (Ghosh, Hossain, & Matthaeus 1993) • The resolution is 256^3 Fourier modes.

23. Ohm’s law

24. Results • Turbulent |B| (upper) and |E| (lower). Yellow shows high, blue shows low. • The energy spectrum of the MHD fields (not shown in the paper) is consistent with a Kolmogorov 5/3 power law.

25. Nonrelativistic Equations of Motion • α=Ωi Ta relates the turbulent field scales with the particle motion scales. In general, α>>1: turbulent time scale is much slower than gyro frequency. In this paper, α=10^2, 10^3, 10^4, 10^5. • Ωi=qi B/ mi c is normalized gyro-frequency. • 50000 particles • Runge-Kutta 4th order.

26. Trajectories • 100 test particles (out of 50000) • The color shows velocity.

27. Particle Energy Distribution -0.6 -2

28. Emax and <E> v.s. α • Emax=2αE||λ|| • Solid line: This simulation • Dotted line: Particle simulation • Dashed line: Integration Emax <E>

29. Emax • Emax=2αE||λ||∝vBL. • These results are consistent with Swarthmore Spheromak laboratory reconnection experiment (Brown et al. 2002, ApJ, 577, L63) and a wide range of space and astrophysical systems (Makishima 1999, Astron. Nachr., 320, 1997Proc. Of ASCA 4th Meeting)

30. Particle Simulations • Tanuma et al. • Nishikawa et al. 2003 • To obtain spectrum. • Naito: Monte-Carlo simulations

31. Summary • Report of conferences • Turbulent reconnection • Particle acceleration • Particle simulations