Electron Surfing Acceleration in Current Sheet of Flares

1. Electron Surfing Acceleration in Current Sheet of Flares Wang De Yu* Lu Quan Ming** *Purple Mountain Observatory, Nanjing **University of Science and Technology in China, Hefei

3. Electron acceleration in the magnetic reconnection of flare • (a) Electric field and induced electric field acceleration. • Litvinenko et al. (1993) • (b) Shock wave acceleration. • Somov et al (1997) • (c) Turbulence acceleration • Miller (1997)

4. Some electrostatic waves can be excited during the magnetic reconnection • It is found from three dimensional particle simulation that • some perpendicular propagating electrostatic waves can be excited during the magnetic reconnection • Two examples:

5. Lower Hybrid Drift Wave Horiuchi and Sato (1999)

6. Fourier Spectrum of Lower Hybrid Drift Wave Horiuchi and Sato (1999)

7. Buneman Instability ( Langmuir Wave ) Drake et al. (2003)

8. A test electron is initially deeply trapped in the potential of electrostatic wave. • The perpendicular magnetic field Bz deflects the test electron across the wave front, which like surfer ( 冲浪) cutting across the face of an ocean wave, thus prevented the electron outrunning the wave.

10. Sketch of perpendicular propagatingelectrostatic wave in magnetic reconnection

12. Wave Frame

13. Analytical approximation solution

14. Vx Vz Vz Vx

15. Particle Particle simulation G>0

16. Particle Simulation

17. S S Vx S For different E0 Vz

18. Discussion • The surfing acceleration for different amplitude E0 of electrostatic wave is different. A larger E0 is provided with a deeper trapping potential, it makes an electron can be accelerated to higher energy. (2) A growing surfing acceleration velocity curve of Vx has a turning point S. That means the test electron de- trap from the potential of electrostatic wave at this point, and then, the test electron cannot be accelerated continuously in the current sheet by electrostatic wave. (3) The limited surfing acceleration velocity and acceleration time. The first term in the right hand of above equation is a trapping term, the second and third term in the right hand are de-trapping terms. When Fy -- 0, the turning point is an equilibrium about trapping term and de-trapping term. (a) Longitudinal magnetic field By-- 0, it is found Vz--0, so that the third term in above equation approaches to zero.

19. (b) By < 0, the second term and third term cancel each other in the above equation. • Therefore, the electron will de-trap from wave potential at larger velocity Vx0, when a stronger longitudinal magnetic field By is superposed in the current sheet.

20. Particle simulation for different By< 0

21. Spectrum of electron surfing acceleration

22. IV. Conclusion • The electron can be rapidly accelerated by perpendicular propagating electrostatic waves during the collisionless magnetic reconnection. • The electron can be effectively accelerated by perpendicular propagating electrostatic waves only in the case of G > 0. The velocity of acceleration electron in the x direction is approximate to . • The electron acceleration are limited by the de- trapping from the potential of electrostatic waves; the electron escape from the boundary of reconnection sheet and nonlinear evolution of electrostatic waves. • Therefore, the electron acceleration by perpendicular propagating electrostatic waves should be a short period acceleration processes during the early stage of collisionless magnetic reconnection.