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S.Tanuma (Kwasan Observatory)

論文紹介 “ Proton acceleration during coalescence of two parallel current loops in solar flares”, J.I.Sakai & K.Shimada 2004, A&A, 426, 333-341. S.Tanuma (Kwasan Observatory). Abstract.

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S.Tanuma (Kwasan Observatory)

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  1. 論文紹介“Proton acceleration during coalescence of two parallel current loops in solar flares”,J.I.Sakai & K.Shimada 2004, A&A, 426, 333-341 S.Tanuma (Kwasan Observatory)

  2. Abstract • We investigate the plasma dynamics during coalescence of two parallel current loops in solar flares by performing a resistive 3D MHD simulations. • As the results, we find the most effective electromagnetic fields for the production of high-energy protons. • Next we investigate the orbit of many protons (test particles) in the electromagnetic fields obtained by the MHD simulations.

  3. 1. Introduction • Observations • Coalescence • Recent papers on simulations

  4. Characteristic Current Loop Coalescence and Related Solar Flares • Quasi-periodic energy release and high-energy particle acceleration: 1980 Jun 7 flare and 1982 Nov 26 flare (Sakai & Ohsawa 1987) • Plasma jet formation driven by tilting motion and shock formation: 1980 May 26 flare (coronal explosion) (Sakai & de Jager 1989a) • 3D point-like explosion following strong magnetic collapse and shock formation: 1994 May 21 flare (Sakai & de Jager 1989b) Sakai & de Jager 1991

  5. Quasi-Periodic Oscillation The 1980 Jun 7 flare The 1980 Nov 26 flare Microwave at 17Ghz Microwave at 17Ghz Hard X-ray at 40-140 keV Heights of two microwave sources X-ray at 300-350 keV Time Gamma-ray lines at 4.1-6.4 MeV Both flares show quasi-periodic amplitude oscillations with double sub-peak structure in both hard X-ray and microwave time profiles. Time Tajima et al. 1987 See also Nakajima et al. 1983 (left fig)

  6. Coalescence of Two Flux Tubes Coalescence of two flux tubes →Energy release and quasi-periodic amplitude oscillation (QPO) (???) unconsistent with Asai et al (2001) and Kamio et al. in press., who explain the QPO(QPP) by the Alfven transit time (I.e., sausage or kink instability ). But physical meaning is same with these instabilities. Sakai et al. 2002b; Tajima et al. 1987

  7. Quasi-Periodic Oscillation by Coalescence B^2/8πkT Fluid (kinetic) energy Reconnected magnetic flux Electrostatic energy E^2/8πkT Ion temperature in x-direction Time Time Time 2.5D particle simulation of coalescence Tajima et al. 1987

  8. Multiple Coalescence 2D distribution in x-y plain T=7.2/Ωi T=9.6/Ωi y B lines B^2/8πkT Electron density Electrostatic energy E^2/8πkT Electric field Ion temperature in x-direction x Multiple coalescence could explain more realistic pattern of quasi-periodic oscillation Tajima et al. 1987

  9. Gamma-ray Observation by RHESSI The X4.8 flare of 2002 Jul 23 The center of 2.223MeV emission is displaced by 20+-6 arcsec from that of 0.3-0.5 emission. The observation could be explained by anisotropic proton acceleration. In this paper, we calculate the motion of protons (test particles). See also Heerikhuisen et al. (2002), Craig et al. (2001), Takasaki et al. in prep. Hurford et al. 2003

  10. 3D Particle Simulations of Two Tubes Coalescence of two twisted flux tubes Nishikawa et al. 1994

  11. 3D MHD Simulations of Two Tubes MHD simulations of the interaction (reconnection and tearing instability)..… between untwisted flux tubes (Linton & Priest 2003) between almost parallel twisted flux tubes (Linton et al. 2001)

  12. Some of Recent Papers on Flux Tubes by Sakai Group • One flux tube: • Sakai & Kakimoto 2004, ApJ, 425, 333 (test particle) • Sakai et al. 2003, ApJ, 584, 1095 (MHD) • Sakai et al. 2002, ApJ, 576, 1018 (MHD) • Sakai et al. 2002, ApJ, 576, 519 (MHD) • Sakai et al. 2000, ApJ, 544, 1108 (MHD) • Two flux tubes: • Sakai & Shimada 2004, A&A, 426, 333 (test particle) • Saito & Sakai 2004, ApJ, 604, L133 (particle) • Sakai et al. 2002, ApJ, 576, 1018 (MHD) • Sakai et al. 2001, ApJ, 556, 905 (MHD)

  13. 2. Simulations and Results

  14. Models • We investigate two cases of the coalescence process between two parallel flux tubes: • (1) “co-helicity reconnection” where only the poloidal magnetic field produced from the axial currents dissipates • (2) “counter-helicity reconnection” where both poloidal and axial magnetic fields dissipates. Sakai et al. 2002b

  15. Initial Conditions We examine the reconnection and coalescence between two flux tubes. x Magnetic field and gas pressure: Bx= qi By (z-zci) / a Bz=-qi By (x-xci) /a z Ny=100, Nx=Nz=300 Radius a=30 Plasmaβ=0.06 at center |B0i|=1 Twist parameter: qi=1 y Schematic illustration of two parallel current loops and the coordinate system.

  16. Normalization Unit • N=10^8 cc • Va=c/300=1000 km/s • Cs=0.4Va=400 km/s • kT=1.6 keV (ambient ions): which is acceptable for a well-developed flare in the pre-flare phase. • L=100 km (radius a=30) • Rm=1300

  17. Basic Equations

  18. Results (2D distributions in y=50) Co-helicity case Counter-helicity case T=3.8TA T=4.7TA T=6.6TA By Ey By Ey Coalescence of two flux tubes Nishikawa et al. 1984

  19. Simulation of Proton Dynamics • The motions of test particles are calculated by the following normalized relativistic equations of the motion of a proton: Parameters: γ=(1+A^2u^2)^1/2 A=VA/c=1/300 R=VA/(ωci a)=10^-8

  20. Proton Velocity Distribution Function Dot-dashed line: the initial proton velocity distribution Doted line: counter-helicity case Solid line: co-helicity case Vx Vy Va=c/300=1000 km/s Cs=0.4Va=400 km/s ～1.6 keV ambient ions 1.6 keV ions can be accelerated to 7 MeV (co-helicity cases) and 5 MeV (counter-helicity cases) Vz

  21. Proton Energy Spectra E=(Vx^2+Vy^2+Vz^2)/Va^2 • We found a “bump-on-tail” distribution in the same direction as the original loop current for both the cases of co-helicity and counter-helicity. Ωci t=1500 Ωci t=2000 Ωci t=2500 1MeV The solid and dodded lines show the co-helicity and counter-helicity case, respectivity. 5MeV 7MeV 1000Eo =1.6MeV Ωci t=100 is 0.1 sec if B=100G.

  22. Proton Energy Spectra E=(Vx^2+Vy^2+Vz^2)/Va^2 • The maximum proton energy exceeds the energy (2.223 MeV) of the observed prompt nuclear de-excitation lines of gamma-ray. • The proton energy spectrum is neither a pure power-law type nor a pure exponential type. Ωci t=1500 Ωci t=2000 Ωci t=2500 1MeV The solid and dodded lines show the co-helicity and counter-helicity case, respectivity. 5MeV 7MeV 1000Eo =1.6MeV

  23. Energy Spectrum • As the results of investigation of complicated structure of electromagnetic fields in the coalescence process, we found that the energy spectrum is neither purely exponential nor purely power-law, in contrast to the result by Mori et al. (1998) (fig: power-law). Mori et al. (1998) examined the proton acceleration near X-type magnetic reconnection. As the results, they found the spectrum is in a power-law with index of 2.0-2.2.

  24. 3. Discussion

  25. Anisotropic Proton Acceleration • The anisotropic proton acceleration along the loop can be realized both for co-helicity and counter-helicity reconnection during two parallel coalescence. • This result is important to understand gamma-ray observation by RHESSI (Hurford et al. 2003) (fig).

  26. Proton Acceleration • The proton-associated gamma-ray source does not coincide with the electron-bremsstrahlung sources. • It suggests that the protons are accelerated in one direction by the DC electric field and could subsequently interact in spatially separated sources.

  27. A Scenario of Proton Acceleration • A possible scenario: • The single loop (with β=0.5) disrupted by kink instability (Sakai et al. 2002a) (fig). • The disrupted part (with high energy protons and hot thermalized protons) could move up and interact with the overlying other loop.

  28. Further Acceleration by Reconnection • The interaction between the ascending magnetized plasma blobs and the other loop can lead to magnetic reconnection in the interaction region (see Linton et al. 2001, Linton & Priest 2003). • The proton could be accelerated further by the inductive electric field associated with the magnetic reconnection mostly in one direction along the guiding magnetic fields.

  29. 4. Conclusion • We may conclude that anisotropic proton acceleration along the loop can be realized both for co-helicity and counter-helicity reconnection during the coalescence of two parallel loops.

  30. Proton Velocity and Co-helicity Counter-helicity Vy Vy x x z z Vy Vy Ey Ey Ωci=2500

  31. Mori et al. 1998 Proton density Magnetic field vectors

  32. Hurford et al. 2003

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