Motivation

1. What is Role of Proton Beams in Solar Radio Bursts? Jun-ichi SakaiLaboratory for Plasma Astrophysics University of Toyama, Japan

2. Motivation • It is believed that solar radio bursts like Type III and Type II are generated from electrons accelerated in the solar flare region or from electrons accelerated near the fast magnetosonic shock front. • It is recognized that some protons can be accelerated by surfing mechanism near the fast magnetosonic shock front. And also some protons are reflected and accelerated near the shock front, resulting in proton beams.

4. Contents • Proton acceleration by shocks--Surfing acceleration • Examples of shock formation • Wave emission from proton beams • Conclusions

5. Simulation Model Magnetic Field Line Shock Wave Model(2):q<90° CME q 90° v Model(1):90° v Solar surface

6. Simulation Model • Two-dimensional fully relativistic electromagnetic Particle-In-Cell code. • System size: Lx=800, Ly=10 • The free boundary condition in the x-direction, and the periodic boundary condition in the y-direction are imposed.

7. Initial Conditions and Parameters Model(1) 10 y v B0 0 Model(2) 10 x 0 200 800 Mass ratio :mi=64me Plasma beta :=0.05 (ce/pe=0.632) ce:Electron cyclotron frequency pe:Electron plasma frequency Alfvén velocity :vA=0.08c (c=light velocity) B=0 n=4n0=400 v=3vA=0.24c B=B0 n=n0=100 v=0 E=v×B (Ez=vyBx)

8. Parameter Runs • Alfvén Mach (v/vA) : 3, 2, 1.5 • Propagation Angle (q) : 90°, 80°, 70° (for Mach3) 90°, 70°, 40° (for Mach2 and 1.5) • Our simulation results are based on Alfvén Mach is 3 and Propagation Angle is 80°.

9. Wave Emission Process Shock region Ex Ex x (pet=0) 1.Some electrons are reflected behind the shock front. 2.The reflected electrons behind the shock front mix up with the in-coming electrons due to the counter- streaming instability. 3.Then there appear the electro- static waves behind the shock. vix/c vex/c x (pet=90)

10. Particle Acceleration Shock region By By x (pet=0) viz/c Both electrons and ions are strongly accelerated in the z- direction near the shock front through the surfing mechanism. vez/c x (pet=90)

11. Surfing Acceleration byElectrostatic wave propagating perpendicular to magnetic field Equation of Motion Ex=E0sin(t-kx) By=B0 Solve for vz In moving frame y Ex Acceleration Factor e x z

12. Spatial Distribution of Ex and Ez (pet=66) (pet=18) Ex Ez x x Red arrow area (x=70〜326) are used to find the dispersion relation of Ex. Blue arrow area (x=540〜796) are used to find the dispersion relation of Ez.

13. Dispersion Relations of Ex and Ez Elecrostatic Langmuir Waves (Z-mode) are generated in the yellow contour line. /pe /pe EM Waves are excited. kc/pe kc/pe Ex Ez

14. Conclusions • We found the wave emission process of Solar Type II Radio Bursts associated with CME. • We also found that fast magnetic shock wave is formed with both protons and electrons accelerated by the surfing mechanism. 1. Some electrons are reflected behind the shock front. 2. Reflected electrons generate electrostatic waves. 3. They could be converted to the extra-ordinary electromagnetic waves through the Direct Linear Mode Conversion.

15. 1.Generation of magnetosonic shocks during collision of two current loops • PIC simulation • Force-Free magnetic configuration • J×B = 0 • Uniform density and uniform temperatur • System size: • 900× 900 • n0=100 • Loop position： (300, 300) & (600, 600) • Loop radius： 100 Simulation System y x

20. 2.Generation of magnetosonic shock during formation of current sheet

24. Emission of electromagnetic waves by proton beams The proton beams propagating to the low-density region are forced to move, together with the background electrons, to keep charge neutrality, resulting in the excitation of electrostatic waves: proton beam modes and Langmuir waves. In the early stage of electrostatic wave excitation, both R and L modes near the fundamental plasma frequency can be generated along a uniform magnetic field. It is also found that, in the late stage, the second harmonics of electromagnetic waves can be excited through the interaction of three waves. During these emission processes, proton beams can move along the magnetic field almost without losing their kinetic energy.

29. Electron(solid line) and Proton(dashed line) velocity distribution:(a) t=0 and (b) pet=1500

30. Sakai and Nagasugi (2007) investigated the dynamics of proton beams propagating along a uniform magnetic field, as well as across the magnetic field in nonuniform solar plasmas, paying attention to the emission process of electromagnetic waves to understand a new solar-burst component emitting only in the terahertz range during the solar flare observed by Kaufmann et al.(2004).

31. Proton beams propagating into high density region

39. From the simulation where the proton beams propagate along a uniform magnetic field into the high-density region, it is found that strong electromagnetic waves are generated behind the proton beams. When the proton beams propagate perpendicular to the magnetic field, the extra-ordinary mode can be excited from two electron Bernstein waves through three-wave interactions. These simulation results could be applied to the electromagnetic wave emission from the solar photosphere during the solar flares.

40. Conclusions 1.Protons can be accelerated by surfing mechanism in shock front 2.Proton beams play an important role for the emission of electromagnetic waves

41. The role of proton beams reflected in the fast magnetosonic shock front is also discussed for the emission mechanism of the Type II radio bursts.

42. Shock formation and double structure(60 degree)

45. Time History of Ex and Ez Ex (Electrostatic) Ez (Electromagnetic) Fundamental Second harmonic wpet wpet Parameters Red line: w/wpe=1.3 〜1.6, kc/wpe=0〜2.5 Black line: w/wpe=1.5 〜2.0, kc/wpe=0〜3.0 Blue line: w/wpe=2.5 〜3.5, kc/wpe=0〜4.0 They are obtained by Inverse Fourier Transformation using the data of dispersion relations.