1. Relativistic Particle Acceleration in a Developing Turbulence Relativistic Particle Acceleration in a Developing Turbulence Shuichi M ATSUKIYO ESST Kyushu Univ. ESST Kyushu Univ. Collaborator : T. Hada

2. Outline Background Background -- motivation -- motivation -- acceleration processes in turbulent plasmas -- acceleration processes in turbulent plasmas -- parametric instability (PI) -- parametric instability (PI) 1D PIC simulation on PIs in a pair plasma 1D PIC simulation on PIs in a pair plasma Acceleration mechanism : modelling Acceleration mechanism : modelling Test particle simulation Test particle simulation Summary Summary

3. Scholer SN1006 Bamba et al. [2003] Alfven turbulence & particle acceleration Best-known acceleration process in astrophysics : Fermi accelerations 1 st order Fermi acc. (DSA) 2 nd order Fermi acc. v  vv v+v+ v-v-

4. SN1006 Bamba et al. [2003] Alfven turbulence & particle acceleration ● Standard Fermi processes take into account wave-particle interactions in ‘fully-developed’ turbulence. Turbulence observed in space plasma is often coherent and time dependent. ● Scales of a relaxation process may be rather large ! Best-known acceleration process in astrophysics : Fermi accelerations How is a particle acceleration process in ‘developing’ turbulence ?

5. Parametric decays of large amplitude Alfven waves  k Alfven acoustic P D1 D2 D3 decay inst. Resonance conditions :  p +  1 =  2,3 k p + k 1 = k 2,3

6. 1D PIC sim. on parametric inst. in a pair plasma x (  B 0 ) k RH circularly polarized parent Alfven wave : P Amplitude spectrum of B

7. 1D PIC sim. on parametric inst. in a pair plasma Electron energy & momentum dist.

8. Acceleration mechanism trapping by a sharp envelope trough ( ,k ) ( ,-k ) Assumption: Two waves with opposite signs of k (same  ) locally become dominant.

9. Motion of an electron where fixed point Assumption: u , x = const.  u  = p  / m 0 c

10. Trajectory in u  -   space Nonresonant trapping Finite amp. is necessary. Also seen in nonrelativistic limit. Relativistic trapping In small amp. limit:  ~  0 /  u  uu u res- u res+ NR

11. Trajectory in u  -   space Max. u  Comparison with sim.

12. 0t0t kc/  0 Log|B z R /B 0 | Preferential acc. of high energy particles 0t0t ee Time variation of electron energy t  (k) (k) 0/0/ resonance cond.

13. Wave amp. spectrum at  0 t = 1616 kc/  0 |B(k)|/B 0 -2.0 How essential in particle acc. is the relativistic effects ? -  ±k±k K 0 =0.1 3.0 Bw(k)Bw(k) 1 k  -3 3 Test particle simulation

14. Non-rel. & Rel. eqs. of motion for 10 5 particles Initial distribution function: isotropic ring with v  /c = 0.1 Non-relativistic case

15. Test particle simulation Non-rel. & Rel. eqs. of motion for 10 5 particles Initial distribution function: isotropic ring with v  /c = 0.1 Relativistic case

16. Summary Local sharp envelope troughs of magnetic fields Local sharp envelope troughs of magnetic fields Relativistic perp. acceleration of particles trapped in the envelope troughs Relativistic perp. acceleration of particles trapped in the envelope troughs Preferential acceleration of high energy particles Preferential acceleration of high energy particles Particle acceleration process through coherent Alfven waves in the course of parametric decay instabilities : 1D PIC simulation Model analysis & test particle simulation Motion of a particle in two oppositely propagating waves Motion of a particle in two oppositely propagating waves Relativistic resonance with the two waves Relativistic resonance with the two waves Maximum attainable energy consistent with the PIC simulation Maximum attainable energy consistent with the PIC simulation Test particle simulation reproduced power-law like tail when the time varying wave spectrum is assumed. Test particle simulation reproduced power-law like tail when the time varying wave spectrum is assumed.