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Particle Acceleration Particle Acceleration and Injection Problem in Shocks and Injection Problem in Shocks

Masahiro Hoshino Masahiro Hoshino University of Tokyo University of Tokyo

Acknowledgments for Advice and Comments:

• A. Amano, Y.
• A. Amano, Y. Kuramitsu

Kuramitsu, T. Kato, , T. Kato, T.

• T. Ebisuzaki

Ebisuzaki, , … …

Energy Phase Space Density Thermal Nonthermal (Fermi Acceleration) Injection(pre-acceleration) Shock Front Upstream Downstream supersonic Vshock vinj Vinj > Vshock

Injection Problem in Fermi Acceleration Injection Problem in Fermi Acceleration

wave (downstream frame)

Ion Injection Problem under Magnetic Field Ion Injection Problem under Magnetic Field

1 tan 1

2 2 1 //

 

Bn

r r V v 

10-1 100 101 102 30 60 90

v///V1

Bn

Shock Front Upstream Downstream BN V1 V2=V1/r B v//

r=4 (compression ratio) 8 3 /

1 2 ,

 V vth

BN < 30  Injection can be explained by thermal plasma, BN > 30  Additional heating/acceleration is needed. escape no escape

10-1 100 101 102 103 104 30 60 90

v///V1

Bn

1 tan 1

2 2 1 //

          

Bn ele ion

r m m r V v  

Shock Front Upstream Downstream BN V1 V2=V1/r B v// Eshock

4 . 1 . 2

2 1

   V m e

ion shock

 

Electron Injection Problem Electron Injection Problem

=0.4 =0.1 =0

i e

T T 

Electron Injection is Very Difficult Ambipolar Electric Field (Eshock)

Pre-Acceleration Process in Shock

• Non-relativistic Shock

– Shock Drift Acceleration – Surfing Acceleration – Shock Surface Rippling – Turbulence,…..

• Relativistic Shock

– Same Processes Above – Precursor Wave Acceleration (Wakefield Acceleration)

Next Talk by Amano This Talk

Relativistic Shock Relativistic Shock

• Extragalactic radio sources ( ~ 10)
• Gamma ray bursts ( > 100)
• Pulsars & Winds ( ~ 106-7)

Crab Nebula GRB model AGN jet (M87)

“ “Large Large-

• Amplitude Precursor Wave

Amplitude Precursor Wave” ” in Relativistic Shock in Relativistic Shock

Relativistic Plasma Flow Large Amplitude Precursor Wave ω2=k2c2+ωpe

2

(ω~2 - 3ωpe) Upstream Downstream Ponderomotive Force Shock Front Langdon et al. PRL (1988), Gallant et al. ApJ(1992), MH et al. ApJ(1992) ….

Electromagnetic Waves

p+ e-

Wakefields (E-field)

• +

+ + + + + + + + + + + + + + + + + + +

• Ponderomotive Force in Precursor Wave

Wakefields (E-field)

Tajima & Dawson, 1979 Laser pulse, electromagnetic Electron Wakefield, electrostatic

Vph ~ c

Wakefield Acceleration in Laboratory Laser Plasma

Chen et al. PRL 2003, Lyubursky ApJ 2007, MH ApJ 2008

Wakefield Acceleration in Relativistic Shock

2002

Livingston Chart

Laser Accelerator

Ux,ion Ux,ele Bz

(EM,photon)

Ex

(ES,plasmon)

Particle (PIC) Simulation of Relativistic Shock Particle (PIC) Simulation of Relativistic Shock

upstream（supersonic flow） downstream（sub-sonic）

Energy Spectra in 1D Shock

max > Mi/me (=50)

Accelerated electron energy is more than upstream ion bulk flow energy

2 2

c m c m

e e i i

  

1) 2)

2 1 2

c m c m

i e e

  

Amplitudes of Bprecursor and Ewake

10-1 100 101 10-2 10-1 100 101 e 

conv=1.0



conv=0.1

10-1 100 101 10-2 10-1 100 101 e 

conv=1.0

tip of precursor max phase Pair Plasma Shock conv = 10 % (tip of precursor wave) Ion-Electron Plasma Shock conv = 100 %

2 2 1 1 2 1

1 4 Flux Particle Flux Poynting

A e e

M c m N B      

2 2

/ , 1 ,    c m eE a a c m E

e e pond pond es

    

I

Electromagnetic Waves (Bz) Electrostatic Waves (Ex) ION ELECTRON

Maximum Energy in Simulation

1 2

1/2 conv 1 2 2 2 1 2 1 max

           a a c m L eE c m

e es e

• Wakefield Acceleration (non-resonant)

Strong Acceleration (if 1=107, max=1020eV)

100 101 102 103 104 105 106 107 101 102 103 104 105 106 107 max/1mec2 1

simulation theory tip of wakefield turbulent region (Lorentz Factor of Upstream Flow)

II

Electromagnetic Waves (Bz) Electrostatic Waves (Ex) ION ELECTRON

• +

+ + + + + + + + + + + + +

• Turbulence in Wakefield

+ + + +

• +
• +
• wave phase speed ~ c,

particles can be in resonance with waves, stochastic acceleration

Resonant Wakefield Acceleration

ph es

v c c L eE  

max



vph : propagation velocity of wakefield

Tajima & Dawson, 1979 Laser pulse, electromagnetic Electron Wakefield, electrostatic

Vph ~ c

) 1 1 (     ct Lsys

pe e

t c m    20 1

2 max 

Time Evolution of Maximum Energy

eff pe sys e

c L c m     

2 max

       3 1 ~ 6 1

eff



Wakefield region increases with increasing time

c L c m

pe sys e

   

2 max

) 1 , ( , , ,

3 2

        

e p e p p p jet jet jet sys

n n n n c n m R L R L

2 / 1 45 2 / 1 12 2 max

erg/s 10 1 10 5                

jet e

L c m  

jet

R

Application to AGN jet

E-2

Energy Spectrum in 2D PIC

Electron EM field EM field ES field ES field

Energy Spectra in 2D Wakefield

Kuramitsu et al., ApJ (2008) N(E) ∝E-2 N(E) ∝E-2

• px/mc

Summary Summary

• Wakefield Acceleration in Relativistic Shock

Wakefield Acceleration in Relativistic Shock

– – Large Amplitude EM Precursor Wave Large Amplitude EM Precursor Wave – – Large Amplitude ES Wave (Wakefield) Large Amplitude ES Wave (Wakefield) – – Particle Acceleration by Wakefield Particle Acceleration by Wakefield

• Turbulence (forward/backward Raman scattering),

Turbulence (forward/backward Raman scattering),

• Towards Understanding Ultra

Towards Understanding Ultra-

• High

High-

• Energy

Energy Cosmic Ray Cosmic Ray