Particle Acceleration Particle Acceleration and Injection Problem - PowerPoint PPT Presentation

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. Kuramitsu Kuramitsu, T. Kato, , T. Kato, T. T. Ebisuzaki Ebisuzaki, , … … A. Amano, Y.

Injection Problem in Fermi Acceleration Injection Problem in Fermi Acceleration Shock Front Thermal supersonic Phase Space Density V inj > V shock Injection(pre-acceleration) v inj Nonthermal (Fermi Acceleration) wave V shock Upstream Downstream Energy (downstream frame)

Ion Injection Problem under Magnetic Field Ion Injection Problem under Magnetic Field v 1    2 2 // r tan 1 Shock Front Bn V r 1 V 1 V 2 =V 1 /r 10 2 r=4 B (compression ratio) 10 1  BN v // /V 1 Upstream Downstream 10 0 3  v // v th / V , 2 1 8 10 -1 0 30 60 90  Bn escape no escape  BN < 30  Injection can be explained by thermal plasma,  BN > 30  Additional heating/acceleration is needed.

Electron Injection Problem Electron Injection Problem   Shock Front v 1 m        2 2 // ion r tan 1   Bn V  r m  V 1 V 2 =V 1 /r 1 ele 10 4 B 10 3  BN  =0.4 10 2 Upstream Downstream v // /V 1  =0.1 T  T 10 1 e i v // 10 0  =0 E shock 10 -1 0 30 60 90  Bn Ambipolar Electric Field (E shock )  2 e     shock 0 . 1 0 . 4 2 Electron Injection is Very Difficult m V ion 1

Pre-Acceleration Process in Shock • Non-relativistic Shock – Shock Drift Acceleration Next Talk – Surfing Acceleration by Amano – Shock Surface Rippling – Turbulence,….. • Relativistic Shock – Same Processes Above – Precursor Wave Acceleration This Talk (Wakefield Acceleration)

Relativistic Shock Relativistic Shock • Extragalactic radio sources (  ~ 10) • Gamma ray bursts (  > 100) • Pulsars & Winds (  ~ 10 6-7 ) Crab Nebula GRB model AGN jet (M87)

“Large Large- -Amplitude Precursor Wave Amplitude Precursor Wave” ” “ in Relativistic Shock in Relativistic Shock Large Amplitude Precursor Wave ω 2 =k 2 c 2 + ω pe ( ω ~2 - 3 ω pe ) 2 Ponderomotive Force Relativistic Plasma Flow Downstream Upstream Shock Front Langdon et al. PRL (1988), Gallant et al. ApJ(1992), MH et al. ApJ(1992) ….

Ponderomotive Force in Precursor Wave Electromagnetic Waves Wakefields (E-field) Wakefields (E-field) - - - - - + + + + + - - - - - + + + + + - - - - - + + + + + - - - - - + + + + + - - - - - p + e -

Wakefield Acceleration in Laboratory Laser Plasma Wakefield, Electron electrostatic Laser pulse, V ph ~ c electromagnetic Tajima & Dawson, 1979 2002 Wakefield Acceleration in Relativistic Shock Chen et al. PRL 2003, Lyubursky ApJ 2007, MH ApJ 2008

Laser Accelerator Livingston Chart

Particle (PIC) Simulation of Relativistic Shock Particle (PIC) Simulation of Relativistic Shock upstream （ supersonic flow ） downstream （ sub-sonic ） U x,ion U x,ele E x (ES,plasmon) B z (EM,photon)

Energy Spectra in 1D Shock  max   > M i /m e (=50)    2 2 m c m c 1) i i e e    2 2 m c m c 2) e e 1 i Accelerated electron energy is more than upstream ion bulk flow energy

Amplitudes of B precursor and E wake Pair Plasma Shock  conv = 10 % (tip of precursor wave) Ion-Electron Plasma Shock  conv = 100 % 10 1 10 1 max phase  conv =1.0 10 0 10 0  conv =1.0 tip of precursor  conv =0.1 10 -1 10 -1 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1  e  e    2 E , Poynting Flux B 1     es pond 1   e 2 2 Particle Flux 4 N m c M      2 2 m c 1 a , a eE / m c 1 1 e A pond e 0 0 0 e 0

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

Maximum Energy in Simulation • Wakefield Acceleration (non-resonant) 10 7  eE L 10 6  max es   2 2 m c m c 10 5 1 e 1 e  max /  1 m e c 2 10 4  theory 2 2 a     1/2 turbulent 0 10 3 1 conv region   2 1 a 10 2 0 simulation 10 1 tip of wakefield 10 0  Strong Acceleration 10 1 10 2 10 3 10 4 10 5 10 6 10 7  1 (if  1 =10 7 ,  max =10 20 eV) (Lorentz Factor of Upstream Flow)

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

Turbulence in Wakefield - - - - - + + + + + - - - - - + + + + + - - - - - + + + + + - - - - - + + + + + - - - - - wave phase speed ~ c, particles can be in resonance with waves, stochastic acceleration

Resonant Wakefield Acceleration c   eE L  max es c v ph v ph : propagation velocity of wakefield Wakefield, Electron electrostatic Laser pulse, V ph ~ c electromagnetic Tajima & Dawson, 1979

Time Evolution of Maximum Energy  max  1  t  pe 2 m c 20 e Wakefield region increases with increasing time  ct    L sys ( 1 1 )     pe max L  sys eff 2 m c c e   1 1     ~ eff   6 3

Application to AGN jet   R   jet pe max L sys 2 m c c e  L R , sys jet    2 3 L R m n c , jet jet p p      , ( , 1 ) n n n n p e p e 1 / 2    1 / 2   L 1       jet 12 max 5 10      2 45   m c 10 erg/s e

Energy Spectrum Electron in 2D PIC EM field E -2 EM field ES field ES field

Energy Spectra in 2D Wakefield N(E) ∝ E -2 N(E) ∝ E -2 -p x /mc Kuramitsu et al., ApJ (2008)

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