Injection of κ-like suprathermal particles into DSA Kang, Hyesung et al. arXiv: by Zhang Xiao,

Part I. Fermi Acceleration

1st order Fermi acceleration 2st order Fermi acceleration head-onback-on (see Grupen 2005, chapter 4) A simple picture...

1. Fermi Acceleration - spectral index Consider a process in which a test particle increases its energy by an amount proportional to its energy with each 'encounter'. after k encounters In each encounter, particle can escape from the acceleration region with probability P esc. The probability of remaining in the accele1'ation region after k encounters is

1. Fermi Acceleration - spectral index consider a particle with initial energy E 0, the encounter nunber needed to reach Ef is

1. Fermi Acceleration - spectral index The proportion of particles accelerated to energies greater than Ef is

1. Fermi Acceleration - spectral index differential spectrum spectral index (proposed by Bell. see Bell, A. R. 1978, MNRAS, 182, 147)

2. Fermi Acceleration - increasing rate ξ A particle with energy E1 goes into the cloud where it begins to diffuse by "scattering" on the irregularities in the magnetic field.

energy before scattering energy after scattering incident angle emergence angle Lab frame K rest frame of cloud K' 2. Fermi Acceleration - increasing rate ξ

Note!

1st order Fermi acceleration 2st order Fermi acceleration head-onback-on (see Grupen 2005, chapter 4) A simple picture... forgot it !

2. Fermi Acceleration - increasing rate ξ 2.1 Case A ： random moving cloud of plasma

2. Fermi Acceleration - increasing rate ξ 2.1 Case A ： random moving cloud of plasma For, 2st order Fermi Acceleration Stochastic Acceleration

2. Fermi Acceleration - increasing rate ξ 2.2 Case B ： plane shock front

2. Fermi Acceleration - increasing rate ξ 2.2 Case B ： plane shock front For, 1st order Fermi Acceleration Diffusive Shock Acceleration

3. Fermi Acceleration - escaping propability P esc Case B ： plane shock front

spectral index for plane shock If compressin ratio r = 4, μ = 2

the Larmor radius < the scale of the moving cloud  Maximum energy In SNR, we have "Knee"

Hillas diagram

 Injection problem For ions, scattering by Alfven and magnetoacoustic waves For electrons, scattering by whistler wave A preacceleration mechanism should be evoked to create a seed population of ions and electrons. shock thickness < the Larmor radius on the one hand on the ohter hand therefore

 Thermal Leakage Injection Q inj : injection parameter

Part II. Introducton of this article

a Maxwellianlike core + a suprathermal tail of power-law form Observation: Vasyliunas 1968; Hellberg et al Theory: Leubner 2004; Pierrard & Lazar 2010

black: Maxwellian color: κ-like distribution

Protons Electrons

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