July 29, 2015 to August 6, 2015
World Forum
Europe/Amsterdam timezone

Diffusive cosmic ray acceleration at relativistic shock waves

Aug 5, 2015, 11:00 AM
Yangtze 2 (World Forum)

Yangtze 2

World Forum

Churchillplein 10 2517 JW Den Haag The Netherlands
Oral contribution CR-TH Parallel CR20 TH accel


Prof. Reinhard Schlickeiser (Ruhr University Bochum)


The analytical theory of diffusive cosmic ray acceleration at parallel shock waves is generalized to arbitrary shock speeds $V_s=\beta _1c$, including in particular relativistic speeds. This is achieved by applying the diffusion approximation to the relevant Fokker-Planck particle transport equation formulated in the mixed comoving coordinate system. In this coordinate system the particle's momentum coordinates $p$ and $\mu =p_{\parallel }/p$ are taken in the rest frame of the streaming plasma, whereas the time and space coordiantes are taken in the observer's system. For magnetostatic slab turbulence the diffusion-convection transport equation for the isotropic (in the rest frame of the streaming plasma) part of the particle's phase space density is derived. For a step-wise shock velocity profile the steady-state diffusion-convection transport equation is solved. For a symmetric pitch-angle scattering Fokker-Planck coefficient $D_{\mu \mu }(-\mu )=D_{\mu \mu }(\mu )$ the steady-state solution is independent of the microphysical scattering details. For nonrelativistic mono-momentum particle injection at the shock the differential number density of accelerated particles is a Lorentzian-type distribution function which at large momenta approaches a power law distribution function $N(p\ge p_c)\propto p^{-\xi }$ with the spectral index $\xi (\beta _1) =1+[3/(\Gamma _1\sqrt{r^2-\beta _1^2}-1)(1+3\beta _1^2)]$. For nonrelativistic ($\beta _1\ll 1$) shock speds this spectral index agrees with the known result $\xi (\beta _1\ll 1)\simeq (r+2)/(r-1)$, whereas for ultrarelativistic ($\Gamma _1\gg 1$) shock speeds the spectral index value is close to unity.
Registration number following "ICRC2015-I/" 134
Collaboration -- not specified --

Primary author

Prof. Reinhard Schlickeiser (Ruhr University Bochum)

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