Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusive cosmic ray acceleration at relativistic shock waves with
  magnetostatic turbulence   The analytical theory of diffusive cosmic ray acceleration at parallel
stationary shock waves with magnetostatic turbulence 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 coordinates 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 speeds 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.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int