Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cosmic ray diffusive acceleration at shock waves with finite upstream
  and downstream escape boundaries   In the present paper we discuss the modifications introduced into the
first-order Fermi shock acceleration process due to a finite extent of
diffusive regions near the shock or due to boundary conditions leading to an
increased particle escape upstream and/or downstream the shock. In the
considered simple example of the planar shock wave we idealize the escape
phenomenon by imposing a particle escape boundary at some distance from the
shock. Presence of such a boundary (or boundaries) leads to coupled steepening
of the accelerated particle spectrum and decreasing of the acceleration time
scale. It allows for a semi-quantitative evaluation and, in some specific
cases, also for modelling of the observed steep particle spectra as a result of
the first-order Fermi shock acceleration. We also note that the particles close
to the upper energy cut-off are younger than the estimate based on the
respective acceleration time scale. In Appendix A we present a new
time-dependent solution for infinite diffusive regions near the shock allowing
for different constant diffusion coefficients upstream and downstream the
shock.

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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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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: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn