Shock acceleration of electrons in the presence of synchrotron losses: I. test particle theory

Abstract

We discuss a semi-analytical solution of the transport equation for electrons at a non-relativistic shock in the presence of synchrotron energy losses. We calculate the spectrum of accelerated (test) particles at any point upstream and downstream of the shock for an arbitrary diffusion coefficient and we specialize the results to three cases: 1) diffusion constant in momentum ($D(p)=D_0$), 2) Bohm diffusion ($D(p)\propto p$), and 3) Kolmogorov diffusion ($D(p)\propto p^{1/3}$). Of special importance is the determination of the shape of the cutoff in the electron spectrum which depends on the diffusion properties felt by particles in the shock region. The formalism can be generalized to the case of a shock with an upstream precursor induced by the dynamical reaction of accelerated particles.

Manuscript accepted for publication in MNRAS

References in corpus (3)

• Analytical solutions for energy spectra of electrons accelerated by nonrelativistic shock-waves in shell type supernova remnants
• The maximum momentum of particles accelerated at cosmic ray modified shocks
• Diffusive shock acceleration in radiation dominated environments

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