Related papers: Diffusive shock acceleration in $N$ dimensions
Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. Accurate analytic expressions for the spectral index s are…
We analytically study diffusive particle acceleration in relativistic, collisionless shocks. We find a simple relation between the spectral index s and the anisotropy of the momentum distribution along the shock front. Based on this…
The spectral index $s$ of particles diffusively accelerated in a relativistic shock depends on the unknown angular diffusion function $\mathcal{D}$, which itself depends on the particle distribution function $f$ if acceleration is…
Diffusive shock acceleration (DSA) by relativistic shocks is thought to generate the $dN/dE\propto E^{-p}$ spectra of charged particles in various astronomical relativistic flows. We show that for test particles in one dimension (1D),…
The present work considers diffusive shock acceleration at non-relativistic shocks using a system of stochastic differential equations (SDE) equivalent to the Fokker-Planck equation. We compute approximate solutions of the transport of…
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…
Diffusive acceleration at collisionless shock waves remains one of the most promising acceleration mechanisms for the description of the origin of cosmic rays at all energies. A crucial ingredient to be taken into account is the reaction of…
We point out that particles accelerated in a non-relativistic shock of compression ratio $r$ attain the standard, $p=(r+2)/(r-1)$ spectral index only under certain conditions. Previous derivations of the spectrum, based on the…
We use 2D and 3D hybrid (kinetic ions - fluid electrons) simulations to investigate particle acceleration and magnetic field amplification at non-relativistic astrophysical shocks. We show that diffusive shock acceleration operates for…
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…
We provide a both qualitative and quantitative comparison among different approaches aimed to solve the problem of non-linear diffusive acceleration of particles at shocks. In particular, we show that state-of-the-art models (numerical,…
Prescriptions for electron injection into the diffusive shock acceleration process are required in many practical considerations of cosmic-ray astrophysics, particularly in modeling of the synchrotron emission of astrophysical sources. In…
Non-relativistic collisionless shock waves are widespread in space and astrophysical plasmas and are known as efficient particle accelerators. However, our understanding of collisionless shocks, including their structure and the mechanisms…
We use large hybrid (kinetic protons-fluid electrons) simulations to investigate the transport of energetic particles in self-consistent electromagnetic configurations of collisionless shocks. In previous papers of this series, we showed…
In this work the theory of diffusive shock acceleration is extended to the case of non-classical particle transport with L\'{e}vy flights and L\'{e}vy traps, when the mean square displacement grows nonlinearly with time. In this approach…
We present results from a fully relativistic Monte Carlo simulation of diffusive shock acceleration (DSA) in unmodified shocks. The computer code uses a single algorithmic sequence to smoothly span the range from nonrelativistic speeds to…
Reaction-diffusion equations (RDEs) model the spatiotemporal evolution of a density field $u(\vec{x},t)$ according to diffusion and net local changes. Usually, the diffusivity is positive for all values of $u,$ which causes the density to…
We investigate the role of the form of the spatial diffusion coefficient in shock acceleration of fast particles. Referring to non-classical diffusion and using the results of numerical (hybrid) simulations tailored for the downstream shock…
Diffusive shock acceleration (DSA) at relativistic shocks is expected to be an important acceleration mechanism in a variety of astrophysical objects including extragalactic jets in active galactic nuclei and gamma ray bursts. These sources…
Context. The diffusive shock acceleration mechanism has been widely accepted as the acceleration mechanism for galactic cosmic rays. While self-consistent hybrid simulations have shown how power-law spectra are produced, detailed…