Related papers: Diffusive acceleration in relativistic shocks: par…
We examine the test-particle solution for diffusive shock acceleration, based on simple models for thermal leakage injection and Alfv'enic drift. The critical injection rate, \xi_c, above which the cosmic ray (CR) pressure becomes…
The shock waves produce relativistic particles via the diffusive shock acceleration (DSA) mechanism. Among various circumstances, fast acceleration has been expected for perpendicular shocks. We investigate the acceleration time and the…
We study relativistic particles undergoing surfing acceleration at perpendicular shocks. We assume that particles undergo diffusion in the component of momentum perpendicular to the shock plane due to moderate fluctuations in the shock…
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…
In the theory of diffusive acceleration at oblique shock fronts the question of the existence of a discontinuity of energetic particle density is contentious. The resolution of this problem is interesting from a theoretical point of view,…
We present a (heuristic) theoretical derivation for the scaling of the diffusion coefficient $D_f$ for fluctuating ``pulled'' fronts. In agreement with earlier numerical simulations, we find that as $N\to\infty$, $D_f$ approaches zero as…
The probability that a particle, crossing the shock along a given direction, be reflected backwards along another direction, was shown to be the key element in determining the spectrum of non--thermal particles accelerated via Fermi…
We examine the problem of particle acceleration at a relativistic shocks assuming pitch-angle scattering and using a Hartree-Fock method to approximate the associated eigenfunctions. This leads to a simple transcendental equation…
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…
We derive a relativistically covariant (although not manifestly so) equation for the distribution function of particles accelerated at shocks, which applies also to extremely relativistic shocks, and arbitrarily anisotropic particle…
The observed energy spectra of accelerated particles at interplanetary shocks often do not match the diffusive shock acceleration (DSA) theory predictions. In some cases, the particle flux forms a plateau over a wide range of energies,…
We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends…
A major attraction of diffusive shock acceleration is the prediction of power-law spectra for energetic particle distributions. However, this property is not fundamental to the theory. We demonstrate that for planar shocks with an oblique…
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…
Diffusive Shock Acceleration (DSA) cannot efficiently accelerate particles without the presence of self-consistently generated or pre-existing strong turbulence ($ \delta B/B \sim 1 $) in the vicinity of the shock. The problem we address in…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
Three approaches are considered to solve the equation which describes the time-dependent diffusive shock acceleration of test particles at the non-relativistic shocks. At first, the solution of Drury (1983) for the particle distribution…
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…
The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion…
The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional…