Related papers: Comparison of Different Methods for Nonlinear Diff…
Collisionless shocks are often studied in two spatial dimensions (2D), to gain insights into the 3D case. We analyze diffusive shock acceleration for an arbitrary number $N\in\mathbb{N}$ of dimensions. For a non-relativistic shock of…
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…
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…
We report simulations of diffusive particle acceleration in oblique magnetohydrodynamical (MHD) shocks. These calculations are based on extension to oblique shocks of a numerical model for ``thermal leakage'' injection of particles at low…
First order Fermi acceleration at astrophysical shocks is often invoked as a mechanism for the generation of non-thermal particles. This mechanism is especially simple in the approximation that the accelerated particles behave like test…
We propose a multilevel Monte Carlo method for a particle-based asymptotic-preserving scheme for kinetic equations. Kinetic equations model transport and collision of particles in a position-velocity phase-space. With a diffusive scaling,…
Particle acceleration in collisionless astrophysical shocks, i.e., diffusive shock acceleration (DSA), is the most likely mechanism for producing cosmic rays, at least below 10^{15} eV. Despite the success of this theory, several key…
Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared…
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 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…
We have modeled the simultaneous first-order Fermi shock acceleration of protons, electrons, and helium nuclei by relativistic shocks. By parameterizing the particle diffusion, our steady-state Monte Carlo simulation allows us to follow…
Particle acceleration at astrophysical shocks may be very efficient if magnetic scattering is self-generated by the same particles. This nonlinear process adds to the nonlinear modification of the shock due to the dynamical reaction of the…
We independently develop a simulation code following the previous dynamical Monte Carlo simulation of the diffusive shock acceleration under the isotropic scattering law during the scattering process, and the same results are obtained.…
This paper deals with a comparison of Fractional Derivative and Monte carlo approaches to the modelling of anomalous diffusion in the field of particle transport. The goal of this research is to provide a better insight on the behavior of…
In this paper we study the problem of the numerical calculation (by Monte Carlo Methods) of the effective diffusivity for a particle moving in a periodic divergent-free velocity filed, in the limit of vanishing molecular diffusion. In this…
It is well accepted today that diffusive acceleration in shocks results to the cosmic ray spectrum formation. This is in principle true for non-relativistic shocks, since there is a detailed theory covering a large range of their properties…
Numerical Monte Carlo simulations of the diffusive shock acceleration in the test particle limit are investigated. We simulate high relativistic flow astrophysical plasmas for upstream $\gamma$ $\sim5$ and up to $\gamma$ $\sim1000$. These…
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…
Cosmic rays are charged particles that are accelerated to relativistic speeds by astrophysical shocks. Numerical models have been successful in confirming the acceleration process for (quasi-)parallel shocks, which have the magnetic field…
Supernova remnants are expected to contain braided (or stochastic) magnetic fields, which are in some regions directed mainly perpendicular to the shock normal. For particle acceleration due to repeated shock crossings, the transport in the…