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We develop a method of stochastic differential equation to simulate electron acceleration at astrophysical shocks. Our method is based on It^{o}s stochastic differential equations coupled with a particle splitting, employing a skew Brownian motion where an asymmetric shock crossing probability is considered. Using this code, we perform simulations of electron acceleration at stationary plane parallel shock with various parameter sets, and studied how the cutoff shape, which is characterized by cutoff shape parameter $a$, changes with the momentum dependence of the diffusion coefficient $beta$. In the age-limited cases, we reproduce previous results of other authors, $aapprox2beta$. In the cooling-limited cases, the analytical expectation $aapproxbeta+1$ is roughly reproduced although we recognize deviations to some extent. In the case of escape-limited acceleration, numerical result fits analytical stationary solution well, but deviates from the previous asymptotic analytical formula $aapproxbeta$.
Synchrotron X-rays can be a useful tool to investigate electron acceleration at young supernova remnants (SNRs). At present, since the magnetic field configuration around the shocks of SNRs is uncertain, it is not clear whether electron acceleration
Weibel instability created in collisionless shocks is responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a rel
Particle acceleration and heating at mildly relativistic magnetized shocks in electron-ion plasma are investigated with unprecedentedly high-resolution two-dimensional particle-in-cell simulations that include ion-scale shock rippling. Electrons are
Aims: We investigate the behavior of the frequency-centered light curves expected within the standard model of Gamma Ray Bursts allowing the maximum electron energy to be a free parameter permitted to take low values. Methods: We solve the spatially
We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple mode