Related papers: Probabilistic description of the first-order Fermi…
We explore properties the solution of Langevin equation when stochastic influence is orthogonal to velocity of a particle. Wiener's process can accept unlimited values. But for these equations, the attraction surfaces exist. For these…
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…
The efficiency of particle acceleration at shock waves in relativistic, magnetized astrophysical outflows is a debated topic with far-reaching implications. Here, for the first time, we study the impact of turbulence in the pre-shock…
We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium…
Diffusive shock acceleration at collisionless shocks is thought to be the source of many of the energetic particles observed in space. Large-scale spatial variations of the magnetic field has been shown to be important in understanding…
A phenomenological model is presented based on the formation of nuclear thermodynamic system during the collision of heavy ions in the regime of intermediate and high energy regions. The formulation and the dynamic picture are determined by…
We describe the theory of Fermi-type acceleration, including first-order Fermi acceleration at a parallel shock front and second-order Fermi acceleration in a test particle limit. Including the theory of the turbulent acceleration and the…
We investigate shock structure and particle acceleration in relativistic magnetized collisionless electron-ion shocks by means of 2.5D particle-in-cell simulations with ion-to-electron mass ratios (m_i/m_e) ranging from 16 to 1000. We…
We present a general model allowing one to calculate the distribution function of energetic particles in the interstellar medium, and hence any relevant nuclear reaction rate, for any given time-dependent injection function, as well as in…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
The first-order Fermi acceleration process at an ultra-relativistic shock wave is expected to create a particle spectrum with the unique asymptotic spectral index sigma_{gamma >> 1} approximately 2.2. Below, we discuss this result and…
We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles are described by a Langevin equation with Rayleigh-Helmholtz…
This paper presents numerical simulations of test particle Fermi acceleration at relativistic shocks of Lorentz factor Gamma_sh = 2-60, using a realistic downstream magnetic structure obtained from the shock jump conditions. The upstream…
We determine the spectrum of particles accelerated at shocks with arbitrary speed and arbitrary scattering properties for different choices of the equation of state of the downstream plasma. More specifically we consider the effect of…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time…
The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and ; (ii) by the solution of the diffusion…
When the pressure of particles accelerated at shock waves is no longer negligible compared to the kinetic pressure of the gas, the linear theory of diffusive shock acceleration breaks down. This is expected in particular when the shock…
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum…
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…