Related papers: Stochastic acceleration in a random time-dependent…
If we have a particle immersed in a field of random forces, each interaction of the particle with the field can enlarge or diminish its kinetic energy. In this work is shown that in general, for any field of random force with uniform…
The mechanism of stochastic electron acceleration in colliding laser waves is investigated by employing proper canonical variables and effective time, such that the new Hamiltonian becomes time independent when the perturbative (weaker)…
In the random acceleration process, a point particle is accelerated according to $\ddot{x}=\eta(t)$, where the right hand side represents Gaussian white noise with zero mean. We begin with the case of a particle with initial position $x_0$…
We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular,…
We consider a basic stochastic particle system consisting of $N$ identical particles with isotropic $k$-particle synchronization, $k\geq 2$. In the limit when both number of particles $N$ and time $t=t(N)$ grow to infinity we study an…
We analyse the influence of the stochastic particle acceleration for the evolution of the electron spectrum. We assume that all investigated spectra are generated inside a spherical, homogeneous source and also analyse the synchrotron and…
We consider a particle moving in continuous time as a Markov jump process; its discrete chain is given by an ordinary random walk on ${\mathbb Z}^d$ , and its jump rate at $({\mathbf x},t)$ is given by a fixed function $\varphi$ of the…
We give a new coherent description of the first-order Fermi acceleration of particles in shock waves from the point of view of stochastic process of the individual particles, under the test particle approximation. The time development of…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
The theory of diffusive acceleration of energetic particles at shock fronts assumes charged particles undergo spatial diffusion in a uniform magnetic field. If, however, the magnetic field is not uniform, but has a stochastic or braided…
In turbulent magnetized plasmas, charged particles can be accelerated to high energies through their interactions with the turbulent motions. As they do so, they draw energy from the turbulence, possibly up to the point where they start…
We consider a particle evolving in the quadratic potential and subject to a time-inhomogeneous frictional force and to a random force. The couple of its velocity and position is solution to a stochastic differential equation driven by an…
The escape of the randomly accelerated undamped particle from the finite interval under action of stochastic resetting is studied. The motion of such a particle is described by the full Langevin equation and the particle is characterized by…
Stochastic acceleration of charged particles due to their interactions with plasma waves may be responsible for producing superthermal particles in a variety of astrophysical systems. This process can be described as a diffusion process in…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
It is well known that the fluid-particle acceleration is intimately related to the dissipation rate of turbulence, in line with the Kolmogorov assumptions. On the other hand, various experimental and numerical works have reported as well…
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…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
In this paper we address the one-dimensional problem of stochastic renewal in different damping environments. An ensemble of particles with some specified initial distribution in phase space are allowed to evolve stochastically till a…
Shock acceleration is considered one of the most important mechanisms for the acceleration of astrophysical energetic particles. In this work, we calculate the trajectories of a large number of test charged particles accurately in a…