Abstract
The study of the Brownian motion of a charged particle in electric and magnetic fields fields has many important applications in plasma and heavy ions physics, as well as in astrophysics. In the present paper we consider the electromagnetic radiation properties of a charged non-relativistic particle in the presence of electric and magnetic fields, of an exterior non-electromagnetic potential, and of a friction and stochastic force, respectively. We describe the motion of the charged particle by a Langevin and generalized Langevin type stochastic differential equation. We investigate in detail the cases of the Brownian motion with or without memory in a constant electric field, in the presence of an external harmonic potential, and of a constant magnetic field. In all cases the corresponding Langevin equations are solved numerically, and a full description of the spectrum of the emitted radiation and of the physical properties of the motion is obtained. The Power Spectral Density (PSD) of the emitted power is also obtained for each case, and, for all considered oscillating systems, it shows the presence of peaks, corresponding to certain intervals of the frequency.
Highlights
The study of runaway electrons, and in particular of their radiation, represents a field of great importance in different areas of research such as astronomy, accelerators, or nuclear fusion [4,5,6].An important physical problem in plasma and fusion physics is the anomalous transport in a magnetically confined plasma in a region where the magnetic surfaces are destroyed [7]
The latter are represented by a random force and the equation of motion becomes a stochastic differential equation, the Langevin equation [7,8,9,10,11]
Where F[r (t), r(t), t] is the systematic (“average”) force acting on the article, and η(t) is a random force modeling the effects of the interparticle collisions
Summary
The study of runaway electrons, and in particular of their radiation, represents a field of great importance in different areas of research such as astronomy, accelerators, or nuclear fusion [4,5,6]. In [35,36,37] it was pointed out that resonant stochastic behavior with a single peak and multi-peaks can be found in PSD curves of the stochastically oscillating accretion disks, described by both standard and generalized Langevin equations It is the purpose of the present paper to consider the electromagnetic radiation of charged, non-relativistic particles, in stochastic motion under the effect of some random exterior forces, in the presence of electric and magnetic fields, of an external non-electromagnetic potential, and interacting with the environment by means of interparticle collisions, described as a friction force. 2 we introduce the Langevin equation describing the motion of a charged particle in electric and magnetic fields, and in an external, non-electromagnetic potential, and we present the basic relation for the stochastic power emitted during the motion. 3.1 Radiation of a charged particle in Brownian motion in the presence of an electric field
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