Electromagnetic radiation of charged particles in stochastic motion

Abstract

The study of the Brownian motion of a charged particle in electric and magnetic 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 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.

Mean square displacement and instantaneous diffusion coefficient of charged particles in stochastic motion

“…In the presence of a non-trivially correlated noise and of a frictional force showing retarded effects, the motion of a charged particle in a harmonic potential is described by the generalized Langevin equation, which in the one-dimensional case can be written as (see, e.g., Harko & Mocanu (2016))…”

“…These cases were previously investigated in Harko & Mocanu (2016), where results regarding the radiation of the charged particle were obtained.…”

“…Note that although the constant electric field is important to the overall energy emission (Harko & Mocanu, 2016), it does not change the characteristics of the fluctuating component of the trajectory and thus it will not affect the diffusion.…”

System Plus Reservoir Approach to Quantum Brownian Motion of a Rod-Like Particle

“…Some authors analyzed Brownian motion from the purely mathematical point of view [6,7,8,9]. The concept of Brownian motion is not limited to the erratic motion of a particle in a fluid, it can be generalized to the fluctuating behavior of a system of interest interacting with its surroundings for instance molecular motion [10,11], a charged particle in an electromagnetic field [12,13,14], biological membranes [15,16,17], motion in a spin bath [18], polar molecules in external fields [19] and even modelling for stock market [20] and so on.…”

Spacetime geometry fluctuations and geodesic deviation

“…The discreteness character of matter (microscopic feature) causes fluctuations in the density of matter, which, in turn, causes observable effects on the motion of the Brownian particle (macroscopic feature) [16]. Recently, the solutions of Langevin-type equations in some astrophysical scenarios have been discussed in the literature [17][18][19][20][21][22][23].The knowledge of the behavior of a Brownian particle immersed in a fluid of much smaller atoms, can give us, in principle, some relevant information about the physics of these objects [24]. Brownian motion of test particles coupled to quantized fields was studied in Refs.…”