Brownian motion of grains and negative friction in dusty plasmas

Abstract

Within the approximation of dominant charging collisions the explicit microscopic calculations of the Fokker-Planck kinetic coefficients for highlycharged grains moving in plasma are performed. It is shown that due to ion absorption by grain the friction coefficient can be negative and thus the appropriate threshold value of the grain charge is found. The stationary solutions of the Fokker-Planck equation with the velocity dependent kinetic coefficient are obtained and a considerable deviation of such solutions from the Maxwellian distribution is established. Lw, 52.20.Hv, 52.25.Fi Description of the Brownian motion in the systems with particle or energy fluxes still remains one of the key problems in the statistical physics of the open systems [1]. Starting from the classical Lord Rayleigh work [2] many studies of the nonequilibrium motion of Brownian particles with additional (inner or external) energy supply have been performed. In particular, such studies are of great importance for physical-chemical [3,4] and biological [5] systems in which non-equilibrium Brownian particle motion is referred to as the motion of active Brownian particles. Recently the dynamical and energetic aspects of motion for the active Brownian particles have been described based on the Langevin equation and the appropriate FokkerPlanck equation [6,7]. The possibility of negative friction (negative values of friction coefficient) of the Brownian particles was regarded as a result of energy pumping. *

Brownian particle in non-equilibrium plasma

“…To describe the Brownian motion in a system with foreign particles is a key problem of the statistical physics of open systems. Stationary distributions of Brownian particles in a dusty plasma with a specified velocity dependence of the friction and diffusion coefficients were found in [10] for the case of the collisionless plasma background. The stationary distribution function has a maximum for some value of the velocity that determines the mean kinetic energy of the grains; the stationary one-particle distribution function is non-Maxwellian.…”

Structure formation in system of Brownian particle in dusty plasma

“…In order to get some analytical estimates let us consider Γ of the order of one. In such a case [9], the stationary solution for the distribution function possesses at Γ > 1 a maximum for non-zero velocity…”

“…To describe the Brownian motion in a system with foreign particles is one of the key problems of statistical physics of open systems. For some velocity dependence of the friction coefficient, the stationary distributions of the Brownian particles in dusty plasma were found in [9]. The stationary distribution function has a maximum for some value of the velocity that determines the mean kinetic energy of the grains.…”

“…Here, we use the kinetic coefficients calculated for dusty plasma on the basis of microscopic distributions [13,14]. Having introduced the coupling parameter Γ ≡ Z g Z i e 2 R T i describing the intensity of the grain-ion interaction, where Z g and Z i are the charge numbers for grains and ions, R is the grain radius and T i is the ion temperature, we can easily show that [9] …”

“…In the case of dominant charging collisions, the calculation of the diffusion coefficient results in [9] …”