Active and passive Brownian motion of charged particles in two-dimensional plasma models

Abstract

The dynamics of charged Coulomb grains in a plasma is numerically and analytically investigated. Analogous to recent experiments, it is assumed that the grains are trapped in an external parabolic field. Our simulations are based on a Langevin model, where the grain-plasma interaction is realized by a velocity-dependent friction coefficient and a velocity-independent diffusion coefficient. In addition to the ordinary case of positive (passive) friction between grains and plasma, we also discuss the effects of negative (active) friction. The latter case seems particularly interesting, since recent analytical calculations have shown that friction coefficients with negative parts may appear in some models of ion absorption by grains as well as in models of ion-grain scattering. Such negative friction may cause active Brownian motions of the grains. As our computer simulations show, the influence of negative friction leads to the formation of various stationary modes (rotations, oscillations), which, to some extent, can also be estimated analytically.

Nonlinear Brownian motion - mean square displacement

“…In several recent papers, the stochastic dynamics of grains have been analyzed in detail [18][19][20][21][22]. In particular, it could be shown that the Brownian motion of grains in a plasma exhibits many parallels to the theory of active Brownian particles [23]. Therefore we believe that the theory explained here may find applications not only to biological problems but also to the dynamics of grains in plasmas.…”

“…In many situations it is sufficient to approximate a more complicated friction coefficient γ(v 2 ) by more simple models [5,23]. In the case of a rather weak driving force all our models may be unified, since in this case only the behaviour around v 2 = 0 is relevant.…”

“…Rather important are charging collisions due to ion absorption by grains. In this case both the friction coefficient γ(v 2 ) and the related diffusion coefficient D(v 2 ) in the Fokker-Planck equation (22) can be calculated explicitely [21,23]. Taking into account both contributions we find…”

“…Negative friction driven by momentum exchange: Following [21,23] let us consider a plasma with highly charged grains. Then the friction is determined at first by passive friction due to collisions of the grains with other particles and due to momentum exchange between grains and the plasma.…”

Approximated center-of-mass motion for systems of interacting particles with space- and velocity-dependent friction and anharmonic potential

“…For dusty plasma it has been shown that a negative friction may appear due to ion absorption by grains and create active particles [8,9]. These features are also used to describe the so-called active Brownian particles in the context of plasma physics [10] or biological physics [11][12][13]. In cold atoms experiments, a space dependent friction may have important dynamical consequences for the stability of magneto-optical traps [14,15].…”