Memory effects in the velocity relaxation process of the dust particle in dusty plasma

Abstract

In this paper, by comparing the time scales associated with the velocity relaxation and correlation time of the random force due to dust charge fluctuations, memory effects in the velocity relaxation of an isolated dust particle exposed to the random force due to dust charge fluctuations are considered, and the velocity relaxation process of the dust particle is considered as a non-Markovian stochastic process. Considering memory effects in the velocity relaxation process of the dust particle yields a retarded friction force, which is introduced by a memory kernel in the fractional Langevin equation. The fluctuation-dissipation theorem for the dust grain is derived from this equation. The mean-square displacement and the velocity autocorrelation function of the dust particle are obtained, and their asymptotic behavior, the dust particle temperature due to charge fluctuations, and the diffusion coefficient are studied in the long-time limit. As an interesting feature, it is found that by considering memory effects in the velocity relaxation process of the dust particle, fluctuating force on the dust particle can cause an anomalous diffusion in a dusty plasma. In this case, the mean-square displacement of the dust grain increases slower than linearly with time, and the velocity autocorrelation function decays as a power-law instead of the exponential decay. Finally, in the Markov limit, these results are in good agreement with those obtained from previous works for Markov (memoryless) process of the velocity relaxation.

Features of the EEDF formation in the dusty plasma of the positive column of a glow discharge

“…Here we should also note the nonphysical sharp growth of EEDF in the low energy region, which is observed in a number of the above-mentioned works (see, e.g. figures 1-3 in [6], figures 1-4 in [11], figures 1-3 in [12], figures 1 and 2 in [13]). However, within the local approximation, dF 0 /dw w=0 = 0 at the nonzero electric field, (for more information, see [17,18]).…”

“…However, within the local approximation, dF 0 /dw w=0 = 0 at the nonzero electric field, (for more information, see [17,18]). So, the unusual behavior of the EEDF observed in some previous works [6,[11][12][13]] also signals the unreliability of the utilized computational procedures.…”

“…[6][7][8][9][10][11]) and nonlocal (see, e.g. [12,13]) approximations. In all the studied cases, it has been shown that, with an increase in the dust density, the additional loss of electrons on the dust particles leads to an increase in the depletion of the EEDF in the corresponding energy region.…”

“…Therefore, when adding dust particles to plasma, it would seem that the opposite effect should be observed, i.e. that the fast part of the EEDF responsible for excitation and ionization should increase and not decrease, as, for example, described in [6][7][8][9][10][11][12][13]. This reflects the fact that all problems in plasma are self-consistent: it is impossible to find the field without knowing the EEDF, and equally impossible to obtaining the EEDF without knowing the self-consistent field.…”

Anomalous diffusion due to the non-Markovian process of the dust particle velocity in complex plasmas

“…We develop a model based on the fractional Langevin equation (FLE) for the motion of the dust grain because this equation includes the memory kernel function, which is non-local in time and shows memory effects in the velocity of the dust particle. The FLE is in the following form 24,25 x(t) +γ Γ(1−α)…”