Particles embedded in a plasma acquire a net charge as a result of collisions with electrons and ions. Due to the stochastic nature of encounters between particle and charged species, the instantaneous charge fluctuates. The static properties of the charge fluctuations are quantified for particles surrounded by an undisturbed plasma in orbital motion limit. For particles that satisfy the condition e2/4πε0RkTe≪1 the charge distribution is a Gaussian function whose average and variance is related to the ion and electron currents toward the particle. For a Maxwellian plasma, in particular, analytical solutions are developed for the average charge and the variance as a function of the parameters of the plasma ne/ni, Te/Ti, and Me/Mi. Finally, the methodology is extended to non-Maxwellian plasmas using the Druyvesteyn as an example.

We consider the stochastic properties of charge fluctuations of noninteracting particles surrounded by a stationary, undisturbed plasma of electrons and singly charged positive ions. For unscreened Coulomb interaction in the orbit–motion limit the mean particle charge and the variance of the fluctuations are proportional to the particle size. The result applies to both Maxwellian and non-Maxwellian electrons as well as to charging by ion winds. When the polarizability of the particle is included in the electrostatic interaction, both the ion and electron currents to the particle increase and the mean particle charge becomes more negative. Except for particles in the low nanometer range, the effect of the polarizability can be neglected at the electron temperatures encountered in typical plasmas.

We present a Fokker-Planck description of the charging of particles weakly in ionized gases and of the charge fluctuations arising from the statistical nature of this process. Charge fluctuations constitute a Markov process and in the limit of linear charging currents or large particles this process is also Gaussian. The time scale of fluctuations is inversely proportional to the particle size and ion concentration and for small particles it is significantly larger than the particle diffusion time. In this regime Brownian diffusion becomes a mechanism by which charge fluctuations are transported into different regions of the plasma.

From the optical emission of and radiative states in the negative glow of DC pulsed discharges at pressures 1 - 4 Torr (133 - 532 Pa) and current densities , it has been determined that the vibrational excitation of the state deviates from a Boltzmann distribution and strong intensities of the second positive system (especially from v = 1) were also observed in the afterglow. Such strong emission is interpreted in terms of the growing of the vibrational distribution in the post-discharge region as the gas temperature is reduced. The ) states are mainly produced by electron collisions on ions under discharge conditions and quickly disappear in the afterglow as a result of - electron recombination.