Kinetic theory for a distribution of ionized dust particles

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Abstract
Dust particles, assumed to be of one size and to exhibit a discrete distribution of electric charges, are treated as heavy ions with a large number of ionization levels. The average of the discrete particle effects on the kinetic equations is approximated by the Lénard–Balescu collision term and by detailed counting to describe transport in velocity space and transitions between the differentionization levels respectively. We estimate analytically and numerically the relaxation times for the dust particles both towards a Maxwellian velocity distribution and towards an equilibrium distribution for the ionization levels. We sum over the ionization levels to obtain a hierarchy of ‘charge-moment’ equations for the single dust density function, and estimate the importance of terms originating from the ionization distribution. Similar terms are also present in the hydrodynamic equations for a dust plasma, and we briefly discuss these.