EFFECT OF A GRAIN SIZE DISTRIBUTION ON THE RESPONSE OF A DUSTY PLASMA TO A MOVING TEST CHARGE

Dust in a plasma modifies the response to a moving test charge. In general, the dust has a distribution of grain sizes. The linear kinetic behaviour is then quite different to the case with single sized grains. For a reasonable choice of the size distribution the contribution of the dust component to the dispersion relation is equivalent to that for a kappa (generalised Lorentzian) distribution of single-sized particles. Expressions for the potential of a slowly moving test charge, correct to second order in the velocity, are found. TEST CHARGE POTENTIAL IN DUSTY PLASMA The linearised potential due to a test charge q moving with velocity vq in a non-magnetised plasma is (cf [1]): φ = q / 4piε 0(2pi 2)−1 exp(ik.x)/{k2 ∫ ε p (k,k.vq)}d3k (1) where εp is the plasma dielectric response function. The dust grains are assumed to have a thermal velocity distribution with temperature T, and size distribution h(a) which has a power law for small radii, a, and for large masses, m(a), decreases with an exponential factor [2]: dnd = f (a,v)dadv = h(a) fT (v)dadv = Ca βe−