THE ACCELERATION OF STATIONARY CHARGED DUST GRAINS BY PROPAGATING COLLISIONLESS SHOCK WAVES

We consider the acceleration of charged particles, which are initially completely at rest with respect to the local upstream plasma rest frame, by collisionless shocks propagating through a static, irregular magnetic field. A relevant example is the interaction of cold, charged interstellar dust grains with a shock associated with a supernova blast wave propagating through the fluctuating interstellar magnetic field. We treat the dust grains as test particles moving under the influence of electromagnetic forces arising from a magnetic field which has an average plus a fluctuating part, and is static in the local plasma frame. The only electric field is that which arises from the flow of plasma across the magnetic field. We find that a significant fraction of the dust grains are accelerated to more than 10 times the shock speed within 100 cyclotron periods. The percentage of those incident on the shock that are accelerated depends strongly on the turbulence variance, but is essentially independent of average shock-normal angle provided the fluctuation amplitude is of the same order as the mean. Our results are relevant to the 'injection problem' in shock acceleration of charged particles.