Hamiltonian dynamics of dust-plasma interactions

Hamiltonian dynamics of a collection of charged dust particles interacting with electric fields in the sheath region of a low-temperature plasma is studied. It is shown that the wake potential is formed behind a moving dust particle when virtual phonons are exchanged between dust grains moving relative to the ambient plasma, while the wake potential vanishes if the dust grains are stationary with respect to the plasma. The semiclassical Hamiltonian formulation is also applied to obtain dispersion relations for transverse and longitudinal oscillations associated with chains of dust grains levitated in the balance of gravitation and electric sheath field.