Particle dynamics in dusty plasma: Classical tunneling

A Hamiltonian formalism for studying the dynamics of a dust particle with variable electric charge in dusty plasma is proposed. The Hamiltonian and the equations of motion are presented, and the dynamics is shown to be conservative. The problem is cast in terms of the motion of a particle with a constant fictitious charge $Q A$ moving in a suitably defined potential, while the actual particle charge is spatially distributed. With this formalism, the problem of trapping of dust particles in potential wells and barriers is studied. The results show that because of the spatial “delocalization”/distribution of the particle charge, a particle with insufficient energy to cross the potential barrier can penetrate it to tunnel out, i.e., “classical tunneling,” similar to a high jumper clearing the bar by the Fosbury flop technique or the usual quantum tunneling. For energies greater than a critical value, the charged particle is shown to tunnel out of even an infinitely deep potential well. A modified criterion for trapping in potential wells is given.