Damping of Collective Excitations in Coulomb Crystals

Abstract

This chapter proposes an expression for the dynamical structure factor, which accounts for collisions and is based on generalized linear response theory. For high values of the coupling parameter, dust grains in a dusty plasma exhibit a solid-state like structure with long range order. Whereas for small values of coupling parameter, a perturbative treatment with respect to momentum eigenstates is well-suited, the ideal crystal represents an appropriate basis. The chapter formulates a systematic approach to the dynamical structure factor of a Coulomb crystal, which is based on a generalized linear response theory and links the response function to equilibrium correlation functions. The chapter also proposes a perturbative expansion starting from the ideal crystal as the unperturbated system, thus expanding the Hamiltonian up to fourth order in the displacement. The dispersion relation is given by the phonon dispersion. Taking into account the collisions in first Born approximation, the corresponding correlation function can be determined. Based on this understanding, an evaluation for a linear chain is feasible. The impact of self-energy effects as well as damping on the dispersion relation can also be studied.