Plasma response to nonlinear time-periodic electric fields in one dimension

Plasma response to spatially nonuniform time-periodic electric fields is of importance in many applications For the case of a spatially linear monochromatic electric field in Paul traps, exact analytic expressions for the time-dependent plasma distribution function have been recently obtained [K Shah and H S Ramachandran, Phys Plasmas 15, 062303 (2008)] In this paper, the problem of plasma response to a one-dimensional time-periodic electric field with a general spatial dependence is considered and analytic expressions for the time-averaged plasma distribution function and density are derived by solving the Vlasov equation under two limiting cases of high and low frequencies Under this approximation, it is shown that the time-averaged plasma density is a function of the square of the oscillatory electric potential (C) 2010 American Institute of Physics [doi 10 1063/1 3496050]