Analytic, nonlinearly exact solutions for an rf confined plasma

RF confined electron plasmas are of importance in Paul traps [W. Paul, Rev. Mod. Phys. 62, 531 (1990)]. The stability of such plasmas is unclear and statistical heating arguments have been advanced to explain the observed heating in such plasmas [I. Siemers, Phys. Rev. A 38, 5121 (1988)]. This study investigates the nature of a one-dimensional collisionless electron plasma that is confined by an rf field of the form [-B+A cos (ωt)] x, where x is the space coordinate and ω is the rf frequency. Nonlinearly exact solutions are obtained. The distribution function and the plasma density are obtained in closed form and have constant shapes with time varying oscillations. These oscillations are at the rf frequency and its harmonics, modulated by a low frequency related to the electron bounce time. The linear limit of weak fields is recovered. Analytic expressions are obtained for the required external field to make it consistent with prescribed distribution functions. These solutions remain valid even in the presence of collisions. Solutions involving multiple species are also obtained, though only for collisionless traps. It is found that the ponderomotive force response needs to be corrected to account for the temperature fluctuations. No stochastic heating is observed in this field configuration. © 2008 American Institute of Physics.