Analytic, nonlinearly exact solutions for an rf confined plasma

Abstract

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 et al., 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+Acos(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.

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

“…19, and it was found that the time-averaged plasma density is different from Eq. 19, and it was found that the time-averaged plasma density is different from Eq.…”

“…9,10 And for the case of electromagnetic waves, one of the most active areas of research over the past decade has been laser wake-field acceleration. [19][20][21] For the case of an oscillatory electric field with a general spatial dependence, conventional ponderomotive theory 10,22-29 has been widely used to predict the time-averaged plasma density. [16][17][18] Under the influence of oscillatory electric fields, the distribution function and density of a plasma also have oscillatory components.…”

Unifying averaged dynamics of the Fokker-Planck equation for Paul traps

“…However, if the externally applied field is much stronger than the induced field, the latter can be ignored [16]. The Vlasov equation has been solved earlier for the case of a spatially linear time-periodic electric field and it has been found that the solutions are typically aperiodic in time, but can also be periodic for certain specific initial conditions [3,17]. This leaves open the question as to which of these infinitely many distributions obtained by solving the Vlasov equation actually gets manifested in an experimental setting.…”

Modified nonlinear evolution of Langmuir waves

“…Though the conventional ponderomotive theory has been widely used for the last few decades in describing plasma dynamics, it has been recently shown to have severe limitations. [13][14][15][16] Under certain conditions, it has been shown that instead of the square of the electric field, the plasma density depends on the square of the electric potential. 16 Thus, instead of Eq.…”