LANDAU DAMPING AND TRANSIT-TIME DAMPING OF LOCALIZED PLASMA-WAVES IN GENERAL GEOMETRIES

Landau's original derivation of the collisionless damping of small-amp litude Langmuir waves in an infinite homogeneous plasma relied on the introduction of complex velocities and was therefore somewhat difficul t to interpret physically. This has inspired many subsequent derivatio ns of Landau damping that involve only real physical quantities throug hout. These ''physical'' derivations, however, have required the calcu lation of quantities to second order in the wave field, whereas Landau 's approach involved only first-order quantities. More recent generali zations of Landau damping to localized fields, often called ''transit- time damping, ''have followed the physical approach, and thus also req uired second-order calculations, which can be quite lengthy. In this p aper it is shown that when the equilibrium distribution function depen ds solely on the energy, invoking the time-reversal invariance of the Vlasov equation allows transit-time damping to be analyzed using only first-order physical quantities. This greatly simplifies the calculati on of the damping of localized plasma waves and, in the limit of an in finite plasma, provides a derivation of Landau damping that is both ph ysical and linear in the wave field. This paper investigates the trans it-time damping of plasma waves confined in slabs, cylinders, and sphe res, analyzing the dependence on size, radius, and mode number, and de monstrating the approach to Landau damping as the systems become large . It is also shown that the same approach can be extended to more gene ral geometries. A companion paper analyzes transit-time damping in a c ylinder in more detail, with applications to the problem of stimulated Raman scattering in self-focused light filaments in laser-produced pl asmas. (C) 1998 American Institute of Physics. [S1070- 664X(98)00912-4 ].