Electrostatic Relaxation Waves in an Isotropic Lorentz Gas

A calculation of the dispersion of electrostatic waves in a Lorentzian electron gas takes Landau damping and the detailed balancing of elastic electron-atom collisions rigorously into account. As a special case, the further analysis is restricted to rigid elastic spherical molecules and a monoenergetic distribution of electron velocities. This eliminates Landau damping and Van Kampen modes in favor of new effects associated with the collision process. One thus exposes a discrete spectrum of pseudo-sound waves and a continuous spectrum of relaxation waves both due to the infinitely many harmonic patterns into which electrons can be scattered by elastic spheres.