Excitation of Longitudinal Waves in a Bounded Collisionless Plasma

The relativistic form of the Vlasov equation is used to derive an integral equation for an externally produced electric field oscillating with frequency ω in a plasma bounded by two specularly reflecting walls. A tentative solution is constructed from exact solutions of the half‐space problem. It is shown that the exact equation is satisfied by the tentative solution up to terms which are exponentially small in the number of Debye lengths across the plasma. It happens that the bounded plasma acts like a medium with a dielectric constant κ=[1−ω p 2 /ω 2 (1−5KT/2mc 2 )] , unless the driving frequency lies in the small band ω p 2 (1−5KT/2mc 2 )