| Abstract: | The linearized Vlasov equation with collision damping is solved by the method of normal modes of Van Kampen and Case. The system considered is an infinitely extended nonrelativistic nondegenerate electron gas with neutralizing ion background and neutral particles. There is no magnetic field. Collision damping is taken into account by complete Bhatnagar-Gross-Krook collision integrals for electron-electron collisions and electronion collisions; in the case of a partially ionized gas elastic collisions between electrons and neutrals can be included likewise. The Vlasov-BGK operator is transformed into an integral operator yielding complex singular normal modes even if the equilibrium distribution is a Maxwellian. The adjoint integral equation belongs to a more complicated type than that of a collision-free system. Its solutions must be orthogonalized. The set of all normal modes is complete rendering the exact solution of the initial value problem possible. The completeness is shown by transformations and regularization of the singular integral equation of the initial value problem, the techniques of Case not being applicable because of the complicated type of this equation. |
