Variational calculations for resonance oscillationsof inhomogeneous plasmas

In this paper, the electrostatic resonance properties of an inhomogeneous plasma column are treated by the Rayleigh-Ritz method. In contrast to Parker, Nickel &Gould (1964), who carried out an exact computation, we use a description of the RF equation of motion and pressure term that allows us to express the system of equations in Euler-Lagrange form. The Rayleigh-Ritz procedure is then applied to the corresponding Lagrangian, to obtain approximate resonance frequences and eigenfunctions. An appropriate set of trial co-ordinate functions is defined, which leads to frequency and eigenfunction estimates in excellent agreement with the work of Parker et al. (1964).