Variational calculations for resonance oscillations of 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).