Radial oscillations of a plasma cylinder with arbitrary density distribution

This research note discusses the radial hydromagnetic oscillations of a plasma cylinder confined by an axial magnetic field for the general case of an arbitrary distribution of mass. The oscillation frequency is expressed in terms of the value for an annular distribution multiplied by a correction factor, g. Values of g are calculated analytically for several simple distributions and the results compared with those obtained by a numerical method and using a variational principle. The numerical and variational methods are used to calculate g -values for other distributions, including examples from the Hain-Roberts theta-pinch code and from a theta-pinch experiment. The value of g varies from 1 for an annulus to about 1.4 for a distribution peaked on the axis. These simple calculations show that an accurate value of the plasma mass can be obtained when the oscillation and density distribution are known.