Slow wave propagation in plasma waveguides

It is shown that the space charge wave modes of propagation which are usually associated with the drifting motion of an electron beam can also propagate and carry energy in stationary electron beams or plasmas of finite transverse cross section. The properties of these modes of propagation have been studied by considering the plasma as a dielectric and solving the field equations. The effect of d.c. magnetic fields have been included, while ion motion and thermal velocities have been neglected. These modes have phase velocities which are generally much less than the velocity of light. Two distinct types of propagation are reported; the first involves charge density variation within the plasma (body wave) and the second involves a perturbation of the surface of the plasma (surface wave). Both of these types have modes which exist down to zero frequency as well as backward wave modes. The angular dependent modes can exhibit Faraday rotation. One of the potentially useful features of these modes of propagation is that of plasma diagnostics. The effect of radial charge density variation within the plasma column has been investigated and methods for experimentally determining this variation, as well as the average charge density, are suggested. The effect of collisions on wave attenuation is examined approximately. The interaction of a moving electron beam with these modes is considered, as well as the backward wave start oscillation conditions for backward wave interaction. A qualitative explanation of these modes is given in terms of an equivalent electrical circuit transmission line. Many of the features of these modes have been verified experimentally by measuring the phase velocity along a mercury arc discharge column in an axial magnetic field.