Electromagnetic Properties of a Plasma-Beam System

There are two electromagnetic modes in a plasma-beam system: the unstable "hybrid" mode characterized by the occurrence of a longitudinal component of the electric intensity E, and the transverse mode which does not show an instability and is characterized by the occurrence of a longitudinal component of the magnetic induction B. The behavior of this system is described in terms of macroscopic quantities such as the electric displacement D and the magnetic intensity H. The unstable hybrid mode in a plasma-beam medium is compared to related hybrid instabilities produced by a beam in a medium comprising harmonic oscillators. It is thus shown that the hybrid instability produced in a plasma is of type "$l$," as defined in Part I. Applying the appropriate criterion, it is found that the hybrid instability and the associated longitudinal instability are convective for $\theta \ne 0$, where $\theta$ is the angle formed by the direction of the beam and the direction of the growing waves resulting from these instabilities. For $\theta$ approaching $\frac{\pi }{2}$ the instability produced by the beam becomes aperiodic. The plasma-beam system is electromagnetically anisotropic and its anisotropy is investigated with reference to transverse and hybrid waves. For transverse waves the anisotropy is described in terms of a dependence between $\phi$ and $\theta$, where $\phi$ is the angle formed by the vectors H and B. For hybrid waves the anisotropy is investigated in the "region of transparency" and in the "region of instability." In the region of transparency there is a dependence between $\psi$ and $\theta$, where $\psi$ is the angle formed by the vectors D and E. In the region of instability there is a similar angular dependence and also a phase difference between the longitudinal and transverse components of the electric intensity E. Some of the effects produced by a beam in a thermal plasma are investigated in hydrodynamic representation. A formal analogy is established between the Vavilov-Cherenkov effect produced by a single particle passing through a thermal plasma and the longitudinal instability produced by a beam having the same velocity as the particle. This analogy does not apply to hybrid waves.