Instability of a thin field-aligned electron beam in a plasma

The formulation of Elliott (Planet. Space Sci.; 23:751 (1975)) is recapitulated somewhat more elegantly for a monoenergetic beam of 'Top Hat' profile. The mode corresponding most closely to the parellel-polarized mode in a uniform beam is explored for phase velocities less than the beam velocity and frequencies between the hybrid frequencies. The mere existence of solutions indicates the possibility of instability in some real case. Solutions are found for all frequencies except for a range above the gyrofrequency, beyond which a ducted solution exists up to the plasma frequency. In the other range radiative solutions exist. The nature of the results provides a guide for several applications, but more realistic models must be specific to the application. (author)