The linear dispersion relation for electrostatic electron waves is analysed in some detail. A method is described which allows the dispersion equation to be solved and the attenuation rate/growth rate to be derived for waves generated by electrons flowing through a stationary plasma along the field lines of a static magnetic field. The solution is derived from three simple curves (one for each of the real and imaginary parts of the dispersion equation and one for the growth rate) and is applicable for any propagation angle relative to the magnetic field lines (below a limiting value), for any wavelength, any magnetic field intensity, any electron density and temperature and any flow speed of a beam plasma component. The effects of cyclotron resonance start to be significant at an angle from the direction of the magnetostatic field lines that depends on most of the variables mentioned, but only in one specific combination, which is the measure of the ratio between thermal velocity of the electrons and the phase velocity of the wave at the cyclotron frequency. In contrast to numerical methods, the method described here provides a parameterization of the solutions to the dispersion equation and of the growth rate. It gives an overview of the dependencies on the variables in the equation over a large part of parameter space without any other computations than those involved in adjusting scale factors.
Narrow-Band Čerenkov Radiation Generated in a Silicon Foil
