Some properties of large-amplitude electrostatic waves (Allis modes)

Allis modes are large-ampliturde, undamped electrostatic plasma waves, in which the trapped electron distribution is the analytic continuation of the untrapped distribution. Allis modes can be pulse-like, as well as periodic. As the amplitude of the periodic solutions increases, the frequency decrsases and the wavelength increases, leading finally to solitary pulse solutions as a limiting case, reached when an appreciable number of electrons are trapped by the wave. These pluse-like solutions imply a maximum amplitude to Allis modes, and a maximum d.c. current they can drive. A simple approximate expression gives the non-linear properties of Allis modes in terms of the linear properties and the maximum amplitude.