Space charge wave packets generated by cathode-directed ionization waves in discharge tubes

A quasi-one-dimensional theory of propagation of ionization waves (IW) stimulated by runaway electron beams accelerated in a low-pressure gas is developed. Such waves determine the virtual anode propagation during the prebreakdown stage of a transient hollow cathode discharge as well as a fast capillary discharge for which the discharge tube is surrounded by a shield that has the cathode potential. It is shown that a wave packet (WP) of plasma oscillations underlies the structure of the IWs. The frequency of the oscillations increases from the leading edge of the IW to its trailing edge due to the continuous ionization. Such a structure of the WPs differs from the classical nonlinear solitary waves that are filled with Langmuir oscillations. A parametric study of the main characteristics of the IWs and the space charge WPs for various values of the initial gas pressure, tube radius, and applied voltage is carried out.