RF Space-Charge Effects in CRM with Arbitrary Phase Velocity of the Operating Wave

The simplest elementary source of RF space-charge field in the form of a helix rotating with the frequency of the operating wave is proposed. The use of these sources (mutually interacting) allows one to describe the main space-charge effects for different varieties of CRMs in both linear and nonlinear regimes. It is shown that, like in the subrelativistic gyrotron, due to development of the quasielectrostatic negative-mass instability, the space charge increases the increment in the amplifier and decreases the starting current in the oscillator.