Ion Compensation for Space Charge in the Helical Electron Beams of Gyrotrons

We solve analytically the problem about ion compensation for the space charge of a helical electron beam in a gyrotron operated in the long-pulse regime. Elementary processes, which take place during ionization of residual gas in the tube under typical pressures of 10⁻⁶–10⁻⁷ mm Hg, are considered. It is shown that distribution of the space charge is affected mainly by the electrons of the initial beam and slow-moving ions produced by ionization of the residual gas. Steady-state density of ions in the operating space of the gyrotron after the end of the transitional processes is found, as well as the electron density profile in the channel of electron beam transportation. The results obtained allow us to evaluate the pitch-factor variations caused by partial compensations for the potential “sagging” in the gyrotron cavity, thus being useful for analysis of starting currents, efficiency, and mode competition in high-power gyrotrons.