EQUILIBRIUM AND SPACE-CHARGE WAVE ANALYSIS OF ELECTRON-BEAMS IN CONDUCTING AND ABSORBING GYROTRON BEAM TUNNELS

The fluid equations for an electron beam are used to calculate the equ ilibrium velocity and density profiles, limiting current and space-cha rge wave properties of an annular beam undergoing magnetic compression in a gyrotron beam tunnel. Both non-relativistic and relativistic equ ations are derived. The beam tunnel may have a conventional smooth wal l or an absorbing dielectric-loaded wall. Small values of magnetic com pression are seen to have large effect on the profiles and the current limit of a given tunnel. Common dielectric-loaded tunnels are also se en to reduce the limiting current by 5%-20%. Limiting current data for a wide range of beam parameters are shown. The dispersion relation fo r a convective instability arising from the gradient in the equilibriu m potential depression profiles is derived using the linearized fluid equations. The growth rate is seen to increase for increasing current and pitch angle, and for increasing wall effects of an absorbing tunne l. The average growth rate is calculated for a typical gyrotron beam a nd beam tunnel as well as for a beam entering an interaction cavity. G rowth rates for all values of k(z) are seen to decrease to zero for a conventional conducting beam tunnel in a constant magnetic field.