Space Charge Waves along Magnetically Focused Electron Beams

The propagation of perturbations along electron beams of finite diameter is determined by boundary conditions. The solutions of the problem-the phase-eigenvalues or the plasma frequency reduction factor-depend on the way the perturbations of the beam surface are taken into account. A cylindrical uncompensated beam (void of ions) confined by an arbitrary coaxial magnetic field is considered. Two different procedures are compared: one assuming a surface current, the other introducing additional but continuous ac space charges and currents over the beam cross section.