A generalized treatment of the electrostatic instability of rippled non-neutral magnetically focused electron beams

A generalization of the stability analysis of rippled non-neutral electron beams is presented. The treatment covers regimes ranging between those known as ‘n flow’e/2i) and ‘ flow’« considers electrostatic surface waves with azimuthal symmetry (l= 0) as well as harmonic modes (I ≠h long-wavelength and short-wavelength domains are analysed. A general discussion of instability is given in terms of the solution of the Mathieu-Hill equation. New unstable modes are found and their growth rates are derived and compared.