Kinetic description of free streaming mode in an electron beam propagating through a tape helix waveguide

Stability properties of the free streaming mode in a relativistic electron beam propagating through a cylindrical waveguide loaded with a tape helix are investigated, in connection with the traveling wave tube amplifier. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations for an electron distribution function, in which all electrons have a Lorentzian distribution in the axial canonical momentum. Closed algebraic dispersion relations of the free steaming mode for both annular and solid beams are obtained. One of the most important features of the analysis is that the growth rate and range of instability increase drastically as the outer conducting wall approaches to the helix. For an appropriate choice of the radii of the helix and the outer conducting wall, it is shown that the instability range can be more than triple that for a traveling wave tube without conducting wall. However, the growth rate and range of instability are substantially reduced by increasing the axial momentum spread.