The electronic theory of tape–helix traveling–wave structures

An electronic theory of the operation of tape-helix traveling-wave structures is given. This includes the case of traveling-wave amplifiers and backward-wave oscillators operating on any space harmonic. The method of solution is based upon an integral equation for the longitudinal electric field which is solved approximately for the case of small beam currents. This method is equally applicable to thin beams, thick beams, and annular beams with or without a transverse variation of dc density or velocity. Explicit expressions are obtained for the impedance and space-charge parameter of each space harmonic.