LINEAR-ANALYSIS OF BACKWARD-WAVE OSCILLATIONS IN AZIMUTHALLY VARYING TRANSVERSE ELECTRIC (TE) MODES

A linear analysis for a gyrotron backward wave oscillator operating at a general transverse electric (TE(ln)) mode of a cylindrical waveguid e (slotted or uniform cross section) has been developed using a Maxwel l-Vlasov equation under the tenuous beam approximation. The equation i s solved by Laplace transformation to allow easy insertion of the boun dary values. The start-oscillations conditions are determined from an interference of the waveguide and beam modes with appropriate amplitud es and phases. The theory is used to determine the design parameters f or stable operation of a second cyclotron harmonic gyropeniotron ampli fier at 35 GHz in the pi mode of a six vane magnetron-type circuit wit h a 70 kV, 3 A beam.