On the theory of longitudinally inhomogeneous waveguides with impedance walls

Abstract

The Maxwell equations for longitudinally inhomogeneous (irregular) waveguides with impedance walls are reduced equivalently to a system of ordinary differential equations by applying transverse expan sions. The obtained system of equations for amplitudes of the coupled modes is used to analyze gyrotron cav ities. Specifically, the effect of mode conversion and ohmic losses on the eigenfrequencies, quality factors, and field distributions in the gyrotron cavities operating in the submillimeter range is investigated.

Mode Discrimination by Lossy Dielectric Rods in Cavities of Second-Harmonic Gyrotrons

“…Moreover, contrary to [16,17,19,23,29], we propose to equip the gyrotron cavity with a uniform coaxial insert, which can be more easily fabricated to close tolerances and causes no or little mode conversion. Note that although the effect of mode conversion is well-known [43][44][45][46][47], its influence on the beam-wave interaction in gyrotron cavities still remains poorly explored [48].…”

Starting currents of modes in cylindrical cavities with mode-converting corrugations for second-harmonic gyrotrons

“…1). We neglect conversion of radial cavity modes due to slow variation of the cavity radius   R z [26][27][28][29][30], and first assume that the cavity is made of a perfect electric conductor. Such a corrugated cavity supports pure TE modes ( 0 z E  ).…”

“…Contrary to conventional cylindrical cavities, these cavities, however, can exhibit unwanted conversion between coupled radial modes due to abrupt change of the longitudinal (axial) structure. Even though such mode conversion is well-studied in cold cavities [26][27][28][29][30], its effect on the beam interaction with first-and second-harmonic modes still remains poorly explored [31] and therefore may present a hidden factor in designing the advanced cavities for secondharmonic gyrotrons.…”

Theory of irregular impedance waveguides: Generalized method of separation of variables

“…After some algebraic manipulations (details are addressed elsewhere [12][13][14]), these equations can be reduced to two sets of ODE:…”

“…All partial zderivatives entering to (8) can be expressed in terms of 0 A , A and 0 B , B and their derivatives [14]:…”