Mode coupling in nonuniform waveguides and optimal design of waveguide tapers and mode converters

Gyrotrons are sources of high-power millimeter waves. Current interest in gyrotrons is mainly because they can act as a source of microwave power for electron-cyclotron-resonance heating (ECRH) for fusion experiments. However, the field pattern of these gyrotron modes is unsuitable for long path waveguide transmission or plasma heating. Here, it is desired to have a linearly polarized wave requiring the use of a mode conversion system which consists of many nonuniform waveguide components.; In this work, we study wave propagation in nonuniform waveguides, i.e., waveguides with conducting walls whose cross sections are not uniform along the waveguide axis, by employing the coupled mode formalism. The coefficients of this system are called the coupling coefficients. In this dissertation, we derive the coupling coefficients for some nonuniform waveguides used in mode converter systems for use with gyrotrons in ECRH systems. The cases considered are tapered circular waveguides with small wall deformations, circular waveguide tapers with conducting walls which are slightly lossy, and coaxial waveguides with varying-radius center- and outer-conductor profiles. All of the waveguides are assumed to be overmoded.; We design a compact quasi-periodic TE{dollar}sb{lcub}02{rcub}{dollar}-TE{dollar}sb{lcub}01{rcub}{dollar} coaxial mode converter with a varying-radius center conductor and a uniform outer conductor and also design short coaxial waveguide tapers for TE{dollar}sb{lcub}01{rcub}{dollar} and TE{dollar}sb{lcub}02{rcub}{dollar} modes where the cross section of the center conductor is gradually increased from some prescribed input diameter to a given output diameter.; We also design optimal waveguide tapers by employing a theorem frequently used in optimal control theory, the Pontryagin minimum principle.; Experimental results are reported for a mode converter which consists of a tapered circular waveguide with small wall deformations which is to convert the TE{dollar}sb{lcub}22,6{rcub}{dollar} gyrotron mode to a mode mixture that gives a nearly Gaussian field distribution in the Vlasov launcher and a coaxial waveguide mode converter with varying-radius center and outer conductors which converts some of the TE{dollar}sb{lcub}02{rcub}{dollar} input mode to the TE{dollar}sb{lcub}01{rcub}{dollar} mode at the output.