Approximate analytic theory of the multijunction grill

A general approximate analytic theory of the multijunction grill is developed. Omitting the evanescent modes in the subsidiary waveguides both at the junction and at the grill mouth and neglecting multiple wave reflection between the same places we derive simple formulae for the reflection coefficient, the amplitudes of the incident and reflected waves and the spectral power density. All these quantities are expressed through the basic grill parameters (the electric length of the structure and the phase shift between adjacent waveguides) and two sets of the reflection coefficients describing wave reflections in the subsidiary waveguides at the junction and at the mouth. The approximate expressions for these coefficients are also given. The results are compared with numerical solution of two specific examples and they prove to be useful for the optimization and design of the multijunction grills. For the JET structure, which is composed of multijunction sections, it is shown that, in the case of the dense plasma, many results can be obtained from the simple formulae for two-waveguide multijunction grill.A part of this work was done at the stay of the second author in the Joint Institute of Nuclear Research in Dubna and he wishes to thank that Institution for hospitality.