Higherorder terms in a perturbation expansion for the impedance of a corrugated waveguide
Abstract
A circular waveguide is considered whose radius a(z) = a(1+ epsilon s(z)) varies periodically with the axial coordinate z. ChatardMoulin and Papiernik introduced a perturbation expansion in powers of epsilon for the longitudinal impedance of such a waveguide. The derivation of this expansion is reformulated in a manner which elucidates the structure of the higherorder terms, and allows the determination of the dependence on epsilon of the resonant frequencies. For a squarewave (SW) wall distortion, there are divergent coefficients in the perturbation expansion. Hence, a special treatment is required in this case, and a calculation of the resonant behavior is presented for small epsilon, using an approach which does not assume an expansion in powers of epsilon. The resulting expression for the resonant impedance involves functions singular at epsilon = 0; however, to leading order in epsilon, the lossfactors and resonant frequencies are in agreement with perturbation theory.
 Publication:

Presented at the Particle Accelerator Conf
 Pub Date:
 1981
 Bibcode:
 1981paac.confR..11K
 Keywords:

 Impedance;
 Perturbation Theory;
 Series Expansion;
 Square Waves;
 Waveguides;
 Circles (Geometry);
 Electromagnetic Fields;
 Kernel Functions;
 Pade Approximation;
 Resonant Frequencies;
 Electronics and Electrical Engineering