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Multipactor discharge in an accelerating superconducting elliptic cavity occurs usually near its equator. As simulations show, the dimensions of the trajectories of multipacting electrons are very small compared to the dimensions of a cavity. This feature gives a way for solving explicit equations of motion instead of cumbersome simulations. Electric and magnetic fields near the cavity equator are presented in a form of expansions up to the third power of coordinates. Comparisons with numerical calculations of fields made with the SLANS code for the TESLA cavity cells, as well as with the analytical solution for a spherical cavity, are done. These fields are used for solving the equations of motion of electrons in crossed rf fields near the equator. Based on the analysis of these equations, general features of multipacting in this area are obtained. Results are compared with simulations and experimental data. The experimental formulas for multipacting zones are explained and their dependence on the cavity geometries is shown. Because of small sizes of electron trajectories, the influence of the weld seams is taken into account. This suggests a possible explanation of multipacting in a cavity which was not found by simulations. The developed approach allows evaluation of multipacting in a cavity without its simulations but after an analysis of fields in the equatorial region. These fields can be computed by any code used for cavity calculation

Multipactor in crossed rf fields on the cavity equator