Multipactor in crossed rf fields on the cavity equator

Abstract

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.

One-point multipactor in crossed fields of rf cavities

“…After each flight, the particles fall on the surface at a new place shifting from the point of start. This is a difference between MP1 and MP2 where stability in both, phase and space, was found [5].…”

“…The value of p in (9) is dimensionless and as it is shown in [5] does not depend on frequency but only on the shape of the cavity. The same is true for the MP1 if q is proportional to x.…”

“…This condition is satisfied when an electron having an initial phase deviation from an equilibrium returns to the surface with the phase deviation reduced. An analogous condition should be used for the coordinate on this surface, in a similar way as it was done in [5], but it appeared that no space stability for MP1 was found: the particles always shift to the equator after each flight.…”

“…The elliptic cavities have a big dq=dx, for example, for the TESLA cavities this value is 0.29 and for the Cornell ERL cavity it is 0.28 [5], so that MP1 is unlikely in such a geometry. On the other hand, the geometric parameter p introduced in [5] (see also in the next section), is about p ¼ dq=dx ¼ 0:07 for the cavity of Fig. 2, and MP2 does not happen at its equator, MP2 happens when p is about 0.3 and higher.…”

“…An analysis of the two-point MP near the cavity equator was presented recently in detail [5]. Now we will concentrate our attention on the MP1 in the SC rf cavities, analyze some existing experimental data, and compare these two kinds of the rf discharges.…”