Optimal choice of cell geometry for a multicell superconducting cavity

Abstract

An algorithm for optimization of the multicell cavity cells is proposed. Inner cells are optimized for minimal losses or minimal magnetic field, when the aperture diameter, ${E}_{pk}/{E}_{\mathrm{acc}}$---the ratio of peak electric field to the accelerating field, and the wall slope angle are given. Optimization of the end cells is done for minimal losses or maximal acceleration in them. Two shapes of the end cells---with and without the end irises---are analyzed. This approach facilitates further optimization for higher order modes extraction because it permits keeping the achieved optimal values nearly the same while changing some dimensions of the cells. Comparison of the proposed cavity geometry with the TESLA cavity geometry illustrates the traits of the presented approach. It is also shown that lower values of the wall slope angle, which lead to the reentrant shape for the inner cells, are also beneficial for the end cells. For the Cornell Energy Recovery Linac most dangerous are dipole modes causing the beam breakup (BBU). Minimization of power of higher order modes (HOMs) in a multicell cavity was done using derivatives of the BBU parameter with respect to geometric parameters of the cavity cells. As a starting point of optimization, the shape with minimal losses at the fundamental mode was taken. Further changing the shape for better propagation of HOMs was done with degradation of the fundamental mode loss parameter $G\ifmmode\cdot\else\textperiodcentered\fi{}{R}_{\mathrm{sh}}/Q$ within 1% while decrease of the BBU parameter was nearly 3 orders of magnitude. The BBU threshold current tends to be inversely proportional to this parameter.