Singular value decomposition as a tool for solving of spectral problems arisen in supercollider simulation

All accelerating part of a linear collider is considered. To maximize the accelerating gradient, profiles of amplifying radial channels of a. supercollider are required to be optimized. A spectral problem - to find profiles of waveguide channels providing zero eigenvalue for Helmholtz type operator under corresponding boundary conditions - is settled. A constructive algorithm for this zero eigenvalue problem basing on the method of discrete sources together with singular value decomposition technique is developed. To check on the possibilities of this numerical algorithm, an analytical test problem is suggested. Several types of boundary profiles for amplifying waveguide channels are considered. Optimal parameters for these profiles are obtained.