The method of calculation of potentials for the field determination elements of non-linear ion mirror

А method for calculating of the non-uniform electrostatic field of the mass reflection reflector is described. The method allows to calculate the axial potential distribution in the reflector theoretically eliminating dispersion of the total time of flight for axial achromatic ion packets in a given range of the initial energy of the ions. By the method of the numerical simulation the analysis of the errors influence for the field physical synthesis close to the real reflector on the focusing accuracy is carried out. The calculation procedure of the reflector with an inhomogeneous field is proposed. The description of the potentials optimization algorithm for field-determination elements is given. The recommendations to reduce execution time of the algorithm are given. The design used for verification of the optimization algorithm is described; the results of simulation of the focusing procedures for ions of different masses and different initial energy spreads are given.