Some problems of mathematical simulation in optimization design of electrostatic image tubes

Three problems of mathematical simulation have been discussed in the present paper when optimizing the electron optical system of electrostatic image tubes. The multigrid method (MGM) is suggested for solving the rotational symmetrical electrostatic field, it proves that the computational efficiency of MGM is 2 - 4 times better than the traditional finite difference method when the same accuracy of iteration is reached. The constrained variable metric method, which ensures the design to have fast convergency, high efficiency and lesser number of times of calling for objective function, is recommended for optimization design. The objective function having a least-square-fit form with weight factors is investigated for the problem of nonlinear multi-objective optimization. The result of optimization appears that the suggested mathematical methods given in the paper for optimization design of electrostatic image tubes are practical and effective ones.