I. Sh. Beluga, I.M.Sokolova
PLATAN RI, Fryasino, Russia

   An electrostatic electron-optic system with a plane thermocathode is calculated. he system of any complexity may contain metallic and dielectric details. A space charge of the electron beam and variations of initial velocities of thermoelectrons are taken into account. Beams with great variations of cross-section radii (beams with a crossover) may be calculated with a sufficient precission. A beam current, beam radis and current density on the axis are calculated. A beam cutting on electrodes is taken into account. The configuration of the system and of the beam and also distributions of the current density on the cathode and in some cross-sections of the begam may be drawn on the display screen. The program may be used for the invertigation the wide class of the electron devices, specially for electron-beam tubes. The electrostatic field is represented by the sum of beam space charge field and the field of surface charges on electrodes. The space charge field is calculated by integration in the beam space. The surface charge density is calculated by the method of integral equations. Then the field in every point of space may be calculated by surface integrals. The field distribution used in calculating of electron trajectories is represented by three terms in power series expansion of a distance r from the axis. Co-ordinates of electron trajectories is represented in any cross-section by three order polynomials of initial co-ordinates and velocities of electrons. Coefficients of these polynomials are calculated as a decisionof Cauchy problem for a system of ordinary differential equations. This permits to calculate many (some thousands) trajectories in a limited time. The space near the cathode is represented by some rings of a small axial thickness (15 - 30 microns). Such a ring is considered as a part of a plane diode. The theory of a plane diode permits to calculate cathode current density taking into account the cathode temperature and the current density of saturation. The program is exploited on personal computers.

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