Last modified: 2017-05-13
Abstract
Processes of interaction of charged particle fluxes with substance are a base of operation of a wide range of devices for scientific researches and vacuum technological installations for various purposes. Besides, an important independent scientific and technical task is a task to control parameters of such fluxes by influencing of electrical and/or magnetic fields of a specified configuration on them.
The paper shows a mathematical instrument and algorithms for simulation of the electrical field in electron-optical systems with complicated configuration of electrodes by the boundary element method (BEM). The boundary element method solves an exterior Dirichlet's problem under digitization of a multiplied connected boundary of the area by straight boundary elements. Integral equation being a basic for the method is found from the second Green’s formula.
Biot-Savart-Laplace law is used for numerical simulation of the magnetic field for a set of arbitrarily oriented round solenoids. Besides, each turn of the solenoid is divided into current elements having a physically short extent. Calculation of the magnetic field of a two-dimensional shape (turn) in space is reduced to calculation of coordinates of elementary current middles and their projections on the axes 0x and 0y. Magnetic field of a solenoid is calculated as a superposition of fields of all its turns. Magnetic field of the arbitrarily oriented solenoid can be found by means of direct and reverse rotations of the Cartesian coordinate system for angles being equal to angles setting an orientation of solenoids in space. Magnetic field of a set of arbitrarily oriented solenoids is calculated according to the superposition principle.
Developed methods have been integrated into the computer application and used under design of the microfocus x-ray tube of high power. Acceleration and focusing of the electron beam in the tube is executed by the electrostatic field and its positioning to the required area on the anode – by the magnetic field of two external solenoids.