Abstract: The focal dimension of the X-ray source with microbeam is in proportion to the size of the e-beam focused on the target surface. The finite difference method is utilized to calculate the distribution of the electrical-field intensity. The track of the electron-beam is traced by using the Runge-Kutta method within the whole symmetrical system. As a result, the diameter of the electron beam focus is 0.6-1.0μm while the total high brightness emission of the LaB₆ crystal cathode is 0.06-0.3mA.

Key words: finite difference method, optimal coefficient, X-ray source with microbeam, Runge-Kutta method