Fast algorithm for numerically integrating equations of motion for large particles in microwave devices

An algorithm for numerically integrating the equations of motion for large particles is formulated. The algorithm is represented in three forms–an explicit form, a predictor–corrector form, and a modified form that is intended for simulating the motion of relativistic particles in an electromagnetic field. The order of precision of the proposed algorithm is analyzed. The results of a comparison with standard algorithms are presented. The efficiency of this algorithm is demonstrated in considering the test example of a harmonic oscillator and in numerically simulating the Pierce diode in the mode of virtual-cathode formation.