New motion algorithm in the particle-in-cell method

Abstract

The article proposes a new method for solving the equations of motion of charged particles in electromagnetic fields. In the algorithm, the velocity of a charged particle at a time step is computed in accordance with the exact solution of the differential equation. The method has been compared with various known modifications of the Boris method. The comparison was carried out both in terms of the accuracy of the methods and the time of their operation. A new modification of the method uses the fact that the electric and magnetic fields are constant at a time step. It allows one to compute more accurately the trajectory and velocity of a charged particle without significant increasing the complexity of the computations. It has been shown that when choosing a modification of the Boris method to solve a problem, one should pay attention first of all to the accuracy of the solution, since a simpler and faster scheme may not give a gain in time.