Multiple Boris integrators for particle-in-cell simulation

We construct Boris-type schemes for integrating gyrationof charged particles in particle-in- cell(PIC) simulation. The new solversvirtually combine the classic 2-step Boris solverarbitrary $n$ times, and therefore we call them the multiple Boris solvers. Using Chebyshev polynomials, a one-step form of the new solversis provided. The new solversgive $n^2$ times smaller errors and allow larger timesteps. We finally present numerical tests of the new solvers, in comparison with other particle integrators.