  We construct Boris-type schemes for integrating the motion of charged
particles in particle-in-cell (PIC) simulation. The new solvers virtually
combine the 2-step Boris procedure arbitrary n times in the Lorentz-force part,
and therefore we call them the multiple Boris solvers. Using Chebyshev
polynomials, a one-step form of the new solvers is provided. The new solvers
give n^2 times smaller errors, allow larger timesteps, and have a long-term
stability. We present numerical tests of the new solvers, in comparison with
other particle integrators.
