# Multiple Boris integrators for particle-in-cell simulation

## TL;DR

This paper introduces multiple Boris integrators for particle-in-cell simulations, significantly reducing errors and enabling larger timesteps through a novel combination of Boris procedures and Chebyshev polynomial techniques.

## Contribution

The paper develops multiple Boris integrators that enhance accuracy and stability in PIC simulations by combining Boris steps and employing Chebyshev polynomials for one-step formulation.

## Key findings

- Errors reduced by a factor of n^2
- Allow larger timesteps without loss of stability
- Demonstrated improved performance in numerical tests

## Abstract

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.