Special unitary particle pusher for extreme fields

TL;DR

This paper introduces a compact, exact momentum update method for particle simulations in extreme fields by leveraging SU(2)xSU(2) representation, preserving invariance and achieving high push rates.

Contribution

It presents a novel, more manageable formulation of the momentum update using SU(2)xSU(2), enhancing accuracy and efficiency in particle pushers for extreme field simulations.

Findings

Achieves exact momentum updates with a compact expression.

Preserves invariance properties through a power series expansion.

Offers push rates comparable to the standard Boris pusher.

Abstract

An exact momentum update useful for particle codes was previously given. The expressions involved were unwieldy. By treating the momentum as a representation of SU(2)xSU(2) instead of SO(3,1), a more compact expression for the exact momentum update is obtained. An expansion in powers of the timestep can be formulated such that invariance properties are exactly preserved, and push rates comparable to the standard Boris pusher are obtained.