Effects of Hyperbolic Rotation in Minkowski Space on the Modeling of Plasma Accelerators in a Lorentz Boosted Frame

TL;DR

This paper demonstrates that hyperbolic rotation effects in Minkowski space, caused by Lorentz boosts, are crucial for stabilizing laser propagation simulations in plasma accelerators, enabling a millionfold speedup in modeling 1 TeV stages.

Contribution

It introduces a novel understanding of hyperbolic rotation effects in Minkowski space that improves the stability and efficiency of plasma accelerator simulations in boosted frames.

Findings

Achieved a million times speedup in simulations

Identified the role of hyperbolic rotation in mitigating numerical instability

Enabled direct simulation of 1 TeV plasma accelerator stages

Abstract

Laser driven plasma accelerators promise much shorter particle accelerators but their development requires detailed simulations that challenge or exceed current capabilities. We report the first direct simulations of stages up to 1 TeV from simulations using a Lorentz boosted calculation frame resulting in a million times speedup, thanks to a frame boost as high as gamma=1300. Effects of the hyperbolic rotation in Minkowski space resulting from the frame boost on the laser propagation in the plasma is shown to be key in the mitigation of a numerical instability that was limiting previous attempts.