Algorithm for calculating spectral intensity due to charged particles in arbitrary motion

TL;DR

The paper presents a novel algorithm for efficiently computing the spectral intensity of radiation from many charged particles in arbitrary motion, enabling high-energy and large-particle simulations.

Contribution

It introduces a mixed analytic and numerical method that allows exact integral calculation between discrete trajectory points, overcoming sampling bandwidth limitations.

Findings

Enables computation of spectral intensity for high photon energies.

Supports large numbers of particles with arbitrary trajectories.

Allows larger time-steps than traditional sampling methods.

Abstract

An algorithm for calculating the spectral intensity of radiation due to the coherent addition of many particles with arbitrary trajectories is described. Direct numerical integration of the Lienard-Wiechert potentials, in the far-field, for extremely high photon energies and many particles is made computationally feasible by a mixed analytic and numerical method. Exact integrals of spectral intensity are made between discretely sampled trajectories, by assuming the space-time four-vector is a quadratic function of proper time. The integral Fourier transform of the trajectory with respect to time, the modulus squared of which comprises the spectral intensity, can then be formed by piecewise summation of exact integrals between discrete points. Because of this, the calculation is not restricted by discrete sampling bandwidth theory, and hence for smooth trajectories, time-steps many orders larger than the inverse of the frequency of interest can be taken.