A fast high-order method to calculate wakefield forces in an electron beam

TL;DR

This paper introduces a high-order, fast computational method combining Newton-Cotes quadrature and FFT to efficiently calculate wakefield forces in electron beams with high accuracy and reduced numerical filtering.

Contribution

It presents a novel $O(Nlog(N))$ method using Simpson quadrature and FFT for accurate wakefield calculations, avoiding numerical filtering of the electron density.

Findings

Achieves $O(Nlog(N))$ computational complexity.

Demonstrates high numerical accuracy with Simpson quadrature.

Avoids numerical filtering by using direct line density.

Abstract

In this paper we report on a high-order fast method to numerically calculate wakefield forces in an electron beam given a wake function model. This method is based on a Newton-Cotes quadrature rule for integral approximation and an FFT method for discrete summation that results in an $O(Nlog(N))$ computational cost, where $N$ is the number of grid points. Using the Simpson quadrature rule with an accuracy of $O(h^4)$, where $h$ is the grid size, we present numerical calculation of the wakefields from a resonator wake function model and from a one-dimensional coherent synchrotron radiation (CSR) wake model. Besides the fast speed and high numerical accuracy, the calculation using the direct line density instead of the first derivative of the line density avoids numerical filtering of the electron density function for computing the CSR wakefield force.