Relativistic Space-Charge Field Calculation by Interpolation-Based Treecode

TL;DR

This paper develops a novel interpolation-based treecode method for accurately calculating relativistic space-charge fields in particle accelerators, addressing limitations of existing electrostatic models at high energies.

Contribution

It introduces a Lagrangian interpolation-based treecode with two error control approaches for relativistic space-charge calculations, extending applicability to high-energy beams.

Findings

The modified admissibility condition enables direct lab-frame computations.

Transforming to the rest-frame simplifies the relativistic kernel handling.

Numerical results compare the two proposed methods effectively.

Abstract

Space-charge effects are of great importance in particle accelerator physics. In the computational modeling, tree-based methods are increasingly used because of their effectiveness in handling non-uniform particle distributions and/or complex geometries. However, they are often formulated using an electrostatic force which is only a good approximation for low energy particle beams. For high energy, i.e., relativistic particle beams, the relativistic interaction kernel may need to be considered and the conventional treecode fails in this scenario. In this work, we formulate a treecode based on Lagrangian interpolation for computing the relativistic space-charge field. Two approaches are introduced to control the interpolation error. In the first approach, a modified admissibility condition is proposed for which the treecode can be used directly in the lab-frame. The second approach is based on the transformation of the particle beam to the rest-frame where the conventional admissibility condition can be used. Numerical simulation results using both methods will be compared and discussed.