An Efficient Computation of Coherent Synchrotron Radiation in a Rectangular Chamber, Applied to Resistive Wall Heating

TL;DR

This paper presents a fast, accurate method for computing coherent synchrotron radiation in rectangular chambers, applied to estimate resistive wall heating in accelerator components like the LCLS-II bunch compressor.

Contribution

A new numerical algorithm for CSR calculation in rectangular chambers that handles complex bunch structures efficiently and accurately.

Findings

Radiated power is approximately 28 W at 1 MHz repetition rate.

All radiated energy is absorbed within 7 meters in the straight section.

The method works for short, complex bunch profiles.

Abstract

We study coherent synchrotron radiation (CSR) in a perfectly conducting vacuum chamber of rectangular cross section, in a formalism allowing an arbitrary sequence of bends and straight sections. We apply the paraxial method in the frequency domain, with a Fourier development in the vertical coordinate but with no other mode expansions. A line charge source is handled numerically by a new method that rids the equations of singularities through a change of dependent variable. The resulting algorithm is fast compared to earlier methods, works for short bunches with complicated structure, and yields all six field components at any space-time point. As an example we compute the tangential magnetic field at the walls. From that one can make a perturbative treatment of the Poynting flux to estimate the energy deposited in resistive walls. The calculation was motivated by a design issue for LCLS-II, the question of how much wall heating from CSR occurs in the last bend of a bunch compressor and the following straight section. Working with a realistic longitudinal bunch form of r.m.s. length $10.4~\mu$m and a charge of 100 pC we conclude that the radiated power is quite small (28 W at a 1 MHz repetition rate), and all radiated energy is absorbed in the walls within 7 m along the straight section.