New Particle-in-cell Code for Numerical Simulation of Coherent Synchrotron Radiation

We present a first look at the new code for selfconsistent, 2D simulations of beam dynamics affected by the coherent synchrotron radiation. The code is of the particle-in-cell variety: the beam bunch is sampled by point-charge particles, which are deposited on the grid; the corresponding forces on the grid are then computed using retarded potentials according to causality, and interpolated so as to advance the particles in time. The retarded potentials are evaluated by integrating over the 2D path history of the bunch, with the charge and current density at the retarded time obtained from interpolation of the particle distributions recorded at discrete timesteps. The code is benchmarked against analytical results obtained for a rigidline bunch. We also outline the features and applications which are currently being developed. INTRODUCTION Coherent synchrotron radiation (CSR) is an effect of curvature-induced self-interaction of a microbunch with a high charge as it traverses a curved trajectory. It can cause a significant emittance degradation, as well as fragmentation and microbunching of the electron bunch. Numerical simulations of the CSR effects have proven to be extremely challenging because of: (i) the memory requirement associated with storing the history of the beam bunch; (ii) difficulty to accurately account for retardation; (iii) large cancellation between E and B fields in Lorentz force; (iv) sensitivity to numerical noise, exacerbated by presence of gradients in relevant equations; (v) scaling of the self-interactions in computations. Here we focus on the self-consistent 2D CSR code developed by Li [1, 2]. The code is based on integration of the retarded potential for a 2D charge distribution (no vertical size). The present work transforms Li’s original code from a particle-particle to a particle-in-cell (mean-field) form, thereby enabling superior performance in terms of efficiency and spatial resolution. EQUATIONS OF MOTION The dynamics of an electron in the bunch is governed by the following equation: d dt (γmev) = e (E + β ×B) , (1) where β ≡ v/c, E ≡ E + E , B ≡ B + B . Here E and B are external electromagnetic (EM) Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. fields, and E and B are the EM fields from bunch self-interaction, which depend on the history of the bunch charge distribution ρ and current density J via the scalar and vector potentials φ and A: E = −∇φ− 1 c ∂tA, (2a) B = ∇×A, (2b) where