Billion particle linac simulations for future light sources

BILLION PARTICLE LINAC SIMULATIONS FOR FUTURE LIGHT SOURCES* J. Qiang # , R. D. Ryne, M. Venturini, A. A. Zholents, LBNL, Berkeley, CA 94720, U.S.A. Abstract In this paper we report on multi-physics, multi-billion macroparticle simulation of beam transport in a free electron laser (FEL) linac for future light source applications. The simulation includes a self-consistent calculation of 3D space-charge effects, short-range geometry wakefields, longitudinal coherent synchrotron radiation (CSR) wakefields, and detailed modeling of RF acceleration and focusing. We discuss the need for and the challenges associated with such large-scale simulation. Applications to the study of the microbunching instability in an FEL linac are also presented. 3D Poisson equation in the beam frame using a convolution of the charge density with the Green function for open boundary conditions (in most applications). This convolution is calculated numerically on a 3D grid using an integrated Green function method [2] with FFT calculation of a cyclic summation in a doubled computational domain [3]. The space-charge fields are Lorentz transformed back to the laboratory frame to advance particle momentum. The wakefield forces are calculated in the laboratory frame using a convolution of the wake function and the particle density. This convolution is also computed using the FFT based method. The CSR effects inside a chicane are calculated using a one-dimensional longitudinal CSR wake model [4]. As a test of our space-charge model, we computed the energy modulation amplitude of an initial 120 MeV round uniform electron beam with 120 A current, 5% modulation, and zero initial temperature propagating through a drift space. Figure 1 shows the amplitude of energy modulation as a function of distance in comparison with an often used analytical model of longitudinal space-charge impedance [5]. This analytical model presupposes that the longitudinal component of the electric field across the beam is uniform and equal to the value on the beam axis. This is a good approximation if the wavelength of the perturbation as measured in the beam commoving frame is large compared to the beam transverse radius (or k*r b /γ <<1, where k=2π/λ is the perturbation wavenumber in the lab frame.) However, as shown in the picture at smaller wavelengths the analytical model tends to overestimate the energy modulation when this is averaged over the beam tranasverse density. See also [6]. INTRODUCTION The electron beam quality at the entrance to FEL undulators plays a crucial role for the success of next generation X-ray light sources. In order to achieve good performance of X-ray output with reasonable cost, the emittance of the electron beam and the energy spread of the electron beam need to be controlled within the tolerance level subject to a high peak current. However, collective effects such as the microbunching instability driven by space-charge, wakefields, and CSR can pose a particular challenge that leads to irreversible degradation in beam quality. In order to accurately predict the beam properties at the end of linac subject to those collective effects and to optimize the linac design, large-scale self- consistent simulation is needed. As will be shown, the use of on the order of a billion macroparticles or close to real number of electrons per bunch in self-consistent particle tracking helps to correctly simulate the shot noise inside the electron beam that can be amplified by the microbunching instability. COMPUTATIONAL AND PHYSICAL MODELS In this study, we have used the IMPACT code [1], a parallel beam dynamics macroparticle tracking code, as our major simulation tool. The IMPACT code is an object-based parallel particle-in-cell code to simulate high intensity, high brightness beam transport in a beam delivery system. It uses a split-operator method to separate the particle advance subject to the given external fields from the particle advance subject to the collective self-consistent space-charge or wakefield forces. The space-charge forces are calculated from the solution of the Figure 1: Energy modulation amplitude as a function of distance with initial 5% current modulation at 15 um, 30 um and 50 um wavelength. The code is implemented on parallel computers using both a domain-decomposition method and a particle-field *Work supported by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. jqiang@lbl.gov