Simulation of E-cloud Using Orbit: Benchmarks and First Application

We have developed an electron cloud module and implemented it in the ORBIT Code for beam dynamics in high intensity rings. In addition to studying the dynamics of the electron cloud, our intent in developing this model is to examine the effect of the electron cloud on the protons. In this presentation, we examine benchmarking and initial applications of the ORBIT electron cloud module to SNS. Specifically, we test the secondary emission surface model and compare instability results with an analytically solvable two-stream model. By taking these benchmarks into account, we also discuss the estimation of computational requirements for a PSR bunched beam case. ELECTRON CLOUD MODULE A new electron cloud module, designed to simulate the self consistent dynamics of the proton beam and the electrons, has been implemented in ORBIT [1]. The secondary electron emission process is calculated using an implementation of the model of Furman and Pivi [2]. We benchmark this model by comparing the secondary energy spectrum and the electron cloud development for a cold proton beam to Pivi and Furman’s results [3]. The instability caused by an electron cloud effect (ECE) may reduce the performance of high intensity proton storage rings, such as the Proton Storage Ring (PSR) at the Los Alamos National Laboratory [4] and the Spallation Neutron Source accumulation ring. We simulate the electron-proton instability for an analytically solvable model, the two-stream model [5], using the SNS parameters. We estimate the computational requirements to simulate the PSR bunched beam case by extrapolating from the benchmark of the two-stream model. BENCHMARK: SECONDARY EMISSION SURFACE MODEL IN ORBIT We implemented the secondary emission surface model of Furman and Pivi into ORBIT using their parameterization but a modified Monte Carlo scheme to save calculation time. The basic feature of the model is to remove the electron-macroparticle hitting the surface from the electron bunch and to add a new electronmacroparticle with its macrosize multiplied by the secondary emission yield (SEY), δ, compared to the macrosize of the removed electron-macroparticle, and with its energy determined by sampling from the model spectrum. We use a flexible Monte Carlo scheme to control the number of macroparticles and their macrosize without changing the physics of the model. Furman and Pivi’s model As in the Furman and Pivi model, ORBIT divides the total SEY, 0 I I = δ , into three components: elastic backscattered electrons 0 I Iel el = δ , rediffused electrons 0 I Ird rd = δ and true secondary electrons 0 I Its ts = δ , so that ( ) 0 0 0 / , I I E ts rd el = + + = δ δ δ θ δ . (1) Here, 0 I is the incident electron beam current and I is the secondary current, which consists of el I , the elastic back scattered current, rd I , the rediffused current, and ts I , the true secondary current. Each component has its own particular spectrum [2]. To determine the energy of emitted electron-macroparticle, we choose the type of emission first and then obtain the energy from its spectrum through random sampling. The choice of emission type depends on the following probabilities: δ δ el = Ρ red backscatte elastic (2a) for elastic backscattered emission, δ δ rd = Ρrediffused (2b) for rediffused emission, and ∑ = ⋅       = Ρ emiss M