Self Consistent Monte Carlo Method to Study CSR Effects in Bunch Compressors
In this paper we report on the results of a self-consistent calculation of CSR effects on a particle bunch moving through the benchmark Zeuthen bunch compressors. The theoretical framework is based on a 4D Vlasov-Maxwell approach including shielding from the vacuum chamber. We calculate the fields in the lab frame, where time is the independent variable, and evolve the phase space density/points in the beam frame, where arc length, s, along a reference orbit, is the independent variable. Some details are given in [2], where we also discuss three approaches, the unperturbed source model (UPS), the self consistent Monte Carlo (SCMC) method and the method of local characteristics. Results for the UPS have been presented for 5 GeV before [3], here we compare them with our new results from the SCMC and study the 500MeV case. Our work using the method of characteristics is in progress. The SCMC algorithm begins by randomly generating an initial ensemble of beam frame phase space points according to a given initial phase space density. The algorithm then reduces to laying out one arc length step. Assume that at arc length s we know the location of the phase space points and the history of the source prior to s. We then (1) create a smooth representation of the lab frame charge and current densities, {rho}{sub L} and J{sub L}, (2) calculate the fields at s from the history of {rho}{sub L} and J{sub L}, and (3) move the beam frame phase space points according to the beam frame equations of motion. This is then iterated. The UPS calculation is similar except the fields are calculated from a function of s computed a priori from the beam frame equations of motion without the self-fields. The phase space points are then evolved according to the equations of motion with these ''unperturbed'' fields. In the UPS we use a Gaussian initial density which evolves under the linear beam frame equations as a Gaussian. This gives us an analytic formula for the source, which significantly speeds up the field calculation. It turns out that the evolution of the unperturbed charge density for an initial Gaussian gives a reasonable estimate of the support of the self-consistently calculated charge density in our study so far. This allows us to follow the phase space points in a fixed grid region defined by the mean center of the Gaussian and an orthonormal transformation which takes the Gaussian ellipses into circles. We put the 5{sigma} circle into the square [-1,1] and take this as our basic region for the calculation. Thus at s we have the spatial position of the particles scattered in this square. We then construct a smooth spatial density using a 2D Fourier expansion on the square, calculating the Fourier coefficients from the scattered data, as a Monte Carlo integration. This is a common technique in statistical estimation [4]. This (analytical) density on the square is then used to calculate the source for the field calculation on grid points. Typically we use 32 x 32 grid points and 16 x 16 Fourier coefficients. The fields are calculated at the grid points and the scattered phase space points are moved by interpolating the fields.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 922222
- Report Number(s):
- SLAC-PUB-13072; TRN: US0801011
- Journal Information:
- Conf.Proc.C070625:3414,2007, Conference: Particle Accelerator Conference PAC07 25-29 Jun 2007, Albuquerque, New Mexico
- Country of Publication:
- United States
- Language:
- English
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