Self Consistent Monte Carlo Method to Study CSR Effects in Bunch Compressors

PDF Version Also Available for Download.

Description

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 ... continued below

Creation Information

Warnock, R.L.; /SLAC; Bassi, G.; Ellison, J.A.; Heinemann, K.A. & U., /New Mexico January 8, 2008.

Context

This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

Who

People and organizations associated with either the creation of this article or its content.

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

Description

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.

Source

  • Journal Name: Conf.Proc.C070625:3414,2007; Conference: Particle Accelerator Conference PAC07 25-29 Jun 2007, Albuquerque, New Mexico

Language

Item Type

Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

  • Report No.: SLAC-PUB-13072
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 922222
  • Archival Resource Key: ark:/67531/metadc899248

Collections

This article is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

What responsibilities do I have when using this article?

When

Dates and time periods associated with this article.

Creation Date

  • January 8, 2008

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

Description Last Updated

  • Dec. 8, 2016, 10:52 p.m.

Usage Statistics

When was this article last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 2

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

Warnock, R.L.; /SLAC; Bassi, G.; Ellison, J.A.; Heinemann, K.A. & U., /New Mexico. Self Consistent Monte Carlo Method to Study CSR Effects in Bunch Compressors, article, January 8, 2008; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc899248/: accessed September 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.