# Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits

## Abstract

We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates. The plates represent shielding due to the vacuum chamber. The vertical distribution of charge is an arbitrary fixed function. Our goal is to follow the time evolution of the phase space distribution by solving the Vlasov-Maxwell equations in the time domain. This provides simulations with lower numerical noise than the macroparticle method, and allows one to study such issues as emittance degradation and microbunching due to CSR in bunch compressors. The fields excited by the bunch are computed in the laboratory frame from a new formula that leads to much simpler computations than the usual retarded potentials or Lienard-Wiechert potentials. The nonlinear Vlasov equation, formulated in the interaction picture, is integrated in the beam frame by approximating the Perron-Frobenius operator. The distribution function is represented by B-splines, in a scheme preserving positivity and normalization of the distribution. For application to a chicane bunch compressor we take steps to deal with energy chirp, an initial near-perfect correlation of energy with position in the bunch.

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center, Menlo Park, CA (US)

- Sponsoring Org.:
- USDOE Office of Science (US)

- OSTI Identifier:
- 833093

- Report Number(s):
- SLAC-PUB-10760

TRN: US0406555

- DOE Contract Number:
- AC03-76SF00515

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 22 Sep 2004

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; BOLTZMANN-VLASOV EQUATION; COMPRESSORS; DISTRIBUTION; DISTRIBUTION FUNCTIONS; PHASE SPACE; PLATES; SHIELDING; SYNCHROTRON RADIATION

### Citation Formats

```
Warnock, R.
```*Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits*. United States: N. p., 2004.
Web. doi:10.2172/833093.

```
Warnock, R.
```*Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits*. United States. doi:10.2172/833093.

```
Warnock, R. Wed .
"Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits". United States.
doi:10.2172/833093. https://www.osti.gov/servlets/purl/833093.
```

```
@article{osti_833093,
```

title = {Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits},

author = {Warnock, R},

abstractNote = {We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates. The plates represent shielding due to the vacuum chamber. The vertical distribution of charge is an arbitrary fixed function. Our goal is to follow the time evolution of the phase space distribution by solving the Vlasov-Maxwell equations in the time domain. This provides simulations with lower numerical noise than the macroparticle method, and allows one to study such issues as emittance degradation and microbunching due to CSR in bunch compressors. The fields excited by the bunch are computed in the laboratory frame from a new formula that leads to much simpler computations than the usual retarded potentials or Lienard-Wiechert potentials. The nonlinear Vlasov equation, formulated in the interaction picture, is integrated in the beam frame by approximating the Perron-Frobenius operator. The distribution function is represented by B-splines, in a scheme preserving positivity and normalization of the distribution. For application to a chicane bunch compressor we take steps to deal with energy chirp, an initial near-perfect correlation of energy with position in the bunch.},

doi = {10.2172/833093},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Sep 22 00:00:00 EDT 2004},

month = {Wed Sep 22 00:00:00 EDT 2004}

}