# FOKKER-PLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS

## Abstract

We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We expand on the work of Suzuki [1], writing out the linear matrix equation including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. The eigenvalues and eigenvectors determine the collective stability of the beam, and we show that the predicted threshold current for transverse instability and the profile of the unstable agree well with tracking simulations. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1389079

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Conference

- Resource Relation:
- Conference: 2016 North American Particle Accelerator Conference, 10/09/16 - 10/14/16, Chicago, IL, US

- Country of Publication:
- United States

- Language:
- English

- Subject:
- FOKKER-PLANCK ANALYSIS; INSTABILITIES IN ELECTRON STORAGE RINGS; STORAGE RINGS

### Citation Formats

```
Lindberg, R. R.
```*FOKKER-PLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS*. United States: N. p., 2017.
Web. doi:10.18429.

```
Lindberg, R. R.
```*FOKKER-PLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS*. United States. doi:10.18429.

```
Lindberg, R. R. Sun .
"FOKKER-PLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS". United States.
doi:10.18429. https://www.osti.gov/servlets/purl/1389079.
```

```
@article{osti_1389079,
```

title = {FOKKER-PLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS},

author = {Lindberg, R. R.},

abstractNote = {We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We expand on the work of Suzuki [1], writing out the linear matrix equation including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. The eigenvalues and eigenvectors determine the collective stability of the beam, and we show that the predicted threshold current for transverse instability and the profile of the unstable agree well with tracking simulations. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.},

doi = {10.18429},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun Jun 25 00:00:00 EDT 2017},

month = {Sun Jun 25 00:00:00 EDT 2017}

}