# The transverse space-charge force in tri-gaussian distribution

## Abstract

In tracking, the transverse space-charge force can be represented by changes in the horizontal and vertical divergences, {Delta}x{prime} and {Delta}y{prime} at many locations around the accelerator ring. In this note, they are going to list some formulas for {Delta}x{prime} and {delta}y{prime} arising from space-charge kicks when the beam is tri-Gaussian distributed. They will discuss separately a flat beam and a round beam. they are not interested in the situation when the emittance growth arising from space charge becomes too large and the shape of the beam becomes weird. For this reason, they can assume the bunch still retains its tri-Gaussian distribution, with its rms sizes {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} increasing by certain factors. Thus after each turn, {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} can be re-calculated.

- Authors:

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 879032

- Report Number(s):
- FERMILAB-TM-2331-AD

TRN: US0701385

- DOE Contract Number:
- AC02-76CH03000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; ACCELERATORS; DISTRIBUTION; SHAPE; SPACE CHARGE; Accelerators

### Citation Formats

```
Ng, K.Y., and /Fermilab.
```*The transverse space-charge force in tri-gaussian distribution*. United States: N. p., 2005.
Web. doi:10.2172/879032.

```
Ng, K.Y., & /Fermilab.
```*The transverse space-charge force in tri-gaussian distribution*. United States. doi:10.2172/879032.

```
Ng, K.Y., and /Fermilab. Thu .
"The transverse space-charge force in tri-gaussian distribution". United States.
doi:10.2172/879032. https://www.osti.gov/servlets/purl/879032.
```

```
@article{osti_879032,
```

title = {The transverse space-charge force in tri-gaussian distribution},

author = {Ng, K.Y. and /Fermilab},

abstractNote = {In tracking, the transverse space-charge force can be represented by changes in the horizontal and vertical divergences, {Delta}x{prime} and {Delta}y{prime} at many locations around the accelerator ring. In this note, they are going to list some formulas for {Delta}x{prime} and {delta}y{prime} arising from space-charge kicks when the beam is tri-Gaussian distributed. They will discuss separately a flat beam and a round beam. they are not interested in the situation when the emittance growth arising from space charge becomes too large and the shape of the beam becomes weird. For this reason, they can assume the bunch still retains its tri-Gaussian distribution, with its rms sizes {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} increasing by certain factors. Thus after each turn, {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} can be re-calculated.},

doi = {10.2172/879032},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu Dec 01 00:00:00 EST 2005},

month = {Thu Dec 01 00:00:00 EST 2005}

}