# A parallel 3D poisson solver for space charge simulation in cylindrical coordinates.

## Abstract

This paper presents the development of a parallel three-dimensional Poisson solver in cylindrical coordinate system for the electrostatic potential of a charged particle beam in a circular tube. The Poisson solver uses Fourier expansions in the longitudinal and azimuthal directions, and Spectral Element discretization in the radial direction. A Dirichlet boundary condition is used on the cylinder wall, a natural boundary condition is used on the cylinder axis and a Dirichlet or periodic boundary condition is used in the longitudinal direction. A parallel 2D domain decomposition was implemented in the (r,{theta}) plane. This solver was incorporated into the parallel code PTRACK for beam dynamics simulations. Detailed benchmark results for the parallel solver and a beam dynamics simulation in a high-intensity proton LINAC are presented. When the transverse beam size is small relative to the aperture of the accelerator line, using the Poisson solver in a Cartesian coordinate system and a Cylindrical coordinate system produced similar results. When the transverse beam size is large or beam center located off-axis, the result from Poisson solver in Cartesian coordinate system is not accurate because different boundary condition used. While using the new solver, we can apply circular boundary condition easily and accurately formore »

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 967024

- Report Number(s):
- ANL/PHY/JA-60286

Journal ID: ISSN 0010-4655; CPHCBZ; TRN: US0904163

- DOE Contract Number:
- DE-AC02-06CH11357

- Resource Type:
- Journal Article

- Journal Name:
- Comput. Phys. Commun.

- Additional Journal Information:
- Journal Volume: 178; Journal Issue: 4 ; Feb. 2008; Journal ID: ISSN 0010-4655

- Country of Publication:
- United States

- Language:
- ENGLISH

- Subject:
- 43 PARTICLE ACCELERATORS; ACCELERATORS; APERTURES; BEAM DYNAMICS; BENCHMARKS; BOUNDARY CONDITIONS; CARTESIAN COORDINATES; CHARGED PARTICLES; ELECTROSTATICS; LINEAR ACCELERATORS; PROTONS; SIMULATION; SPACE CHARGE

### Citation Formats

```
Xu, J, Ostroumov, P N, Nolen, J, and Physics.
```*A parallel 3D poisson solver for space charge simulation in cylindrical coordinates.*. United States: N. p., 2008.
Web. doi:10.1016/j.cpc.2007.09.008.

```
Xu, J, Ostroumov, P N, Nolen, J, & Physics.
```*A parallel 3D poisson solver for space charge simulation in cylindrical coordinates.*. United States. doi:10.1016/j.cpc.2007.09.008.

```
Xu, J, Ostroumov, P N, Nolen, J, and Physics. Fri .
"A parallel 3D poisson solver for space charge simulation in cylindrical coordinates.". United States. doi:10.1016/j.cpc.2007.09.008.
```

```
@article{osti_967024,
```

title = {A parallel 3D poisson solver for space charge simulation in cylindrical coordinates.},

author = {Xu, J and Ostroumov, P N and Nolen, J and Physics},

abstractNote = {This paper presents the development of a parallel three-dimensional Poisson solver in cylindrical coordinate system for the electrostatic potential of a charged particle beam in a circular tube. The Poisson solver uses Fourier expansions in the longitudinal and azimuthal directions, and Spectral Element discretization in the radial direction. A Dirichlet boundary condition is used on the cylinder wall, a natural boundary condition is used on the cylinder axis and a Dirichlet or periodic boundary condition is used in the longitudinal direction. A parallel 2D domain decomposition was implemented in the (r,{theta}) plane. This solver was incorporated into the parallel code PTRACK for beam dynamics simulations. Detailed benchmark results for the parallel solver and a beam dynamics simulation in a high-intensity proton LINAC are presented. When the transverse beam size is small relative to the aperture of the accelerator line, using the Poisson solver in a Cartesian coordinate system and a Cylindrical coordinate system produced similar results. When the transverse beam size is large or beam center located off-axis, the result from Poisson solver in Cartesian coordinate system is not accurate because different boundary condition used. While using the new solver, we can apply circular boundary condition easily and accurately for beam dynamic simulations in accelerator devices.},

doi = {10.1016/j.cpc.2007.09.008},

journal = {Comput. Phys. Commun.},

issn = {0010-4655},

number = 4 ; Feb. 2008,

volume = 178,

place = {United States},

year = {2008},

month = {2}

}