# Traceless Totally Symmetric Tensor Based Fast Multipole Method for Space Charge Field Calculation

## Abstract

The fast multipole method (FMM) is widely used to calculate the Coulomb interaction between a huge amount of charged particles. The efficiency of FMM scales with $O(N)$ for $N$ particles with any arbitrary distribution. Hence it is apposite for problems with complicated charge distribution or geometry. We developed a new FMM code for Coulomb interaction. In the new code the Coulomb potential is expressed as traceless totally symmetric tensors in Cartesian coordinates, in which the number of independent element is only $2n+1$ for the $$n^{\mathrm{th}}$$ rank, while it is $$3^{n}$$ for a general Cartesian tensor. The significant reduce of independent element number in Cartesian tensor helps to achieve high efficiency in the new algorithm. Result of test runs for space charge field calculation and multi-particle tracking using the new algorithm will be presented.

- Authors:

- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1483793

- Report Number(s):
- JLAB-ACP-15-2004; DOE/OR/23177-4606

R&D Project: 2015-LDRD-07

- DOE Contract Number:
- AC05-06OR23177

- Resource Type:
- Conference

- Resource Relation:
- Conference: FEIS-2: Femtosecond Electron Imaging and Spectroscopy, May 6 - 9, 2015, Michigan State University, East Lansing, MI

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Zhang, He, Huang, He, Li, Rui, Chen, Jie, and Luo, Li-Shi.
```*Traceless Totally Symmetric Tensor Based Fast Multipole Method for Space Charge Field Calculation*. United States: N. p., 2015.
Web.

```
Zhang, He, Huang, He, Li, Rui, Chen, Jie, & Luo, Li-Shi.
```*Traceless Totally Symmetric Tensor Based Fast Multipole Method for Space Charge Field Calculation*. United States.

```
Zhang, He, Huang, He, Li, Rui, Chen, Jie, and Luo, Li-Shi. Wed .
"Traceless Totally Symmetric Tensor Based Fast Multipole Method for Space Charge Field Calculation". United States. https://www.osti.gov/servlets/purl/1483793.
```

```
@article{osti_1483793,
```

title = {Traceless Totally Symmetric Tensor Based Fast Multipole Method for Space Charge Field Calculation},

author = {Zhang, He and Huang, He and Li, Rui and Chen, Jie and Luo, Li-Shi},

abstractNote = {The fast multipole method (FMM) is widely used to calculate the Coulomb interaction between a huge amount of charged particles. The efficiency of FMM scales with $O(N)$ for $N$ particles with any arbitrary distribution. Hence it is apposite for problems with complicated charge distribution or geometry. We developed a new FMM code for Coulomb interaction. In the new code the Coulomb potential is expressed as traceless totally symmetric tensors in Cartesian coordinates, in which the number of independent element is only $2n+1$ for the $n^{\mathrm{th}}$ rank, while it is $3^{n}$ for a general Cartesian tensor. The significant reduce of independent element number in Cartesian tensor helps to achieve high efficiency in the new algorithm. Result of test runs for space charge field calculation and multi-particle tracking using the new algorithm will be presented.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {5}

}