# Forces in a Thin Cosine (nTheta) Helical Wiggler

## Abstract

We wish to calculate the Lorentz body force associated with pure multipole helical magnetic fields (i.e, proportional to cos(n{theta})) whose strength varies purely as a Fourier sinusoidal series of the longitudinal coordinate z (say proportional to cos(2m-1){pi}z)/L, where L denotes the half-period of the wiggler field and m= 1,2,3... We also wish to apply such forces to the current sheet, and solve for the stress distribution required to maintain such a coil in equilibrium. In the calculations of Lorentz forces we include the self field contribution as well as possible contributions arising from additional nested helical windings. We shall demonstrate that in cases where the current is situated on a surface of discontinuity at r=R (i.e. J=f({theta},z)) and the Lorentz body force is integrated on that surface, a closed form solution for the stress distribution can be obtained and such a solution includes contributions from possible nested multi pole magnets. Finally we demonstrate that in the limiting 2D case where the field strength does not vary with z ( period 2L tends to infinity) the stress reduces to known 2D expressions.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- Accelerator& Fusion Research Division

- OSTI Identifier:
- 1001640

- Report Number(s):
- LBL-36988Rev1

TRN: US201104%%101

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99; COORDINATES; DISTRIBUTION; EQUILIBRIUM; HELICAL CONFIGURATION; LORENTZ FORCE; MAGNETIC FIELDS; MAGNETS; MULTIPOLES; SOLUTIONS; SURFACES; WIGGLER MAGNETS

### Citation Formats

```
Caspi, S.
```*Forces in a Thin Cosine (nTheta) Helical Wiggler*. United States: N. p., 1997.
Web. doi:10.2172/1001640.

```
Caspi, S.
```*Forces in a Thin Cosine (nTheta) Helical Wiggler*. United States. https://doi.org/10.2172/1001640

```
Caspi, S. 1997.
"Forces in a Thin Cosine (nTheta) Helical Wiggler". United States. https://doi.org/10.2172/1001640. https://www.osti.gov/servlets/purl/1001640.
```

```
@article{osti_1001640,
```

title = {Forces in a Thin Cosine (nTheta) Helical Wiggler},

author = {Caspi, S},

abstractNote = {We wish to calculate the Lorentz body force associated with pure multipole helical magnetic fields (i.e, proportional to cos(n{theta})) whose strength varies purely as a Fourier sinusoidal series of the longitudinal coordinate z (say proportional to cos(2m-1){pi}z)/L, where L denotes the half-period of the wiggler field and m= 1,2,3... We also wish to apply such forces to the current sheet, and solve for the stress distribution required to maintain such a coil in equilibrium. In the calculations of Lorentz forces we include the self field contribution as well as possible contributions arising from additional nested helical windings. We shall demonstrate that in cases where the current is situated on a surface of discontinuity at r=R (i.e. J=f({theta},z)) and the Lorentz body force is integrated on that surface, a closed form solution for the stress distribution can be obtained and such a solution includes contributions from possible nested multi pole magnets. Finally we demonstrate that in the limiting 2D case where the field strength does not vary with z ( period 2L tends to infinity) the stress reduces to known 2D expressions.},

doi = {10.2172/1001640},

url = {https://www.osti.gov/biblio/1001640},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1997},

month = {5}

}