# Impedance Scaling for Small-angle Tapers and Collimators

## Abstract

In this note I will prove that the impedance calculated for a small-angle collimator or taper, of arbitrary 3D profile, has a scaling property that can greatly simplify numerical calculations. This proof is based on the parabolic equation approach to solving Maxwell's equation developed in Refs. [1, 2]. We start from the parabolic equation formulated in [3]. As discussed in [1], in general case this equation is valid for frequencies {omega} >> c/a where a is a characteristic dimension of the obstacle. However, for small-angle tapers and collimators, the region of validity of this equation extends toward smaller frequencies and includes {omega} {approx} c/a.

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center (SLAC)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 972231

- Report Number(s):
- SLAC-TN-10-001

TRN: US201005%%190

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; COLLIMATORS; IMPEDANCE; SCALARS; MAXWELL EQUATIONS; FREQUENCY RANGE; Accelerators,ACCPHY, XFEL

### Citation Formats

```
Stupakov, G, and /SLAC.
```*Impedance Scaling for Small-angle Tapers and Collimators*. United States: N. p., 2010.
Web. doi:10.2172/972231.

```
Stupakov, G, & /SLAC.
```*Impedance Scaling for Small-angle Tapers and Collimators*. United States. https://doi.org/10.2172/972231

```
Stupakov, G, and /SLAC. Thu .
"Impedance Scaling for Small-angle Tapers and Collimators". United States. https://doi.org/10.2172/972231. https://www.osti.gov/servlets/purl/972231.
```

```
@article{osti_972231,
```

title = {Impedance Scaling for Small-angle Tapers and Collimators},

author = {Stupakov, G and /SLAC},

abstractNote = {In this note I will prove that the impedance calculated for a small-angle collimator or taper, of arbitrary 3D profile, has a scaling property that can greatly simplify numerical calculations. This proof is based on the parabolic equation approach to solving Maxwell's equation developed in Refs. [1, 2]. We start from the parabolic equation formulated in [3]. As discussed in [1], in general case this equation is valid for frequencies {omega} >> c/a where a is a characteristic dimension of the obstacle. However, for small-angle tapers and collimators, the region of validity of this equation extends toward smaller frequencies and includes {omega} {approx} c/a.},

doi = {10.2172/972231},

url = {https://www.osti.gov/biblio/972231},
journal = {},

number = ,

volume = ,

place = {United States},

year = {2010},

month = {2}

}

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