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Title: 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}
}