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Title: Impedance Scaling for Small-angle Tapers and Collimators

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:
OSTI Identifier:
972231
Report Number(s):
SLAC-TN-10-001
TRN: US201005%%190
DOE Contract Number:
AC02-76SF00515
Resource Type:
Technical Report
Research Org:
Stanford Linear Accelerator Center (SLAC)
Sponsoring Org:
USDOE
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