Impedance Scaling for Small-angle Tapers and Collimators

Technical Report · Thu Feb 11 00:00:00 EST 2010

DOI:https://doi.org/10.2172/972231· OSTI ID:972231

Stupakov, G

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.

• Research Organization: SLAC National Accelerator Lab., Menlo Park, CA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC02-76SF00515
• OSTI ID: 972231
• Report Number(s): SLAC-TN-10-001; TRN: US201005%%190
• Country of Publication: United States
• Language: English

Related Subjects

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