Modification of the Coupled Integral Equations Method for Calculation of the Accelerating Structure Characteristics

Abstract

In this paper we present modification of coupled integral equations method (CIEM) for calculating the characteristics of the accelerating structures. In earlier developed CIEM schemes the coupled integral equations are derived for the unknown electrical fields at interfaces that divide the adjacent volumes. In addition to the standard division of the structured waveguide by interfaces between the adjacent cells, we propose to introduce new interfaces in places where electric field has the simplest transverse structure. Moreover, the system of coupled integral equations is formulated for longitudinal electrical fields in contrast to the standard approach where the transverse electrical fields are unknowns. The final vector equations contain expansion coefficients of the longitudinal electric field at these additional interfaces. This modification makes it possible to deal with a physical quantity that plays an important role in the acceleration of particles (a longitudinal electric field), and to obtain approximate equations for the case of a slow change in the waveguide parameters.

Nonuniform Structured Waveguides. WKB Approach

“…We divide the segment into subregions, each of which is a circular waveguide. Unlike earlier works [9], we divide each volume with large cross-section into two equal subvolumes (in general, they can be different) [11]. Volumes with large cross section will be numbered by the index k…”

“…where J 0 (λ m ) = 0. Using in each volume the standard expansion of the field into simple cylindrical waves and equating the fields on the boundary surfaces, we obtain the matrix difference equation [11]…”

“…We will use the possibilities of the CASCIE code [12] for computing T (k) , T +(k) , T −(k) matrices and to compare the approximate results with the results obtained from solving Equation (2).…”

“…We will investigate the characteristics of a smooth transition between two disk loaded waveguides with The aperture and resonator radii change according the formulas (see [12])…”

“…The method of Coupled Integral Equations (CIE) has been developed to calculate the characteristics of structured waveguides used to create high-frequency filters [9]. Recently, it has been proposed to use it to calculate the characteristics of accelerating structures [10][11][12]. Since the surfaces in the CIE method are flat, an efficient method for solving the CIE system is to expand the unknown field distributions in an orthonormal basis.…”