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Closed analytical expression for the electric field profile in a loaded rf structure with arbitrarily varying vg and R′/Q

G. Guignard and J. Hagel

  • European Organization for Nuclear Research (CERN), Geneva, Switzerland

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Phys. Rev. ST Accel. Beams 3, 042001 – Published 6 April, 2000

DOI: https://doi.org/10.1103/PhysRevSTAB.3.042001

Abstract

The design of a detuned and damped accelerating structure implies variations in the geometry which induce, in turn, a variation of the group velocity vg and the impedance per unit length R′, divided by the quality factor Q. The resulting differential equation for the longitudinal electric field (fundamental mode) contains coefficients that depend on the distance z along the structure. This report describes a possible method to solve this nonlinear, first-order differential equation analytically and how to obtain approximate closed algebraic forms, by using the sequence of Gauss integration methods. Analytical expressions of the longitudinal field profile in a loaded or unloaded accelerating section are deduced for both linear and arbitrary variations of vg and R′/Q. Simple relations between the average field 〈E〉 and the field at the entrance of the structure E(0) make it possible to provide the dependence of the field function E(z) on the design value for 〈E〉 and on the structure parameters. The results are in good agreement with the direct numerical integration. Applications are presented for particular structure designs.

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References (7)

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Phys. Rev. ST Accel. Beams 3, 042001– Published 6 April, 2000
  • Received 1 November 1999
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This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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