Abstract
We study the transverse geometric impedance of elliptical cross-section tapers in the lowfrequency ‘‘inductive regime.’’ We have followed a dual approach: computer simulations have been carried out using the finite element electromagnetic code GDFIDL and analytic results for the dipolar and quadrupolar components of the impedance have been derived extending a perturbation technique introduced by Stupakov. Our work provides new insight into the behavior of the impedance of axially asymmetric tapered structures at low frequency. In particular, we clarify the frequency range characterizing the inductive regime, suggesting new criteria relating the extent of the inductive regime for dipolar and quadrupolar components of the impedance to the dimensions of the minimal cross section of a tapered transition.
Highlights
It is well known that vacuum chamber discontinuities in particle accelerators lead to strong wakefield interactions that can cause collective instabilities and other unwanted effects
Since small-gap undulators are central to the design of modern high-brightness synchrotron light sources, the determination of the transverse impedance of the tapered vacuum chambers for these devices is of paramount importance
We have found that over the full range of aspect ratios [ratio of major (x) to minor (y) axes] the major-axis dipolar impedance, ZDx, and the quadrupolar impedance, ZQ, exhibit a broad low-frequency inductive regime
Summary
It is well known that vacuum chamber discontinuities in particle accelerators lead to strong wakefield interactions that can cause collective instabilities and other unwanted effects. Stupakov [3] presented an analysis of a flat tapered structure with rectangular cross section, and found that the impedance at low frequency can be significantly larger than that of a chamber with circular cross section. We have found that over the full range of aspect ratios [ratio of major (x) to minor (y) axes] the major-axis dipolar impedance, ZDx , and the quadrupolar impedance, ZQ , exhibit a broad low-frequency inductive regime (up to k 1=bmin , where bmin is the minor-axis of the elliptical chamber at the minimal cross section). The paper is organized as follows: In Sec. II, we present results of GDFIDL calculations of the impedance and wakefield for elliptic tapers, and clarify the frequency range of the inductive regime. In the Appendix we provide more details of our GDFIDL calculations
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