Abstract
A metallic pipe with wall corrugations is of special interest in light of recent proposals to use such a pipe for the generation of terahertz radiation and for energy dechirping of electron bunches in free electron lasers. In this paper we calculate the surface impedance of a corrugated metal wall and show that it can be reduced to that of a thin layer with dielectric constant $ϵ$ and magnetic permeability $\ensuremath{\mu}$. We develop a technique for the calculation of these constants, given the geometrical parameters of the corrugations. We then calculate, for the specific case of a round metallic pipe with small corrugations, the frequency and strength of the resonant mode excited by a relativistic beam. Our analytical results are compared with numerical simulations, and are shown to agree well. They are also shown to be more accurate when compared to the earlier used analytical model.
Highlights
Calculation of the impedance due to beam interaction with the walls of a vacuum chamber is an important part of the design of modern accelerators
The situation here is analogous to the effective boundary condition introduced in electrodynamics when the skin depth in the metal is much smaller than the thickness of the metal wall and the wavelength of the electromagnetic field—the so-called Leontovich boundary condition [9]
A metallic pipe with wall corrugations is of special interest in light of recent proposals to use pipes with corrugated surfaces for the generation of terahertz radiation [13], and for energy dechirping of electron bunches in free electron lasers [14]
Summary
Calculation of the impedance due to beam interaction with the walls of a vacuum chamber is an important part of the design of modern accelerators. In some cases the elements of the vacuum chamber that generate the beam impedance are small and uniformly distributed over the surface of the wall One example of such an impedance is that due to surface roughness, which may be important, for example, in undulator vacuum chambers of modern x-ray free electron lasers [1,2,3,4,5,6]. For such a structure it is known that (for parameters of interest) a synchronous mode can be excited by a relativistic beam, and the amplitude and frequency of the mode can be approximated by simple analytical formulas [5,6].
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