Surface impedance formalism for a metallic beam pipe with small corrugations

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 and magnetic permeability . 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.

Cherenkov Radiation from Short Relativistic Bunches: General Approach

“…Indeed, the loss factor attains exactly the same value for all disk-loaded cylindrically symmetric structures [14,17,18,22], for a resistive pipe [1, 16,23], a pipe with small periodic corrugations [19,20], and a cylindrical metal structure with a thin dielectric layer [19][20][21]24]. The same equivalence of the loss factor can be found for noncylindrical structures as well [14].…”

“…Relativistic, high intensity, and small emittance electron bunches are the basis of linear collider [11,12] and free electron laser [13] projects. These bunches excite Cherenkov wakefields as long as electrons pass through the accelerating structures or other longitudinally extended components of a beam line (pipes, collimators, bellows) [1, [14][15][16][17][18][19][20][21][22].…”

“…This includes Cherenkov imaging and capillary generation if the high frequency spectral range is not of interest [2][3][4][5][6][7][8]. This also holds for accelerating structures and other accelerator components, where the longitudinal size of electron bunches are significantly smaller than the lowest wavelength of the wakefields excited [1, [14][15][16]19]: this defines a "short" bunch in this context.…”

Electron beam energy chirp control with a rectangular corrugated structure at the Linac Coherent Light Source

“…In addition, from the point of view of manufacturing feasibility with relaxed tolerances, the preferred size of corrugations should not be too small (e.g., ≳0.5 mm). In this case, the corrugation parameters become comparable to the gap of the two plates and the analytical solutions of wakefields for the structure [7,14] are no longer applicable.…”

Using surface impedance for calculating wakefields in flat geometry

“…[7]). Known surface impedance models include dc [2], ac [1], and anomalous skin models of wall resistance [8], all of which can also be found in the classic paper of Reuter and Sondheimer [9]; other surface impedance models developed for accelerator physics applications are a model of wall roughness [10], and one for a pipe with small, periodic corrugations [11].…”