Abstract
(Received 18 April 2008; published 14 July 2008)Within the ultrarelativistic limit, analytical expressions are found for the high-frequency resistive-wallcoupling impedance of an elliptical cross-section vacuum chamber. Subsequently, the corresponding wakefunctions are derived by performing inverse Fourier transformations numerically. The electromagneticfields have been developed working out two systems of solutions, namely for the vacuum and for theresistive wall. The constants involved in these systems have been determined by matching boundaryconditions at the interface vacuum wall. Several study cases have been considered concerning the aspectratio of the elliptical cross section and the transverse position of the leading charge in order to exemplifythe behavior of the longitudinal and transverse wake functions.
Highlights
Free electron laser (FEL) projects aim to achieve highbrightness photon beam pulses of minimum bandwidth.such pulses may be corrupted by possible large wakefields along the undulator small-gap vacuum chamber
II we describe the physical model used to obtain the expressions of the electromagnetic fields inside the vacuum and inside the resistive parts of the beam pipe, respectively
Since the coefficients on the diagonals are not zero, the system can be determined by Gaussian elimination without pivoting
Summary
Free electron laser (FEL) projects aim to achieve highbrightness photon beam pulses of minimum bandwidth Such pulses may be corrupted by possible large wakefields along the undulator small-gap vacuum chamber. A possible choice for a small-gap vacuum chamber is one with elliptical cross section, for which there are references to analytically derived expressions for the low-frequency resistive-wall coupling impedance (see for example [1,2,3]). V, the constants involved in the two series expansions are determined by imposing the boundary conditions at the interface vacuumresistive wall VII applications and examples are illustrated, involving different aspect ratios of the cross section, different materials using both AC and DC conductivity models, and different leading and trailing charges displacement from the beam pipe axis
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