Abstract
A novel calculation of the transverse space-charge impedance in an elliptical vacuum chamber reveals the frequency range at which the impedance can be described by Laslett coefficients.
Highlights
Collective effects due to self-induced electromagnetic fields in a particle accelerator are generally studied by introducing the concepts of wakefield and coupling impedance [1,2,3], which represent, in time and frequency domain respectively, the response of the environment to a point charge traveling inside the beam vacuum chamber or in any of the accelerator devices
The study of the impedance in the nonrelativistic case for an elliptic cross section has been performed in Ref. [8], where, the choice of the field expansions has led to complicated expressions, not allowing to disentangle, for example, from the total impedance, the direct and indirect effect of space charge, important in the transverse plane for collective effects studies of low energy accelerators
II we review the basic functions that we use to express the electromagnetic fields and the impedances in elliptic geometry, i.e. the Mathieu functions, taking, as reference work, the book of McLachlan [13]
Summary
Collective effects due to self-induced electromagnetic fields in a particle accelerator are generally studied by introducing the concepts of wakefield and coupling impedance [1,2,3], which represent, in time and frequency domain respectively, the response of the environment to a point charge traveling inside the beam vacuum chamber or in any of the accelerator devices These effects can be very important [4], and in some cases they could compromise the machine performance leading to partial or total beam losses [5]. [8], where, the choice of the field expansions has led to complicated expressions, not allowing to disentangle, for example, from the total impedance, the direct and indirect effect of space charge, important in the transverse plane for collective effects studies of low energy accelerators Another formulation, written as an integral form, taking into account the finite resistivity of the beam vacuum chamber, and by considering the classical regime of a good conductor, has been derived in Ref.
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