Abstract
The effect of an electron cloud on the longitudinal coupling impedance is studied by idealizing it as a cold and uniformly distributed non-neutral plasma of electrons. The beam pipe is assumed to be of circular cross section with a thick resistive wall and the beam charge is idealized as a uniform disk. The electron contribution to the charge and current densities is obtained from the collective electron response to the beam passage through the pipe. In the presence of the electron background, a general closed formula for the longitudinal coupling impedance is obtained. The screening of the coupling impedance with the density of the electron plasma is studied and discussed for typical parameters in an accelerator beam pipe for the under-dense and the over-dense plasma regions.
Highlights
Present addressPredicted for the GSI synchrotrons (see [15]), or measured in different ring accelerators, correspond to electron plasma frequencies of the order of fec = ωec/2π = 1 · · · 10 MHz. It turns out that the longitudinal EC effect is governed by the ratio ωec/ω with ω being the excitation frequency
Predicted for the GSI synchrotrons, or measured in different ring accelerators, correspond to electron plasma frequencies of the order of fec = ωec/2π = 1 · · · 10 MHz
The paper is organized as follows: in section 2, we present the wave equations for the electromagnetic field components in the presence of a beam perturbation and the uniformly distributed non-neutral plasma of electrons
Summary
Predicted for the GSI synchrotrons (see [15]), or measured in different ring accelerators, correspond to electron plasma frequencies of the order of fec = ωec/2π = 1 · · · 10 MHz. It turns out that the longitudinal EC effect is governed by the ratio ωec/ω with ω being the excitation frequency. The paper is organized as follows: in section 2, we present the wave equations for the electromagnetic field components in the presence of a beam perturbation and the uniformly distributed non-neutral plasma of electrons.
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