Abstract
We discuss a signal theorem for charged particle detectors where the finite propagation time of the electromagnetic waves produced by a moving charge cannot be neglected. While the original Ramo–Shockley theorem and related extensions are all based on electrostatic or quasi-electrostatic approximations, the theorem presented in this report is based on the full extent of Maxwell’s equations and does account for all electrodynamic effects. It is therefore applicable to all devices that detect fields and radiation from charged particles.
Highlights
Ever since the publication of Shockley [1] and Ramo [2] discussing the theorems for induction of currents on grounded electrodes by moving charges, there have been efforts to extend these relations to more general situations: geometries including space-charge [3], signals on electrodes connected with impedance elements [4], formulation of equivalent circuits [5], inclusion of permittivity and non-linear materials [6, 7] as well as geometries that contain material of finite resistivity [8, 9, 10]
While the Ramo-Shockley theorem and extensions based on quasi-static approximations are only applicable to traditional particle detectors where the velocity of the charge movement is much smaller that the speed of light, the present theorem is not restricted to these cases
It allows the calculation of signals in detectors where signal propagation times and radiation effects are not negligible, like transmission lines and antennas
Summary
Ever since the publication of Shockley [1] and Ramo [2] discussing the theorems for induction of currents on grounded electrodes by moving charges, there have been efforts to extend these relations to more general situations: geometries including space-charge [3], signals on electrodes connected with impedance elements [4], formulation of equivalent circuits [5], inclusion of permittivity and non-linear materials [6, 7] as well as geometries that contain material of finite resistivity [8, 9, 10] All of these extensions are based on static or quasi-static approximations of Maxwell’s equations together with Green’s reciprocity theorem relating electro-static potentials and charge distributions. Two appendices show the explicit equivalence of the direct signal calculation from the Lienard-Wiechert potentials and the calculation using weighting fields, for the cases of infinitesimal electric and magnetic dipole antennas
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