An Interpolation Formula for the Energy Radiated by a Point Charge Passing Through a Hole in a Plane

Abstract

The radiative energy loss [Formula: see text] accompanying the transition of a uniformly moving nonrelativistic point charge e through a hole of radius a in an infinite, ideally conducting plane is obtained. The technique of solution involves a quasistatic approximation to the dynamic problem in the regime [Formula: see text]. In this limit, the presence of the hole is found to induce an array of slowly accelerating linear multipoles whose associated radiation leads to a finite energy loss proportional to β3. An interpolation formula [Formula: see text] for the energy loss valid for arbitrary β is constructed from this result and the known ultrarelativistic expression. Application of this formula in conjunction with the relativistic Maxwellian allows computation of a temperature dependent, radiation loss expression appropriate to the passage of a relativistic pulse through an iris-type aperture. A formula incorporating finite beam length coherence effects for the radiation loss in low energy particle accelerators is also developed.