Wake field and the diffraction model due to a flat beam moving past a conducting wedge

To clean a beam of its excessive tail particles, one often uses a collimator. If the beam intensity is high enough or if the beam is brought too close to the collimator, however, the wake fields generated by the beam-collimator interaction can cause additional beam tails to grow, thus defeating, or even worsening the beamtail cleaning process. The wake field generated by a sheet beam moving past a conducting wedge has been obtained in closed form by Henke (1991) using the method of conformal mapping. This result is applied in the present work to obtain the wake force and the transverse kick received by a test charge moving with the beam. For the beam to be approximated as sheet beams, it is assumed to be flat and the collimator is assumed to have an infinite extent in the flat dimension. We derive an exact expression for the transverse wake force delivered to particles in the beam bunch. Implication of emittance growth as a beam passes closely by a collimator is discussed. We consider two idealized wedge geometries.