Analysis of the Blowout Plasma Wakefields Produced by Drive Beams with Elliptical Symmetry

In the underdense, or blowout regime, of plasma wakefield acceleration, the particle beam is denser than the plasma. In this scenario, the plasma electrons are nearly completely rarefied from the beam channel, leaving only a nominally uniform ion-filled "bubble." Extensive investigations of this interaction assuming axisymmetry have been undertaken. However, the blowout produced by a transversely asymmetric (flat) driver, which would be present in linear collider "afterburner" schemes, possesses quite different characteristics. Such beams create an asymmetric plasma bubble which leads to unequal focusing in the two transverse dimensions, accompanied by a nonuniform accelerating gradient. The asymmetric blowout cross section is found through simulation to be elliptical, and treating it as such permits a simple extension of the symmetric theory. In particular, focusing fields linear in both transverse directions inside the bubble are found. The form of the wake potential and the associated beam-matching conditions in this elliptical cavity are discussed. We also examine blowout boundary estimation in the long driver limit and applications of the salient asymmetric features of the wakefield.