Final focusing and enhanced disruption from an underdense plasma lens in a linear collider

In this work we examine the viability of employing an underdense plasma lens as a final focusing method for a linear $e^{+}$ $e^{\mathrm{-}}$ collider. The underdense plasma lens is superior to the overdense lens in that it improves focusing linearity and background event rate, but works well only for electrons. We thus consider the interaction of an $e^{\mathrm{-}}$ beam which is smaller than the $e^{+}$ beam at collision, a case we term ‘‘bootstrap disruption.’’ The potential luminosity enhancement is determined by analysis of the lens optics and simulation of the bootstrap disruption.