Beam optics of a self-focusing plasma lens

In this paper we analyze the optics of a high-energy beam which is focused by its own wakefields in a plasma. We calculate the effects of lens aberrations on the focusing strength of the lens and on the dilution of the beam’s phase space. From this we derive the minimum spot size achievable using a bi-Gaussian beam and, after inclusion of the beam-beam pinch effect, the luminosity enhancement that can be gained in principle. We estimate the luminosity enhancement in the case of SLAC Linear Collider beam design parameters, and discuss limitations and possible improvements in plasma-lens performance.