Luminosity Limitations in Linear Colliders Based on Plasma Acceleration
  Particle acceleration in plasma creates a possibility of exceptionally high accelerating gradients and appears as a very attractive option for future linear electron-positron and/or photon-photon colliders. These high accelerating gradients were already demonstrated in a number of experiments. However, a linear collider requires exceptionally high beam brightness which still needs to be demonstrated. In this article we discuss major phenomena which limit the beam brightness of accelerated beam and, consequently, the collider luminosity. 
Valeri Lebedev, Alexey Burov and Sergei Nagaitsev
physics.acc-ph