Effect of plasma inhomogeneity on plasma wakefield acceleration driven   by long bunches
  Effects of plasma inhomogeneity on self-modulating proton bunches and accelerated electrons were studied numerically. The main effect is the change of the wakefield wavelength which results in phase shifts and loss of accelerated particles. This effect imposes severe constraints on density uniformity in plasma wakefield accelerators driven by long particle bunches. The transverse two stream instability that transforms the long bunch into a train of micro-bunches is less sensitive to density inhomogeneity than are the accelerated particles. The bunch freely passes through increased density regions and interacts with reduced density regions. 
K.V.Lotov, A.Pukhov, A.Caldwell
physics.plasm-ph physics.acc-ph