Parameter sensitivity of plasma wakefields driven by self-modulating   proton beams
  The dependence of wakefield amplitude and phase on beam and plasma parameters is studied in the parameter area of interest for self-modulating proton beam-driven plasma wakefield acceleration. The wakefield sensitivity to small parameter variations reveals the expected level of shot-to-shot jitter of experimental results. Of all the parameters, the plasma density stands out, as the wakefield phase is extremely sensitive to this parameter. The study of large variations determines the effects that limit the achievable accelerating field in different parts of the parameter space: nonlinear elongation of the wakefield period, insufficient charge of the drive beam, emittance-driven beam divergence, and motion of plasma ions. 
K.V.Lotov, V.A.Minakov, A.P.Sosedkin
physics.plasm-ph physics.acc-ph