We discovered a novel effect that can cause witness emittance growth in plasma wakefield accelerators. The effect appears in linear or moderately nonlinear plasma waves. The witness experiences a time-varying focusing force and loses quality during the time required for the drive beam to reach transverse equilibrium with the plasma wave. The higher the witness charge, the lower the emittance growth rate because of additional focusing of the witness by its own wakefield. However, the witness head always degrades, and the boundary between degraded and intact parts gradually propagates backward along the witness bunch.

We propose a new method of estimating the mean diameter and dispersion of clusters formed in a cooling gas, right after the nucleation stage. Using a moment model developed by Friedlander [S.K. Friedlander, Ann. N.Y. Acad. Sci. 354 (1983)], we derive an analytic relationship for both cluster diameter and diameter dispersion as a function of two of the characteristic times of the system -the cooling time and primary constituents collision time. These formulas can be used to predict diameter and dispersion variation with process parameters such as the initial monomer pressure or cooling rate. It is also possible to use them as an input to the coagulation stage, without the need to compute complex cluster generation during the nucleation burst. We compared our results with a nodal code and got excellent agreement.