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investigating, with the aid of simulations, the attributes of an optimized PWFA experiment using the LCLS 2 fs beam. We examine as well the attendant challenges in implementing such a scenario, in which the beam temporal scales and phase space qualities have as yet not been experimentally encountered. 

In the case of the highly compressed LCLS beam, the optimization ω$_{p}$σ$_{t}$ ≃ 1 yields a plasma electron density n$_{0}$ = [4 πr$_{e}$ ( cσ$_{t}$ ) $^{2}$] − 1 ≃ 7 . 8 × 10 $^{19}$cm − 3 corresponding to a gas density of several atm. Further, one may estimate whether this scenario may access the blowout regime, which requires that the beam density n$_{b}$ exceed n$_{0}$ , by evaluating the ratio of beam electrons to plasma electrons found within a volume of a cubic plasma skin-depth ( k − 1 p = c/ω$_{p}$ ), ˜ Q ≃ N$_{b}$k 3 $_{p}$/n$_{0}$ = 4 πk$_{p}$r$_{e}$N$_{b}$ [7]. In our case we have ˜ Q = 7 . 4. Additionally, one must focus the beam to a rms size σ$_{x}$ smaller than a skin-depth, k$_{p}$σ$_{x}$ < 1, to enter the blowout regime ( n$_{b}$/n$_{0}$ ≫ 1). The equilibrium beam size in the plasma arising from ion focusing in the plasma-electron-free region is a function of ϵ$_{n,x}$ and the equilibrium β -function, β$_{eq}$ = k − 1 p √ γ/ 2, as σ$_{x,eq}$ ≃ √ β$_{eq}$ϵ$_{n,x}$/γ . For the parameters above we have β$_{eq}$ = 140 µ m and, taking the maximum of the achieved ϵ$_{n}$ , σ$_{x,eq}$ = 45nm, and k$_{p}$σ$_{x,eq}$ = 0 . 075. The associated beam density is n$_{b}$ = 6 . 5 × 10 $^{21}$cm − $^{3}$, giving n$_{b}$/n$_{0}$ ≃ 84, a highly nonlinear blowout scenario. In such a case, one may expect the onset of effects such as ion motion. 

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It will be seen that it is difficult and unnecessary to inject the beam into the plasma with β = β$_{eq}$ ; one must minimally create the conditions for plasma and wake formation, and then tolerate the beam size oscillations that result from having an initially mismatched β . Thus to gauge the strength of the plasma wakes in initial particle-in-cell (PIC) simulations 

