Figure 4

(a) The green circles correspond to the electron bunch length measurements with beamloading turned off. The green line is a fit using Eq. (3) with C ₁ = 0.83 and C ₂ = 0. The red plus signs are data points from the simulation of the electron bunch length, the dashed red curve represents a fit according to Eq. (3). The blue crosses and dotted line represents the same values for a gentler gradient slope. (b) Spatial electron density profiles of three different acceleration densities: n ₂ = 3, 4 and 5 ⋅ 10¹⁸ cm⁻³. Here, ∂n/∂x = 0.76n ₁/λ _p1 with beamloading. (c) The peak normalized vector potential a ₀ (in blue) and FWHM width (dashed red) as function of the laser pulse’s peak position during a simulation with n ₂ = 3 ⋅ 10¹⁸ cm⁻³ and ∂n/∂x = 0.76n ₁/λ _p1. For the different simulation, the peak value of a ₀ varies between 3.8 and 4.3, but the behaviour is the same for all simulations, a ₀ increases and the width of the pulse decreases.