Figure 1

One-dimensional fluid simulations of the electron density (dashed gray line), trapping parameter $\Delta \mathcal{H}$ (thin solid green line), and fractional ionization of ${\mathrm{N}}^{5+}$ ions (dash-dotted black line) produced by (a) a single laser pulse with a peak normalized vector potential $a_{\mathrm{drive}}=1.3$ and a pair of laser pulses with $a_0^{\mathrm{drive}}=1.0$ and $a_0^{\mathrm{inj}}=2$ and a relative delay of (b) $\Delta t=2\pi /{\omega }_p$, (c) $\Delta t=\pi /{\omega }_p$, and (d) $\Delta t=0$. For all plots, the laser pulses (thick solid red line) have a Gaussian temporal profile of rms duration ${\tau }_{\mathrm{rms}}=1/k_{p}c$.Reuse & Permissions

Figure 2

Calculated density of electrons for (a) $z=0.2$ and 2.3 mm and (c) 4.5 mm. Shown in gray scale are electrons ionized from hydrogen and ${\mathrm{N}}^{<5+}$ ions; the color scale shows electrons ionized from ${\mathrm{N}}^{\ge 5+}$ ions. Laser-plasma parameters are $n_e(0)=2\times {10}^{18}{\mathrm{cm}}^{-3}$, injection pulse $a_0=2$, and drive pulse $a_0=1$; both laser pulses have a Gaussian temporal profile with $L=k_{p}c{\tau }_{\mathrm{rms}}$.Reuse & Permissions

Figure 3

(a) Calculated phase space distribution and (b) energy spectrum of electrons ionized from ${\mathrm{N}}^{n+}$ ions, with $n\ge 5$, at distances of $z=0.2$, 1.8, 3.6, and 6.4 mm of acceleration. Only electrons remaining in the simulation box are included.Reuse & Permissions

Figure 4

Evolution with position $z$ of the drive laser pulse along the plasma channel of the parameters of electrons ionized from ${\mathrm{N}}^{\ge 5+}$ for drive and injection laser pulses with identical duration equal to (a),(c) $k_{p}c{\tau }_{\mathrm{rms}}=1$ and (b),(d) $k_{p}c{\tau }_{\mathrm{rms}}=2.2$. Shown are the relative energy spread $\Delta E_{\mathrm{rms}}/E$ (solid blue line) and $\Delta E_{\mathrm{rms}}$ (dashed black line), where $\Delta E_{\mathrm{rms}}$ is the rms energy spread, the geometric emittance ${ϵ}_{\mathrm{rms}}$ (dashed green line), and normalized emittance ${ϵ}_{n,\mathrm{rms}}$ (solid blue line). Also shown is a plot of $A/\gamma$ (dotted red line), where $\gamma$ is the mean relativistic factor of the trapped electrons, with the parameter $A$ adjusted to fit the minimum value of ${ϵ}_{\mathrm{rms}}$. The inset shows the beam transverse distribution of the electron bunch at the point where the energy spread is minimum. The dotted vertical line shows where injection stops, and the dash-dotted vertical line shows where the mean velocity of the injected electrons first exceeds the phase velocity of the plasma wakefield. Only electrons in the first injected bunch which remain in the simulation box are included in calculations of these parameters.Reuse & Permissions