Phase-Space Dynamics of Ionization Injection in Plasma-Based Accelerators

The evolution of beam phase space in ionization injection into plasma wakefields is studied using theory and particle-in-cell simulations. The injection process involves both longitudinal and transverse phase mixing, leading initially to a rapid emittance growth followed by oscillation, decay, and a slow growth to saturation. An analytic theory for this evolution is presented and verified through particle-in-cell simulations. This theory includes the effects of injection distance (time), acceleration distance, wakefield structure, and nonlinear space charge forces, and it also shows how ultralow emittance beams can be produced using ionization injection methods.

Figure 1

Phase-space snapshots from single particle model illustrating the transverse phase mixing process. (a)–(c) $x{\text{−}p}_x$ phase space at different times: (a) $t=3({\omega }_p^{-1})$ when the ionization is just terminated, (b) $t=8$, (c) $t=94$. (d) $x\text{−}{p}_x$ phase-space trajectory for a typical particle, where the color represents the relativistic factor $\gamma$. Note that at early time, $\gamma$ is correlated with the ionization time $s_i$.

Figure 2

(a) 2D PIC simulation of ionization injection by a laser into a beam driven wake. Drive beam (green): ${\sigma }_r=15\mu \mathrm{m},{\sigma }_z=25\mu \mathrm{m},n_b=2.6\times 10^{17}{\mathrm{cm}}^{-3},E_b=2\mathrm{GeV}$. Laser: $\lambda =800\mathrm{nm}$, $a_0=0.04$, $w_0=3\mu \mathrm{m}$, $\tau \approx 30\mathrm{fs}$. (b) Comparison of the emittance evolution between simulations and theory. The red line and the black line are for the laser polarized in or out of the simulation plane, respectively. The $x\text{−}{p}_x$ phase space when the injection is terminated (c) and when $z=z_0(d)$.

Figure 3

(a) Emittance evolution with space charge effect. The red line and the black line show the emittance evolution for the laser in or out of the 2D simulation plane, respectively, with $n_{\mathrm{He}}=1.6\times 10^{16}{\mathrm{cm}}^{-3}$. The green line shows the emittance evolution for limited helium range ($19\mu \mathrm{m}$), $n_{\mathrm{He}}=1.6\times 10^{17}{\mathrm{cm}}^{-3}$. The charge value (blue curve) is estimated by assuming the beam is symmetric in 3D. (b) The quadratic dependence of the saturated emittances on ${\sigma }_{x0}$ for large injection phase ($>\pi$) with space charge effect. The laser intensity was fixed at $a_0=0.04$ for different spot sizes, and the inner plot shows the dependence of ${\sigma }_{x0}$ on the laser spot size.

Figure 4

(a) The dependence of ${\xi }_f$ on ${\xi }_i$ from simulation and the comparison with theoretical estimation. (b) The dependence of ${\xi }_f$ on $x_i$. Note that different colors represent different electron birth times.