Transverse emittance growth in staged laser-wakefield acceleration

We present a study on the emittance evolution of electron bunches, externally injected into laser-driven plasma waves using the three-dimensional particle-in-cell (PIC) code OSIRIS. Results show order-of-magnitude transverse emittance growth during the injection process, if the electron bunch is not matched to its intrinsic betatron motion inside the wakefield. This behavior is supported by analytic theory reproducing the simulation data to a percent level. The length over which the full emittance growth develops is found to be less than or comparable to the typical dimension of a single plasma module in current multistage designs. In addition, the analytic theory enables the quantitative prediction of emittance degradation in two consecutive accelerators coupled by free-drift sections, excluding this as a scheme for effective emittance-growth suppression, and thus suggests the necessity of beam-matching sections between acceleration stages with fundamental implications on the overall design of staged laser-wakefield accelerators.

Figure 1

Ellipses representing bunch slices from PIC simulation C2 (see below) at position $z=-0.03\mathrm{mm}$ (left) and $z=1.06\mathrm{mm}$ (right). The gray scale of the ellipse was chosen according to the ratio of the charge in a slice $q$ and total bunch charge $q_b$.

Figure 2

Plasma density profile and evolution of the Courant-Snyder parameters for the three considered cases in PIC simulations.

Figure 3

Evolution of the normalized emittance ${ϵ}_n$ in PIC simulations for the three considered cases. Arrows show the analytic predictions of the emittance growth. The betatron-decoherence length for the injection phase in the simulations $k_p{\xi }_0=1.00$ relative to position $z_0$ is indicated by the dash-dotted line.

Figure 4

Relative per-stage emittance growth $\Delta {ϵ}_n={ϵ}_{n,\mathrm{fin}}/{ϵ}_{n,\mathrm{init}}-1$ according to Eq. (19) as a function of beam energy for different values of $\eta =a_0{k}_p{L}_c/(k_p{r}_s)$.