Generating high quality ultrarelativistic electron beams using an evolving electron beam driver

A new method of controllable injection to generate high quality electron bunches in the nonlinear blowout regime driven by electron beams is proposed and demonstrated using particle-in-cell simulations. Injection is facilitated by decreasing the wake phase velocity through varying the spot size of the drive beam and can be tuned through the Courant-Snyder (CS) parameters. Two regimes are examined. In the first, the spot size is focused according to the vacuum CS beta function, while in the second, it is focused by the plasma ion column. The effects of the driver intensity and vacuum CS parameters on the wake velocity and injected beam parameters are examined via theory and simulations. For plasma densities of $\sim 10^{19}{\mathrm{cm}}^{-3}$, particle-in-cell simulations demonstrate that peak normalized brightnesses $\gtrsim 10^{20}\mathrm{A}/{\mathrm{m}}^2/{\mathrm{rad}}^2$ can be obtained with projected energy spreads of $\lesssim 1\%$ within the middle section of the injected beam, and with normalized slice emittances as low as $\sim 10\mathrm{nm}$.

Figure 1

(a) Schematic of self-injection in PWFA. Simulation results are shown in two regimes for electron drivers with $\mathrm{\Lambda }=6$ focused into a plasma. (b) The projected spot size ${\sigma }_r$ of the driver is calculated from the simulation data (solid) and for vacuum propagation (dashed) for case A (black) and case B (red). The plasma density profile is shown in blue. The plasma wake is shown at propagation distances into the plasma of (c) $z=45c/{\omega }_p$, (d) $z=100c/{\omega }_p$, (e) $z=155c/{\omega }_p$ for case A and (f) $z=1630c/{\omega }_p$ for case B.

Figure 2

(a) Trajectories of the most energetic sheath electrons for ${\sigma }_r=\frac{1}{32}\sqrt{\mathrm{\Lambda }}c/{\omega }_p$ and $\frac{3}{4}\sqrt{\mathrm{\Lambda }}c/{\omega }_p$ when $\mathrm{\Lambda }=6$. The change in the bubble length $\mathrm{\Delta }{L}_b$ is shown by the red dashed lines. (b) The initial position of the plasma sheath electrons $r_i$, (c) the change in bubble length $\mathrm{\Delta }{L}_b$, and (d) the maximum sheath electron forward velocity ${\gamma }_{z,m}$ as a function of the spot size ${\sigma }_r$ for quasistatic plasma wakes. Lengths are normalized by $\sqrt{\mathrm{\Lambda }}c/{\omega }_p$. Nonevolving electron drivers with energy ${\gamma }_b=20000$ and ${\sigma }_z=0.7c/{\omega }_p$ were used. $\mathrm{\Delta }{L}_b$ is also calculated from the evolving wake in case A [see Fig. 1] and plotted in (c) with dashed black lines.

Figure 3

(a) ${\gamma }_{z,m}$ (solid) and ${\gamma }_{\varphi }$ (dashed) calculated from Eq. (2) as a function of ${\sigma }_r$ for case A. The blue dashed lines enclose regions of injection where ${\gamma }_{z,m}>{\gamma }_{\varphi }$. (b) The phase space of injected electron charge in the ${\xi }_f-z_i$ plane for case A (black) and case B (red). The dashed lines are calculated from Eq. (4). (c) The phase space $\gamma -\xi$ and (d) slice energy spread ${\sigma }_{\gamma }$ of injected electrons at position $z=260(1630)c/{\omega }_p$ for case A (B). The injected beams are subdivided into 128 (64) slices for cases A (B), respectively, in (d).

Figure 4

The beam slice parameters of the injected electrons for case A and case B: (a) the current, in units of the Alfven current $I_A$ and (b) the normalized brightness $B_n$ in units of $[(n_0{\mathrm{cm}}^{-3})\mathrm{A}/{\mathrm{m}}^2/{\mathrm{rad}}^2]$. The injected beams are subdivided into 128 (64) slices for cases A (B), respectively. (c) Slice current corresponding to the (d) peak normalized brightness of the injected electron beam as a function of the driver parameter $\mathrm{\Lambda }$. Each marker corresponds to a unique simulation. Approximately 95% of injected electrons are used when calculating the beam parameters.