High quality electron bunch generation using a longitudinal density-tailored plasma-based accelerator in the three-dimensional blowout regime

The generation of very high quality electron bunches (high brightness and low energy spread) from a plasma-based accelerator in the three-dimensional blowout regime using self-injection in tailored plasma density profiles is analyzed theoretically and with particle-in-cell simulations. The underlying physical mechanism that leads to the generation of high quality electrons is uncovered by tracking the trajectories of the electrons in the sheath that are trapped by the wake. Details on how the intensity of the driver and the density scale-length of the plasma control the ultimate beam quality are described. Three-dimensional particle-in-cell simulations indicate that this concept has the potential to produce beams with peak brightnesses between $10^{20}$ and $10^{21}\mathrm{A}/{\mathrm{m}}^2/{\mathrm{rad}}^2$ and with absolute slice energy spreads of $\sim O(0.1)\mathrm{MeV}$ using existing lasers or electron beams to drive nonlinear wakefields. We also show projected energy spreads as low as $\sim 0.3\mathrm{MeV}$ for half the charge can be generated at an optimized acceleration distance.

Figure 1

(a) Schematic of density downramp injection. The plasma density decreases linearly from $n_{p,h}$ at $z=0$ to $n_{p0}$ at $z=L$. (b) The plasma wake produced by a short electron bunch with $\mathrm{\Lambda }=1$ before (left) and after (right) it propagates through the density downramp. The black lines are the on-axis $E_z$ and the purple (blue) marker indicates the position where $E_z=0$ when the beam is before (after) the ramp. (c) Evolution of the phase velocity ${\gamma }_{\varphi ,E_z=0}$ from Eq. (1) (solid lines) and 3D PIC simulations (dashed lines). The parameters are: ${\gamma }_b=2500,n_b=16n_{p0},{\sigma }_z=0.7\frac{c}{{\omega }_{p0}}$, ${\sigma }_r=0.25\frac{c}{{\omega }_{p0}}$ when $\mathrm{\Lambda }=1$ and ${\sigma }_r=0.5\frac{c}{{\omega }_{p0}}$ when $\mathrm{\Lambda }=4$.

Figure 2

(a) The trajectories (solid lines) and the $-{\gamma }_z$ (dashed lines) of the electrons in a uniform plasma with $n_p=1.5n_{p0}$ and ${\omega }_p$ is the corresponding plasma frequency. The red dotted line is the on-axis ${\psi }_0$. The inset shows the dependence of ${\gamma }_{z,M}$ of the electrons on the initial radius under different drivers. The black and blue markers correspond to $\xi =6.4c/{\omega }_p$ and $10.7c/{\omega }_p$. (b) The source term $S$ and pseudo-potential $\psi$ at different $\xi$. The blue dashed line is an average. The parameters of the beam drivers are the same as the $\mathrm{\Lambda }=4$ case in Fig. 1.

Figure 3

(a) The transverse forces experienced by a sample of the sheath electrons with initial positive $x_i$. (b) The trajectories of the electrons in the transverse phase space. The initial positions $(x=x_i)$ are indicated by dots. The solid lines are for a uniform plasma (no injection) while the dashed line is for a sample injected electron in a downramp. The electrons in (a) and (b) have $y_i\approx 0$ and the same colors correspond to the same electrons. The normalized charge density distribution of the injected electrons in $r_i-z_i$ plane (c) and $\xi -z_i$ plane (d). The lines are from Eq. (3). The beam parameters are the same as in Fig. 1.

Figure 4

The parameters of the injected beams in two conditions: (a) the slice emittance, (b) the current, (c) the slice energy spread and (d) the brightness. Here $I_A\approx 17\mathrm{kA}$ is the Alfven current. The beam is divided into 128 slices. The red (black) lines corresponds to $\mathrm{\Lambda }=1(4)$. The curves right of the blue dashed lines are attenuated by 10.

Figure 5

The simulation results in a laser driven density ramp injection. (a) The emittance and the current at $z_{\text{plasma}}=0.18\mathrm{mm}$. The black lines are the emittance and the red line is the current. (b) The longitudinal phase space (black dots) and the slice energy spread (red line) at $z_{\text{plasma}}=0.18\mathrm{mm}$. Note that about 94% electrons are contained when calculated the beam parameters and the whole beam is divided into 64 slices.