Optimization of laser-plasma injector via beam loading effects using ionization-induced injection

Simulations of ionization-induced injection in a laser driven plasma wakefield show that high-quality electron injectors in the 50–200 MeV range can be achieved in a gas cell with a tailored density profile. Using the PIC code Warp with parameters close to existing experimental conditions, we show that the concentration of ${\mathrm{N}}_2$ in a hydrogen plasma with a tailored density profile is an efficient parameter to tune electron beam properties through the control of the interplay between beam loading effects and varying accelerating field in the density profile. For a given laser plasma configuration, with moderate normalized laser amplitude, $a_0=1.6$ and maximum electron plasma density, $n_{e0}=4\times {10}^{18}{\mathrm{cm}}^{-3}$, the optimum concentration results in a robust configuration to generate electrons at 150 MeV with a rms energy spread of 4% and a spectral charge density of $1.8\mathrm{pC}/\mathrm{MeV}$.

Figure 1

(a) Schematic side view of gas cell. Normalized density profiles (b) obtained using simulations with full 3D geometry (black solid line) and reduced geometry (blue dashed line) for $L_{\text{cell}}=1\mathrm{mm}$ and for plate of $200\mu \mathrm{m}$ aperture diameter and $500\mu \mathrm{m}$ thickness. (c) obtained with reduced geometry and $600\mu \mathrm{m}$ aperture diameter, $500\mu \mathrm{m}$ thick entry plate and $500\mu \mathrm{m}$ (black solid line) $750\mu \mathrm{m}$ (blue dashed line) and $1000\mu \mathrm{m}$ (red dotted line) thick exit plate.

Figure 2

Electron density profile along laser propagation axis (left vertical axis, red curve and shaded area), identical to the black solid curve in Fig. 1. Evolution of $a_0(z)$ along propagation axis $z$ (right vertical axis) in vacuum (green dashed line) and in plasma at different $C_{{\mathrm{N}}_2}$: 2% (black solid line), 1% (blue dashed line), 0.5% (red dashed-dotted line) and 0.35% (magenta dotted line). The gray solid line represents the evolution of $a_0(z)$ with respect to the propagation axis $z$ for slightly different laser parameters, beam waist $17\mu \mathrm{m}$ and focal position at 2.9 mm, discussed in Sec. 5.

Figure 3

Energy distribution of electrons having an energy $\ge 20\mathrm{MeV}$ at the exit of the plasma target. Each figure corresponds to a specific value of $C_{{\mathrm{N}}_2}$, representing the proportion of nitrogen in the gas cell. (a) $C_{{\mathrm{N}}_2}=2\%$; (b) $C_{{\mathrm{N}}_2}=1\%$; (c) $C_{{\mathrm{N}}_2}=0.5\%$; (d) $C_{{\mathrm{N}}_2}=0.35\%$. In these figures, the blue dashed line shows the contribution of electrons coming from the ionization process ${\mathrm{N}}^{5+}\to {\mathrm{N}}^{6+}$, while the red dashed-dotted line is for the ionization process ${\mathrm{N}}^{6+}\to {\mathrm{N}}^{7+}$. The sum of these two contributions is represented by the black solid line. Energy peak values are written on top of energy peaks.

Figure 4

Illustration of beam loading effects taken at $z=3.3\mathrm{mm}$. (a) $E_z$ fields with 2% of ${\mathrm{N}}_2$ in blue solid curve and with 0% of ${\mathrm{N}}_2$ in red solid curve with respect to $z-ct$; (b) Beam loaded electric field in red solid curve given by subtracting $E_z$ fields with 0% of ${\mathrm{N}}_2$ from the one with 2% of ${\mathrm{N}}_2$. In blue solid line is the charge distribution of the 6th electrons and in green solid line is the charge distribution of the 7th electrons. The color bar represents the average energy distribution of electrons, with a bin size along $z-ct$ of $0.7\mu \mathrm{m}$. High energy electrons are located at the front of the bunch.

Figure 5

Average energy $⟨\mathcal{E}⟩$ of electrons situated in the FWHM of the energy distribution of accelerated electrons at the early phase of acceleration, around $z=2.7\mathrm{mm}$.

Figure 6

Same as Fig. 5 at the exit of the gas cell.

Figure 7

Accelerated beam energy properties for each $C_{{\mathrm{N}}_2}$. (a) Peak energy ${\mathcal{E}}_{\text{peak}}$ (blue crosses) and average energy $⟨\mathcal{E}⟩$ (red dots) with respect to $C_{{\mathrm{N}}_2}$; (b) Energy spread in full width at half maximum (FWHM), represented by blue crosses and root-mean-square (RMS), represented by red dots with respect to $C_{{\mathrm{N}}_2}$.

Figure 8

Accelerated beam charge with respect to $C_{{\mathrm{N}}_2}$. (a) On the left axis: Charge $Q$ (blue crosses) and linear charge density $Q/{\sigma }_z$ (blue dots) on the right axis with respect to $C_{{\mathrm{N}}_2}$, the black dashed lie represents a linear regression of $Q$ with respect to $C_{{\mathrm{N}}_2}$ passing by the value $Q$ at $C_{{\mathrm{N}}_2}=0.35\%$. On the right axis: Electron rms bunch length $\sigma z$ with respect to $C_{{\mathrm{N}}_2}$; (b) Maximum charge density $(\mathrm{d}Q/\mathrm{d}\mathcal{E}{)}_{\max }$ (blue crosses) and average charge density $⟨\mathrm{d}Q/\mathrm{d}\mathcal{E}⟩$ (red dots).

Figure 9

Accelerated beam divergence and emittance with respect to $C_{{\mathrm{N}}_2}$, evaluated at the exit of the plasma target. (a) On the left axis: rms divergence ${\theta }_x$ in $x$-direction (blue crosses), and ${\theta }_y$ in $y$-direction (blue dots) with respect to $C_{{\mathrm{N}}_2}$. On the right axis: normalized rms emittance ${ϵ}_{nx}$ in $x$-direction (red diamonds), and ${ϵ}_{ny}$ in $y$-direction (red stars) with respect to $C_{{\mathrm{N}}_2}$; (b) Apparent electron bunch length ${\sigma }_x$ in $x$-direction (blue crosses), and ${\sigma }_y$ in $y$-direction (red dots) with respect to $C_{{\mathrm{N}}_2}$.

Figure 10

Accelerated beam normalized phase emittance as a function of divergence angle in the $y$-direction, evaluated at the exit of the plasma target for the case with $C_{{\mathrm{N}}_2}=0.35\%$. On the left axis: normalized phase emittances, ${ϵ}_{nx}$ (blue crosses), and ${ϵ}_{ny}$ (green triangles) as a function of divergence in the $y$-direction ${\theta }_y$. On the right axis: beam charge (red circles) with respect to divergence in the $y$-direction ${\theta }_y$.

Figure 11

Evolution of four beam quantities over the longitudinal traveling distance: (a) Peak energy (${\mathcal{E}}_{\text{peak}}$); (b) FWHM energy spread ($\mathrm{\Delta }\mathcal{E}/\mathcal{E}$); (c) Charge ($Q$) of electrons; (d) rms values of the angular divergence in $x$- and (e) in $y$-directions. In each figure, three curves are represented, each corresponds to a concentration value: 1% (red crosses), 0.5% (blue dots), and 0.35% (green triangles).