Optimal Beam Loading in a Laser-Plasma Accelerator

Applications of laser-plasma accelerators demand low energy spread beams and high-efficiency operation. Achieving both requires flattening the accelerating fields by controlled beam loading of the plasma wave. Here, we optimize the generation of an electron bunch via localized ionization injection, such that the combination of injected current profile and averaged acceleration dynamics results in optimal beam loading conditions. This enables the reproducible production of 1.2% rms energy spread bunches with 282 MeV and 44 pC at an estimated energy-transfer efficiency of $\sim 19\%$. We correlate shot-to-shot variations to reveal the phase space dynamics and train a neural network that predicts the beam quality as a function of the drive laser.

Figure 1

Laser-plasma accelerator. (a) Schematic of the lux laser and electron beam line. (b) Structured plasma source supplied with ${\mathrm{H}}_2$ and doped with 10% ${\mathrm{N}}_2$ in the front for controlled injection of electron bunches into the laser-driven plasma wave.

Figure 2

Particle-in-cell simulation of the injection and acceleration process. (a)–(e) 2D snapshots $(\zeta =z-ct,x,y=0)$ of the laser, plasma wave, and electron bunch at different propagation distances $z$, showing the charge density $\rho$, laser field envelope $\overline{E_x}$, and on-axis longitudinal wakefield $E_z$. (f) Evolution of the longitudinal phase space $(\xi ,E)$ corresponding to (b)–(e) and projections to the energy axis; Current profile at position (e). (g) Molecular gas ($10\%{\mathrm{N}}_2+90\%{\mathrm{H}}_2$; $100\%{\mathrm{H}}_2$) and resulting plasma electron density profile; $z$ positions of (a)–(e) (markers); injection region (yellow), laser (red), and electron beam (blue) waist evolution.

Figure 3

Experimental results showing the phase space dynamics and optimal beam loading. (a) Measured series of energy spectra sorted by median energy $\tilde{E}$; (b) 100-shot moving average $\overline{Q}$ (solid line) and standard deviation $\pm {\sigma }_Q$ (shaded area) of the corresponding sorted charges $Q$. (c) 100-shot average spectrum (solid lines) and standard deviation (shaded area) in regions of strong ($A$), optimal ($B$) and weak ($C$) beam loading. Locations of ($A$)–($C$) and a schematic interpretation of the corresponding longitudinal phase spaces $(\xi ,E)$ are shown in (a). Correlations of bunch charge $Q$ with (d) median energy $\tilde{E}$ and (e) energy spread (median absolute deviation) $\mathrm{\Delta }E$. (f) Relative energy spectrum at optimal beam loading. 500-shot average (black solid line) and standard deviation (shaded area) of beams with lowest energy spread; Gaussian fit (magenta dashed line). Corresponding statistics of mean energy $\overline{E}$, rms energy spread ${\sigma }_{E,\mathrm{fit}}$ and charge $Q$.

Figure 4

Influence of the drive laser. Correlation of median electron energy $\tilde{E}$ with (a) laser focus position $\mathrm{\Delta }{z}_{\mathrm{foc}}$ and (b) pulse energy $E_{\text{laser}}$ with (colored; black dashed line) and without (grayed out) filtering the data by $\pm 0.5{\sigma }_{z_{\mathrm{foc}}}$ [gray area in (a)]. (c) Correlation of energy spread $\mathrm{\Delta }E$ with $\mathrm{\Delta }{z}_{\mathrm{foc}}$. Overlaid are results from a longitudinal target position scan (black dots; 100-shot average) and particle-in-cell simulations (magenta diamonds). (d) Corresponding longitudinal phase spaces $(\xi ,E)$ and charges $Q_{\mathrm{sim}}$ (green circles) from the simulations.

Figure 5

Single-shot electron beam quality prediction by a neural network and from a set of input laser parameters. Measured (blue) and predicted (green) (a) median energy $\tilde{E}$ and (b) energy spread $\mathrm{\Delta }E$ for a series of 50 consecutive shots. Prediction error (red).