Direct Laser Acceleration in Underdense Plasmas with Multi-PW Lasers: A Path to High-Charge, GeV-Class Electron Bunches

The direct laser acceleration (DLA) of electrons in underdense plasmas can provide hundreds of nC of electrons accelerated to near-GeV energies using currently available lasers. Here we demonstrate the key role of electron transverse displacement in the acceleration and use it to analytically predict the expected maximum electron energies. The energy scaling is shown to be in agreement with full-scale quasi-3D particle-in-cell simulations of a laser pulse propagating through a preformed guiding channel and can be directly used for optimizing DLA in near-future laser facilities. The strategy towards optimizing DLA through matched laser focusing is presented for a wide range of plasma densities paired with current and near-future laser technology. Electron energies in excess of 10 GeV are accessible for lasers at $I\sim {10}^{21}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 1

(a) Schematic representation of the laser pulse propagating through the preformed guiding channel. (b) Electron density during the interaction of the 10 PW laser pulse focused to $a_0=85$ interacting with the channel with the density at the center $n_e=0.1n_c$ and the laser pulse transverse magnetic field component after $\approx 1\mathrm{mm}$ of propagation.

Figure 2

(a) Maximum energies achieved for test particles, scanning different initial values of $y_0$ and ${\omega }_p/{\omega }_0$. The highest energies are achieved at the maximum resonance distance $y_{\max }$ given by Eq. (2). (b) Maximum expected distance of resonant electrons according to Eq. (2) for different laser intensities compared with the measured maximum resonant distance in quasi-3D PIC simulations. (c) Maximum energies observed in quasi-3D PIC simulations compared with the scaling given by combining Eqs. (1) and (2).

Figure 3

(a) Distribution function of electrons after the maximum cutoff energy is achieved. (b) Maximum energy (in the simulation) over time. The acceleration stops after accomplishing the theoretical maximum energy associated with the amplitude $y_0$. (c)–(d) Electron distribution in energy and instantaneous distance from the axis $y$ (not the same as $y_0$ as for most of electrons $y$ can be midoscillation). Each panel shows electrons accelerated by lasers with different intensities, but the same spot size, where in (c) $W_0=8$ (d) $W_0=15\mathrm{\mu }\mathrm{m}$. The background plasma density is $n_e=0.01n_c$ for all panels. Increasing $a_0$ resulted in electron acceleration further from the axis, and consequently higher maximum energies. Increasing the spot size had a similar effect.

Figure 4

(a) Optimal focusing of the laser as a function of total power. At the given density, the maximum energy is achieved if the stable propagation of the laser pulse is ensured for long enough. (b) The value of electron energy that should be achieved at ideal focusing of the laser pulse according to values in (a). (c) The value of laser $a_0$ resulting from the optimal focusing. (d) The acceleration length needed to achieve the maximum predicted energies.

Figure 5

Comparison of cutoff energies obtained in various experiments and simulations with our scaling Eq. (3). The density is normalized to the critical density. Triangles depict the values obtained from simulations and stars depict experiments.

Figure 6

(a) Snapshot of the laser transverse electric field component at the moment, when electron maximum energies were achieved. (b) Line-out of the transverse ion channel focusing field at $x=830\mathrm{\mu }\mathrm{m}$ compared with the field used in the analytical model. (c) Electron energies as a function of transverse displacement at the moment when the maximum energies were achieved. Panels (a)–(c) depict the evolution in the self-guided regime (transversely constant plasma) and panels (d)–(f) depict the interaction in the externally guided regime with the preformed plasma channel. Simulation parameters are $a_0=27$, $W_0=8\mathrm{\mu }\mathrm{m}$ and $n_e=0.1n_c$. In the externally guided case the density $n_e$ refers to the plasma density at the channel axis.

Figure 7

Distribution function of electrons accelerated by the 1PW laser pulse focused optimally and slightly off optimal focusing interacting with the plasma of density $0.1n_c$. The channel spotsize was controlled by the pre-formed plasma guiding channel, which resulted in $a_0=27$ for the case with $W_0=8\mathrm{\mu }\mathrm{m}$ and $a_0=54$ for the case with $W_0=4\mathrm{\mu }\mathrm{m}$.

Figure 8

Total electron charge with energies exceeding 300 MeV obtained in simulations with different plasma frequencies and laser intensities. The total charge was extracted at the moment when the maximum energy in the simulation was achieved.