Electron acceleration and generation of high-brilliance x-ray radiation in kilojoule, subpicosecond laser-plasma interactions

Petawatt, picosecond laser pulses offer rich opportunities in generating synchrotron x-rays. This paper concentrates on the regimes accessible with the PETAL laser, which is a part of the Laser Megajoule (LMJ) facility. We explore two physically distinct scenarios through Particle-in-Cell simulations. The first one realizes in a dense plasma, such that the period of electron Langmuir oscillations is much shorter than the pulse duration. Hallmarks of this regime are longitudinal breakup (“self-modulation”) of the picosecond-scale laser pulse and excitation of a rapidly evolving broken plasma wake. It is found that electron beams with a charge of several tens of nC can be obtained, with a quasi-Maxwellian energy distribution extending to a few-GeV level. In the second scenario, at lower plasma densities, the pulse is shorter than the electron plasma period. The pulse blows out plasma electrons, creating a single accelerating cavity, while injection on the density downramp creates a nC quasi-monoenergetic electron bunch within the cavity. This bunch accelerates without degradation beyond 1 GeV. The x-ray sources in the self-modulated regime offer a high number of photons ($\sim 10^{12}$) with the slowly decaying energy spectra extending beyond 60 keV. In turn, quasimonoenergetic character of the electron beam in the blowout regime results in the synchrotron-like spectra with the critical energy around 10 MeV and a number of photons $>10^9$. Yet, much smaller source duration and transverse size increase the x-ray brilliance by more than an order of magnitude against the self-modulated case, also favoring high spatial and temporal resolution in x-ray imaging. In all explored cases, accelerated electrons emit synchrotron x-rays of high brilliance, $B>10^{20}\mathrm{photons}/\mathrm{s}/{\mathrm{mm}}^2/{\mathrm{mrad}}^2/0.1\%\mathrm{BW}$. Synchrotron sources driven by picosecond kilojoule lasers may thus find an application in x-ray diagnostics on such facilities such as the LMJ or National Ignition Facility (NIF).

Figure 1

Hot electron generation in the SM-LWFA at the plasma density $n_e=1.1\times 10^{18}{\mathrm{cm}}^{-3}$. The columns (from left to right) correspond to the propagation distances 0.9, 3.9, 7.9, and 10.8 mm (the Rayleigh length being 5.5 mm). Snapshots of the laser envelope (a–d) reveal longitudinal breakup of the pulse into beamlets with the size close to the plasma wavelength, ${\lambda }_p\approx 30\mu \mathrm{m}$. Images (e–h) of the longitudinal accelerating field (in units $m_{e}c{\omega }_0/e$) reveal excitation of a broken plasma wake, which traps and accelerates electrons to GeV energies, as evidenced by the snapshots of longitudinal phase space (i–l).

Figure 2

Accumulation of electron charge and generation of thermal energy distributions in the SM-LWFA. (a) Electron charge $Q$ in the energy range above 70 MeV as a function of the propagation distance. (b) Electron energy distribution after 2 cm of propagation. From lighter to darker blue: (1) $n_e=2.8\times 10^{17}{\mathrm{cm}}^{-3}$, (2) $n_e=5.6\times 10^{17}{\mathrm{cm}}^{-3}$, (3) $n_e=1.1\times 10^{18}{\mathrm{cm}}^{-3}$ and (4) $n_e=2.8\times 10^{18}{\mathrm{cm}}^{-3}$.

Figure 3

Sketch of the plasma profile used in the blowout simulations, with $n_e=2.5\times {10}^{-5}{n}_c=2.8\times 10^{16}{\mathrm{cm}}^{-3}$.

Figure 4

Long-term pulse and wake evolution in the blowout regime. (a) WAKE simulation: evolution of the normalized peak vector potential of the pulse over 22 cm for the parameters used in the CALDER-Circ simulation (the reference case: $a_0=4$, $n_e=2.8\times 10^{16}{\mathrm{cm}}^{-3}$—solid black line), and for matched parameters corresponding to $a_0=4$ and $n_e=6.6\times 10^{16}{\mathrm{cm}}^{-3}$ (dashed red line), $a_0=3.5$ and $n_e=4.4\times 10^{16}{\mathrm{cm}}^{-3}$ (dashed green line) and $a_0=3.18$ and $n_e=3.3\times 10^{16}{\mathrm{cm}}^{-3}$ (dashed blue line). (b) Accelerating field $E_x$ (in units $m_{e}c{\omega }_0/e$) on the propagation axis after 1.5 cm (blue), 4 cm (red), 6.5 cm (green) and 9 cm (gold) in the reference case (CALDER-Circ simulation).

Figure 5

Monoenergetic electron acceleration in the blowout regime. All quantities are shown at $x=4\mathrm{cm}$ (two Rayleigh lengths). (a) Snapshot of electron density (in units of $n_c$, gray), and the laser field (in units of $m_{e}c{\omega }_0/e$, blue). (b) The longitudinal field $E_x$ on axis (in units $m_{e}c{\omega }_0/e$, blue) and normalized density of electrons in the longitudinal phase space (gray). (c) Electron energy spectrum.

Figure 6

Evolution of electron energy spectra in the blowout regime. Electron distribution after 9 cm of propagation (blue) and 4 cm (black dashed line).

Figure 7

Photon distribution per 0.1%BW integrated over a $100\times 100{\mathrm{mrad}}^2$ angle, obtained in the SM-LWFA regime. From lighter to darker blue: (1) $n_e=2.8\times 10^{17}{\mathrm{cm}}^{-3}$, (2) $n_e=5.6\times 10^{17}{\mathrm{cm}}^{-3}$, (3) $n_e=1.1\times 10^{18}{\mathrm{cm}}^{-3}$ and (4) $n_e=2.8\times 10^{18}{\mathrm{cm}}^{-3}$.

Figure 8

Angular energy distribution $\frac{dI}{d\mathrm{\Omega }}$ ($\mathrm{J}/\mathrm{sr}$) of the synchrotron source in the SM-LWFA regime. (a) $n_e=2.8\times 10^{17}{\mathrm{cm}}^{-3}$, (b) $n_e=5.6\times 10^{17}{\mathrm{cm}}^{-3}$, (c) $n_e=1.1\times 10^{18}{\mathrm{cm}}^{-3}$ and (d) $n_e=2.8\times 10^{18}{\mathrm{cm}}^{-3}$.

Figure 9

Characteristics of x-ray emission in the blowout regime after 9 cm of propagation. (a) Solid curves: number of photons per $0.1\%\mathrm{BW}$ emitted through the entire simulation (blue) and only over the last centimeter of propagation (green). Dashed curves: synchrotron fits. (b) Angular energy distribution $\frac{dI}{d\mathrm{\Omega }}$ ($\mathrm{J}/\mathrm{sr}$).