Hard X Rays from Laser-Wakefield Accelerators in Density Tailored Plasmas

Betatron x-ray sources from laser-plasma accelerators reproduce the principle of a synchrotron at the millimeter scale. They combine compactness, femtosecond pulse duration, broadband spectrum, and micron source size. However, when produced with terawatt class femtosecond lasers, their energy and flux are not sufficient to compete with synchrotron sources, thus limiting their dissemination and its possible applications. Here we present a simple method to enhance the energy and the flux of betatron sources without increasing the laser energy. The orbits of the relativistic electrons emitting the radiation were controlled using density tailored plasmas so that the energetic efficiency of the betatron source is increased by more than one order of magnitude.

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Popular Summary

Femtosecond x-ray sources have become invaluable tools to reveal ultrafast atomic and molecular dynamics. While most of the experiments are performed with x-ray free-electron lasers, research on alternative sources is crucial to democratize the use of femtosecond x-ray radiation. One promising avenue is the betatron source, which produces x rays from a relativistic laser-plasma interaction. However, betatron sources remain marginalized because of their limited photon energies. To overcome this hurdle, we demonstrate a novel and simple method to drastically improve the efficiency of a betatron source and use it to produce high-energy femtosecond radiation.

A betatron source reproduces the principle of a synchrotron in a millimeter-scale laser-produced plasma: An intense femtosecond laser produces a cavity in a plasma in which trapped electrons accelerate and produce x rays. Typically, the best way to boost the brightness of the emitted x rays is to raise the laser power. We try a different approach and instead modify the plasma density, which, in turn, alters the orbits of the trapped electrons. In our experiments, we find that this increases the x-ray photon energy by an order of magnitude compared with an unaltered plasma.

By boosting the x-ray energies without requiring a more powerful laser, our improved betatron source is an important milestone in the development of tabletop femtosecond x-ray sources.

Figure 1

Schematic representation of the role of density gradients to improve the efficiency of the betatron source. (a) A longitudinal density gradient results in an increase of $\gamma$ due to rephasing and an increase of the betatron oscillation frequency ${\omega }_{\beta }$. (b) A sharp transverse density gradient results in a shift of the cavity axis due to the refraction of the laser pulse and in an increase of the oscillation amplitude $r_{\beta }$. (c) Combining longitudinal and transverse density gradients increases simultaneously $\gamma$, ${\omega }_{\beta }$, and $r_{\beta }$.

Figure 2

Measurements and simulations of the density profiles used to improve the efficiency of the betatron source. (a) Measured density profiles of the gas used for the reference case (dotted line) and the longitudinal gradient (solid line). The beveled and tilted gas jets were used to produce the longitudinal gradient. (b),(c) openfoam simulation of the transverse gradient obtained by placing a $100\mu \mathrm{m}$ wire on top of the nozzle. Density profile along the laser propagation (red line) without (solid line) and with (dotted line) the wire.

Figure 3

Measurements of the betatron radiation spectra for a constant density plasma (purple) and for an up-ramp density plasma (green). The shaded area represents the intervals of betatron spectra that fit the x-ray signal measured through metallic filters. The thick solid lines within these areas are the fits obtained from particle-test simulations. Only the density gradient, set as initial condition, distinguishes the two cases in the numerical simulation. The experimental measurements and numerical fit agree and demonstrate that a longitudinal density gradient enhances the energy and flux of the betatron radiation. The critical energy $E_c$ characterizing the spectrum shifts from 5 to 10 keV.

Figure 4

Measurements of the x-ray beam profiles corresponding to the plasma density profiles displayed in Fig. 2. The upper image corresponds to the case without the wire and the lower image to the case with the wire. The images were obtained by imaging a scintillator screen intercepting the x-ray beam (the vertical line is a damage on the camera). The fact that the beam divergence is increased in one direction only demonstrates that the energy $\gamma$ and the transverse amplitude of oscillation $r_{\beta }$ of the electrons are both increased thanks to the density gradient produced by the wire.

Figure 5

Betatron radiation spectra measured for the constant density (purple), longitudinal gradient (green), and combined longitudinal and transverse gradients (blue). Thin and thick lines respectively correspond to the test-particle and particle-in-cell simulations. As expected, the increase of $\gamma$ and $r_{\beta }$ deduced from Fig. 4 results in a shift of the radiation spectrum toward higher energies. The critical energies shift from 5 to 10 and to 50 keV for, respectively, for the purple, green, and blue fits.

Figure 6

Particle-in-cell simulations showing the laser propagation (thick curve) and the particle trajectories (thin curves) in $(z,y)$ plane. The orbits are colored according to the laser peak field and the particle energy, respectively. Gray levels represent plasma density. (a) Up-ramp gradient. (b) Up-ramp gradient and transverse density gradient.