Radiation of relativistic electrons created in tunnel ionization of atomic gases by laser beams of extreme intensity

TL;DR

This work addresses diagnosing the peak intensity and field structure inside focused ultra-intense lasers by analyzing radiation from relativistic photoelectrons produced via tunnel ionization of argon in a $10^{21}-10^{22}$ W/cm$^2$ regime. It combines tunnel-ionization theory (SC/PPT) with classical post-ionization dynamics and Jackson–Landau radiation formulas, and it extends the analysis with a weak counter-propagating probe described by nonlinear Thomson scattering in a Lorentz-transformed frame. The results show that the radiation pattern is highly sensitive to the local peak intensity, is initially dominated by inner-shell ($1s$) electrons near their ionization thresholds, and can reach Lorentz factors up to $\gamma\sim 10^3$, yielding forward-peaked spectra. Importantly, a weak counter-propagating probe with $a_0'\sim 1$ and a suitable delay can enhance the emitted energy to detectable levels (a few photons per atom) in a focal volume of order $10^3-10^4$ atoms, enabling in situ diagnostics of the focal field and informing studies of laser-plasma acceleration and quantum-electrodynamics cascades.

Abstract

We consider tunnel ionization of atomic argon in a femtosecond laser pulse of intensity $10^{21}-10^{22}{\rm W/cm}^2$ aiming to investigate the relativistic dynamics and radiation of photoelectrons released from their parent ions inside the laser focus. Radiation of such electrons accelerated along the laser field propagation direction appears to have moderate power but can be considerably enhanced by a collision with a relatively weak counter-propagating laser pulse. Using the theory of laser-induced tunneling in atoms and ions and that of nonlinear Thomson scattering, we demonstrate that angular distributions and spectra of emitted photons can serve as a probe of the peak intensity in the focus. The angular distribution of emitted radiation in the plane of polarization and propagation of the ionizing laser beam appears narrow and peaked around an intensity-dependent angle, making this ionization setup a source of collimated XUV radiation.

Figures (7)

• Figure 1: Sketch of the interaction setup: a focused laser beam with the wave vector ${\bf k}$; a diluted atomic gas jet crossing the laser focus (red dots); trajectories of electrons released in multiple tunnel ionization of atoms (blue lines); emitted photons (yellow curling lines).
• Figure 2: Distributions in the number of electrons $N_e$ released through tunneling per interval $\Delta t=T_L/15$ with the rate defined by Eq.(\ref{['PPT']}) from $N_{\rm at}=100$ ions ${\rm Ar}^{8+}$ randomly distributed in the interaction volume. The ion charge is shown by color (see the color coding bars in the right upper corner). The laser field time envelope (\ref{['gaussian']}) is shown by a black solid line. Time is given in laser periods. Panel (a) corresponds to intensity ${\cal I}=10^{21}$W/cm$^2$, panel (b) -- to ${\cal I}=10^{22}$W/cm$^2$. For the lower intensity, the $1s$ shell is not ionized.
• Figure 3: Electron trajectories in the $(x,z)$ (a) and $(y,z)$ (b) planes for an atom with coordinates $x_0=0.06\lambda,~y_0=-0.25\lambda,~z_0=-1.35\lambda$. The central part of the focus with ${\cal I}\ge {\cal I}_0/{\rm e}^2$ is shown blue. The color code for the electron number inside the shell is shown in the upper right corner.
• Figure 4: Time-dependent Lorentz factors $\gamma(t)$ for 10 electron trajectories with the parameters of Fig.2. Panels (a) and (b) correspond to those of Fig.2. Panel (c) shows the same as (b) in a different scale to make the trajectories of the two $1s$ electrons visible. The electron number inside the shell is coded by the same colors as in Fig.2.
• Figure 5: Dependence of the polar angle $\theta_0$ between the laser wave vector $\bf k$ and the maximum of the angular distribution at fixed frequency $\omega$ on the azimuthal angle in the plane orthogonal to $\bf k$ for $a_0=50$ (upper row), $a_0=100$ (middle row) and $a_0=200$ (lower row). The radiation frequency is $6\cdot10^4\omega_L$ (left column), $2.5\cdot 10^4\omega_L$ (middle column) and $6\cdot10^3\omega_L$ (right column). The electric field polarization direction is horizontal $(\psi=0,\pi)$. The relative radiation power is color-coded.