Ionization states for the multipetawatt laser-QED regime

A paradigm shift in the physics of laser-plasma interactions is approaching with the commissioning of multipetawatt laser facilities worldwide. Radiation reaction processes will result in the onset of electron-positron pair cascades and, with that, the absorption and partitioning of the incident laser energy, as well as the energy transport throughout the irradiated targets. To accurately quantify these effects, one must know the focused intensity on target in situ. In this work, a way of measuring the focused intensity on target is proposed based upon the ionization of xenon gas at low ambient pressure. The field ionization rates from two works [Phys. Rev. A 59, 569 (1999) and Phys. Rev. A 98, 043407 (2018)], where the latter rate has been derived using quantum mechanics, have been implemented in the particle-in-cell code SMILEI [Comput. Phys. Commun. 222, 351 (2018)]. A series of one- and two-dimensional simulations are compared and shown to reproduce the charge states without presenting visible differences when increasing the simulation dimensionality. They provide a way to accurately verify the intensity on target using in situ measurements.

Figure 1

Ratio of the focused peak intensity of a beam pulse of central wavelength 800 nm and bandwidth of 50 nm having PFT degradation to the focused peak intensity of the STC-free beam pulse (thus called reduction), as a function of the beam's diameter for fixed degradation or as a function of the degradation's magnitude for fixed diameter.

Figure 2

Xe charge states in a 1D PIC simulation. The gas density was low enough to allow neglecting collective plasma effects and relativistic self-focusing.

Figure 3

Xe representative charge states' populations at the end of 15 000 1D PIC simulations. These $c_n\left(I\right)$ curves can be used to calculate the number of ions produced in the focus.

Figure 4

(a) Xenon representative charge states' populations at the end of 1000 2D Gaussian beam PIC simulations. (b) Squared electric field at one time step, across the 2D PIC simulation box, for a simulation with $a_0=707.19$. (c) Results of the integration of the 1D charge states across the 2D PIC simulation box.

Figure 5

Number of xenon ions produced in the focus of the Gaussian beam from Eq. (5). One data point on each curve corresponds to the number of ions arising from one, fixed, peak intensity $I_m$ value in Eq. (5). Results on the $y$ axis are numerical calculations for $N\left({\text{Xe}}^{n+}\right)$ from Eq. (4).

Figure 6

Model evidence as a function of the polynomial order at the start of the training procedure.

Figure 7

Test-set mean-squared error as a function of the polynomial order at the start of the training procedure.

Figure 8

Predicted response as a function of the input for the model for which we list the values of ${\vec{\alpha }}^{*}$ and ${\beta }^{*}$. The two-sigma deviation is highlighted in blue and represents the 95% uncertainty in the predictions, as from Eq. (B10).