Bayesian Optimisation of Non-linear Breit-Wheeler Pair Production in Simulated Laser Experiments

Abstract

High laser intensities enable the production of electron-positron pairs from bright gamma rays passing through strong fields. Potentially the most promising approach for all-optical experiments in the near term uses dense but higher divergence electron beams from laser wakefield acceleration to produce gamma rays through inverse Compton scattering. Achieving many-photon collisions between these gamma rays and the high intensity laser pulse in practice is extremely difficult, however, due to significant shot-to-shot jitter in laser pointing and timing. We model these practical difficulties using simulated Monte-Carlo experiments. By using a more efficient algorithm for sampling infrequent pair production with particle splitting, we enable the exploration of a multi-dimensional parameter space. Using Gaussian Process Regression we then efficiently find optimal conditions for maximising pair production by changing the laser spot size, the energy in the colliding beam, and the stand-off distance between the laser wakefield accelerator and the focus of the colliding laser pulse. We find that the optimal stand-off distance increases with the degree of laser jitter and that the best conditions for producing electron-positron pairs are not the same as the best conditions for maximising the energy in the gamma rays. With \unit[100]{J} of laser energy, we estimate rates of pair production of around 1 pair per 100 electrons are achievable even with jitter of 10s of microns and 10s of femtoseconds.

Figures (7)

• Figure 1: a) Rate of electron-positron pair production in a tightly focussed 1 PW beam against photon energy, comparing results without splitting (blue circles), with naive splitting (red 'x's), with Poisson-sampling splitting (purple crosses), and with additive optical depths (green diamonds). b) Positron spectra predicted without splitting (blue) and with naive (red) and corrected splitting (purple), for photons at 400 MeV (i) and 1 GeV (ii).
• Figure 2: a) Rate of pair production for 400 MeV photons in a 1 PW beam against the number of photon particles $N_\gamma$ and the rate of splitting $u$, showing results with no splitting ($u=1$) and with a fixed number of particles but variable splitting ($N_\gamma=10$). b) Accuracy of the estimated rate of pair production plotted against $uN_\gamma$. c) Runtime of the simulation plotted against $uN_\gamma$
• Figure 3: a) Set up of the simulated experiment, with a laser pulse driving an electron beam from a laser wakefield accelerator, which then collides with an intense laser pulse at an angle of $\theta$. A stand-off distance of $l_0$ allows the electron beam to expand before it collides with the laser pulse. The colliding laser pulse is focussed to a spot size of $w_0$ and contains $s E_\mathrm{tot}$ of energy, compared to $(1-s)E_\mathrm{tot}$ in the accelerator beam. There is a random offset in both space and time between the peak intensity at the focus of the laser pulse and the electron beam. b) Prior distributions of normally distributed offsets $\Delta x$, $\Delta y$, and $\Delta t$ over 100 simulated shots. c) The corresponding posterior distribution of positron production rate for $\theta=15^\circ$, $l_0=\unit[10]{cm}$, $w_0=\unit[2]{\mu m}$, and $\unit[7.5]{GeV}$ electrons colliding with $sE_\mathrm{tot}=\unit[25]{J}$.
• Figure 4: Top panels) Positron production at different stand-off distances $l_0$ predicted by simulated experiments, overlaid on the surrogate model produced by Gaussian Process Regression. Circles show the mean of $log_{10}(N_+/N_-)$ while the error bars show the standard error over 100 simulated shots, including $\unit[10]{\mu m}$ spatial jitter and $\unit[25]{fs}$ temporal jitter. The model's predictions after each number of points $n$ are shown by the black line and the standard deviation on the model is shown by the shaded region. New points are shown in purple while previous points are shown in blue. Bottom panels) The expected improvement acquisition function predicted by the model against the stand-off distance. Peaks in the expected improvement are marked with dots and are used to calculate the next location to sample at $n+1$.
• Figure 5: a) Gaussian process optimisation of the rate of pair production at different levels of spatial jitter, from $\unit[0]{\mu m}$ standard deviation up to $\unit[40]{\mu m}$ standard deviation. 100 simulations were run at each point in parameter space, with the mean and error shown by the coloured points. In each case, the results were fitted to a Gaussian Process surrogate model, with the mean shown by the black lines and an error shown by the shaded region. b) Summary of the maximum rate of pair production (left axis, shown in blue) and the optimal stand-off distance (right axis, shown in red), plotted against the level of spatial jitter. The blue dotted trend line shows a power law fit $N_+/N_- = 0.7 \sigma^{-1.7}$ and the orange dashed trend line shows a linear fit $l_0 = \sigma / \unit[0.6]{mrad}$ respectively, for a spatial jitter given by $\sigma$.