Inverse modelling of a laser-plasma accelerator

Abstract

The electron beams of a laser-plasma accelerator depend non-linearly on the laser and gas settings. This dependence is explored using particle-in-cell (PIC) simulations, and machine-learning models trained on these simulations predict the beam from the settings. Here we address the reverse problem: given a measured beam, which settings produced it? We infer three of them: the gas pressure $p\_1$, the normalised vector potential $a\_0$ and the nitrogen concentration $c\_{N\_2}$. The solution is not guaranteed to be unique. We train an ensemble of mixture density networks that, for each beam, output several possible sets of settings with their probabilities and uncertainties, and test them on simulated beams with realistic measurement noise. On average, the predictions are accurate ($R^2 = 0.91$), yet for about two-thirds of the beams the inferred distribution has two competing solutions. These share nearly the same value of $a\_0^2 p\_1$, which controls how strongly the laser focuses itself in the plasma and, in earlier PALLAS studies, when electrons start to be injected. Keeping this quantity fixed gives beams that are practically indistinguishable with realistic diagnostics. A forward model used as a check removes unphysical solutions but cannot choose between the two plausible ones. We then test two ways to resolve the ambiguity. Adding the full electron energy spectrum improves the mean prediction ($R^2 = 0.94$), mostly through $a\_0$. It changes the weights of the two solutions but does not move them. A second measurement at a deliberately different plasma density is more effective. In paired PIC simulations, it reduces the error on $a\_0$ by a factor of 2.6, whereas repeating the measurement at the same density brings almost no gain.