The interaction of relativistically intense lasers with opaque targets represents a highly non-linear, multi-dimensional parameter space. This limits the utility of sequential 1D scanning of experimental parameters for the optimisation of secondary radiation, although to-date this has been the accepted methodology due to low data acquisition rates. High repetition-rate (HRR) lasers augmented by machine learning present a valuable opportunity for efficient source optimisation. Here, an automated, HRR-compatible system produced high fidelity parameter scans, revealing the influence of laser intensity on target pre-heating and proton generation. A closed-loop Bayesian optimisation of maximum proton energy, through control of the laser wavefront and target position, produced proton beams with equivalent maximum energy to manually-optimized laser pulses but using only 60% of the laser energy. This demonstration of automated optimisation of laser-driven proton beams is a crucial step towards deeper physical insight and the construction of future radiation sources.
Plasma supports collective modes and particle-wave interactions that leads to complex behavior in inertial fusion energy applications. While plasma can sometimes be modeled as a charged fluid, a kinetic description is useful towards the study of nonlinear effects in the higher dimensional momentum-position phase-space that describes the full complexity of plasma dynamics. We create a differentiable solver for the plasma kinetics 3D partial-differential-equation and introduce a domain-specific objective function. Using this framework, we perform gradient-based optimization of neural networks that provide forcing function parameters to the differentiable solver given a set of initial conditions. We apply this to an inertial-fusion relevant configuration and find that the optimization process exploits a novel physical effect that has previously remained undiscovered.
Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects become important and a turbulence closure is required, and in systems with a large Knudsen number, kinetic effects become important and a kinetic closure is required. By adding an equation governing the growth and transport of the quantity requiring the closure relation, it becomes possible to capture microphysics through the introduction of ``hidden variables'' that are non-local in space and time. The behavior of the ``hidden variables'' in response to the fluid conditions can be learned from a higher fidelity or ab-initio model that contains all the microphysics. In our study, a partial differential equation simulator that is end-to-end differentiable is used to train judiciously placed neural networks against ground-truth simulations. We show that this method enables an Euler equation based approach to reproduce non-linear, large Knudsen number plasma physics that can otherwise only be modeled using Boltzmann-like equation simulators such as Vlasov or Particle-In-Cell modeling.