Optimized matching conditions for self-guided laser wakefield accelerators

We revisit the matching conditions for self-guided laser pulse propagation in plasma and refine their formulation to maximize the energy of electrons produced via laser wakefield acceleration. Bayesian optimization, combined with particle-in-cell simulations carried out in a quasi-three-dimensional geometry and a Lorentz-boosted frame, is employed. The optimization identifies the maximum electron energy that a self-guided laser wakefield accelerator, driven by a laser of a given energy, can produce, together with the corresponding acceleration distance. Our results further demonstrate that electrons with energies close to the maximum value can be obtained across a relatively wide range of input parameters and without the need for their precise tuning. This provides substantial flexibility for experimental implementation and significantly relaxes the operational constraints associated with self-guided laser wakefield accelerators.