Surrogate modeling of capillary-discharge on-axis density profiles for laser guiding: forward prediction and inverse design

Abstract Laser wakefield acceleration (LWFA) are promising sources of high-energy electron beams, but their performance is highly sensitive to the plasma target properties, making optimization challenging. In this work we present and validate the first module of a reverse-design workflow: a neural-network surrogate of a capillary-discharge plasma source trained on COMSOL Multiphysics hydrodynamic simulations. The model predicts the on-axis electron density profile along the capillary from the discharge control parameters (gas pressure and applied voltage) for a fixed capillary geometry. We assess generalization on held-out data and demonstrate a differentiable, gradient-based inverse design procedure that retrieves pressure and voltage values consistent with target density profiles within the surrogate model. Extensions to an LWFA-stage surrogate and downstream coupling to particle-transport simulations (e.g. via ONNX) are outlined as future work.