Quantitative schlieren imaging of a laser-ionized plasma channel in atomic vapor using symbolic regression

Abstract

The plasma channel of the AWAKE plasma wakefield acceleration experiment is created by laser ionization of rubidium vapor in a 10~m long vapor source. Verifying the properties of the channel --- the radius of its fully ionized core and the width of its boundary sheath --- that are vital for ensuring good-quality wakefields is important as is validating numerical models of ionizing pulse propagation. Near-resonant schlieren imaging can detect the plasma channel in the low-density vapor, but there is no direct inversion to obtain channel parameters from the images. We use symbolic regression to find compact analytical formulas that connect measurable properties of the schlieren signal to plasma profile parameters. Using databases of simulated signals generated with three different plasma edge-profile families, we obtain formulas with one and two fitting constants to predict the equivalent channel radius with an accuracy below twice the camera pixel size and formulas to predict the sheath width. Re-evaluating previous measurements with these formulas, we confirm a theoretically predicted power-law relationship between the channel radius and the energy of the ionizing laser pulse. The formulas can be adapted to new experimental conditions by refitting the constants on a modest set of new samples, providing a lightweight, interpretable alternative to evaluation with deep neural networks.