  While laser wakefield acceleration (LWFA) in the bubble regime demands
ultra-short, high-peak-power laser pulses, operation in the self-modulated
regime (SM-LWFA) works with more relaxed pulse conditions, albeit at the cost
of lower beam quality. Modern laser systems can deliver pulses with durations
of a few tens of femtoseconds and peak powers on the order of a few terawatts,
at kHz repetition rates. These systems are well-suited for developing SM-LWFA
applications where high average energy and charge are prioritized over beam
quality. Such beams could be used to generate high-energy bremsstrahlung
photons, capable of triggering photonuclear reactions to produce radioisotopes
like molybdenum-99. This isotope decays into technetium-99m, the most widely
used medical radioisotope, with over 30 million applications worldwide per
year. This work explores the use of Bayesian optimization to maximize the
energy and charge of electron beams accelerated via SM-LWFA. Particle-in-cell
(PIC) simulations model a 5 TW, 15 fs-long Gaussian laser pulse, propagating
through tailored hydrogen gas-density profiles. In these simulations, over
multiple iterations, the algorithm optimizes a set of input parameters
characterizing the gas-density profile and the laser focal position. Three
distinct profiles, with total lengths ranging from 200 to 400 micrometers and
combining ramps and plateaus, were investigated. Optimal configurations were
found to produce electron beams with median energies ranging from 14 to 17 MeV
and charges of 600 to 1300 pC, considering electrons with energies above 8 MeV.
Preliminary estimates of the molybdenum-99 yields for the optimal beams were
obtained by employing their phase spaces, retrieved from PIC simulations, as
radiation source inputs in Monte Carlo simulations irradiating a combined
tantalum and molybdenum target.
