  Magnetic field generation in ultra-intense laser-solid interactions is
studied over a range of laser intensities relevant to next-generation laser
facilities ($a_0 = 50-500$) using 2D particle-in-cell simulations. It is found
that fields on the order of 0.1 MT (1 GigaGauss) may be generated by
relativistic electrons traveling along the surface of the target. However a
significant fraction of the energy budget is converted to high-energy photons,
~38% at $a_0=500$, greatly reducing the available energy for field generation.
A model for the evolution of the target-surface fields and their scaling with
$a_0$ is developed using laser parameters and assumed values for the average
radial electron velocity and reflectivity. The model and empirical scaling
allow for the estimation of field strengths on the next generation of laser
facilities, a necessary component to the proposal of any future magnetized
experiment.
