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Magnetic field generation in ultra-intense laser-solid interactions isstudied over a range of laser intensities relevant to next-generation laserfacilities ($a_0 = 50-500$) using 2D particle-in-cell simulations. It is foundthat fields on the order of 0.1 MT (1 GigaGauss) may be generated byrelativistic electrons traveling along the surface of the target. However asignificant 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 averageradial electron velocity and reflectivity. The model and empirical scalingallow for the estimation of field strengths on the next generation of laserfacilities, a necessary component to the proposal of any future magnetizedexperiment.

Magnetic field generation in laser-solid interactions at strong-field QED relevant intensities