First-principles kinetic simulations are used to investigate magnetic field generation processes in expanding ablated plasmas relevant to laser-driven foils and hohlraums. In addition to Biermann-battery-generated magnetic fields, strong filamentary magnetic filaments are found to grow in the corona of single expanding plasma plumes; such filaments are observed to dominate Biermann fields at sufficiently large focal radius, reaching saturation values of $sim$ 100 T at National Ignition Facility-like drive conditions. The filamentary fields result from the ion Weibel instability driven by relative counterstreaming between the ablated ions and a sparse background population, which could be the result of a gas prefill in a hohlraum or laser pre-pulse. The ion-Weibel instability is robust with the inclusion of collisions and grows on a timescale of 100 ps, with a wavelength on the scale of 100-250 $mu$m, over a wide range of background population densities; the instability also gives rise to coherent density oscillations. These results are of particular interest to inertial confinement fusion experiments, where such field and density perturbations can modify heat-transport as well as laser propagation and absorption.
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