Powerful laser-plasma processes are explored to generate discharge currents of a few $100,$kA in coil targets, yielding magnetostatic fields (B-fields) in excess of $0.5,$kT. The quasi-static currents are provided from hot electron ejection from the laser-irradiated surface. According to our model, describing qualitatively the evolution of the discharge current, the major control parameter is the laser irradiance $I_{mathrm{las}}lambda_{mathrm{las}}^2$. The space-time evolution of the B-fields is experimentally characterized by high-frequency bandwidth B-dot probes and by proton-deflectometry measurements. The magnetic pulses, of ns-scale, are long enough to magnetize secondary targets through resistive diffusion. We applied it in experiments of laser-generated relativistic electron transport into solid dielectric targets, yielding an unprecedented 5-fold enhancement of the energy-density flux at $60 ,mathrm{mu m}$ depth, compared to unmagnetized transport conditions. These studies pave the ground for magnetized high-energy density physics investigations, related to laser-generated secondary sources of radiation and/or high-energy particles and their transport, to high-gain fusion energy schemes and to laboratory astrophysics.
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