High-energy-density flows through dense matter are needed for effective progress in the production of laser-driven intense sources of energetic particles and radiation, in driving matter to extreme temperatures creating state regimes relevant for planetary or stellar science as yet inaccessible at the laboratory scale, or in achieving high-gain laser-driven thermonuclear fusion. When interacting at the surface of dense (opaque) targets, intense lasers accelerate relativistic electron beams which transport a significant fraction of the laser energy into the target depth. However, the overall laser-to-target coupling efficiency is impaired by the large divergence of the electron beam, intrinsic to the laser-plasma interaction. By imposing a longitudinal 600T laser-driven magnetic-field, our experimental results show guided >10MA-current of MeV-electrons in solid matter. Due to the applied magnetic field, the transported energy-density and the peak background electron temperature at the 60micron-thick targets rear surface rise by factors 5, resulting from unprecedentedly efficient guiding of relativistic electron currents.
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