  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.
