The quest for the inertial confinement fusion (ICF) ignition is a grand challenge, as exemplified by extraordinary large laser facilities. Fast isochoric heating of a pre-compressed plasma core with a high-intensity short-pulse laser is an attractive and alternative approach to create ultra-high-energy-density states like those found in ICF ignition sparks. This avoids the ignition quench caused by the hot spark mixing with the surrounding cold fuel, which is the crucial problem of the currently pursued ignition scheme. High-intensity lasers efficiently produce relativistic electron beams (REB). A part of the REB kinetic energy is deposited in the core, and then the heated region becomes the hot spark to trigger the ignition. However, only a small portion of the REB collides with the core because of its large divergence. Here we have demonstrated enhanced laser-to-core energy coupling with the magnetized fast isochoric heating. The method employs a kilo-tesla-level magnetic field that is applied to the transport region from the REB generation point to the core which results in guiding the REB along the magnetic field lines to the core. 7.7 $pm$ 1.3 % of the maximum coupling was achieved even with a relatively small radial area density core ($rho R$ $sim$ 0.1 g/cm$^2$). The guided REB transport was clearly visualized in a pre-compressed core by using Cu-$K_alpha$ imaging technique. A simplified model coupled with the comprehensive diagnostics yields 6.2% of the coupling that agrees fairly with the measured coupling. This model also reveals that an ignition-scale areal density core ($rho R$ $sim$ 0.4 g/cm$^2$) leads to much higher laser-to-core coupling ($>$ 15%), this is much higher than that achieved by the current scheme.
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