Rapid heating of a compressed fusion fuel by a short-duration laser pulse is a promising route to generating energy by nuclear fusion, and has been demonstrated on an experimental scale using a novel fast-ignitor geometry. Here we describe a refinement of this system in which a much more powerful, pulsed petawatt (10(15) watts) laser creates a fast-heated core plasma that is scalable to full-scale ignition, significantly increasing the number of fusion events while still maintaining high heating efficiency at these substantially higher laser energies. Our findings bring us a step closer to realizing the production of relatively inexpensive, full-scale fast-ignition laser facilities.