Proton-boron-11 is the clean fusion reaction par excellence, but it is very difficult to exploit it because of the very high ignition temperature of this reaction and its moderate fusion yield. In this paper, a proposal is made to induce these reactions by a heat-detonation wave that expands across a compressed target. The front of the wave has a double-layer structure, with a first front driven by electron heat conduction and a second front heated by α-particle energy deposition. Both fronts create a hot plasma where the stopping power is dominated by ions. The wave is originated by an ignitor triggered by an ultraintense lightning beam. This beam can be made of photons (laser), plasma (ramjets), or ions (proton beams, borane clusters). Proton beam shots of 1022. W/cm2 and several GA for some picoseconds would be needed for this purpose. The supersonic propagation of the fusion wave and the ignitor requirements are analyzed in this paper. The main conclusion is that the burning wave can only propagate if a substantial fraction of the radiation losses from the already burning fuel is reabsorbed in the colder fuel. It is calculated that for densities larger than few thousands g/cm3 most of the bremsstrahlung radiation created in the hot plasma can be reabsorbed by the Compton effect in a region of 1 g/cm2 optical thickness of the surrounding compressed and cold fuel.