The proton + ~11B -> 3 alpha fusion reaction is considered to be the cleanest (i.e.neutronless) method of exploiting nuclear energy. However, the very high ignition temperature (approx 200 keV), the bremsstrahlung losses and the relatively moderate fusion yield per reaction (8.7 MeV) make in veyr difficult to achieve a high energy gain. The idea proposed in the paper is based on the creation of a heat detonation wave (energy supplied by alpha particles) and a non-linear heat wave (by electron transport), where both waves move with some delay, but at the same speed, into a precompressed target. These heat waves move with some delay, but at the same speed, into a precompressed target. These heat waves are induced by a proton beam, by proton plasmas, by a laser beam fast ignitor or by jets, directed into a region called the 'ignitor', and they propagate into the 'cold' (<=1 keV) and compressed (< 10~3 g/cm~3) ~11-proton fuel. It is crucial that the boron to proton number ratio is smaller than one third. The heat waves propagate supersonically, and thus a large fraction (>30
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