The prerequisites and mechanism for the implementation of efficient pulsed (flashing) nuclear fusion in a low-temperature hydrogen plasma with a temperature of 10 to 20 eV in a constant magnetic field are considered. It is shown for the first time that the natural very frequent alternation of the processes of ionization of atoms and recombination of ions leads to the synchronous formation of coherent correlated states of hydrogen nuclei and its isotopes. The formation of such states leads to the generation of very large fluctuations of kinetic energy (up to 10 to 100 keV) at the initial stage of each ionization event, which exists for most of the lifetime of the ionized state before ion recombination. It is shown that the relatively long duration of the existence of these fluctuations and their very large amplitude are sufficient for efficient nuclear fusion in such a magnetized low-temperature plasma.