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As Lattice confinement fusion (LTC for short) is triggered at relatively small temperatures as compared to more traditional Tokamak methods, it reminded me of the need of quantum tunnelling for Stellar fusion processes to work. However, in these scenarios there is so much mass in a star's core that is makes proton tunnelling statistically likely.

Yet in LTC, the mass is minuscule, but as stated above, the temperatures achieved are very low. Hence, if there were to be quantum tunnelling, the potential energy barrier for proton tunnelling must be very low. From were would this value come/be calculated? Am I right or wrong in this assesment?

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Thanks for alerting us on this new method of fusion reactions. From the NASA description of the process

Called Lattice Confinement Fusion, the method NASA revealed accomplishes fusion reactions with the fuel (deuterium, a widely available non-radioactive hydrogen isotope composed of a proton, neutron, and electron, and denoted “D”) confined in the space between the atoms of a metal solid.

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In the new method, conditions sufficient for fusion are created in the confines of the metal lattice that is held at ambient temperature. While the metal lattice, loaded with deuterium fuel, may initially appear to be at room temperature, the new method creates an energetic environment inside the lattice where individual atoms achieve equivalent fusion-level kinetic energies.

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In the new method, a neutron source “heats” or accelerates deuterons sufficiently such that when colliding with a neighboring deuteron it causes D-D fusion reactions. In the current experiments, the neutrons were created through photodissociation of deuterons via exposure to 2.9+MeV gamma (energetic X-ray) beam. Upon irradiation, some of the fuel deuterons dissociate resulting in both the needed energetic neutrons and protons.

From this description no proton tunneling is needed. The lattice is used as the "container" of the reaction, and all the reaction necessary for fusion happen between the inserted in the lattice atoms.

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