Crystal Ball: A Toy Model for a Novel Fusion Method

It is known that lattices under compression can undergo phase transitions, allowing nuclei to potentially gain non-negligible kinetic energy over the timescale of the transition. In such a system, doping the lattice with fusion reactants may create energetically favorable conditions for fusion to occur. We call this Lattice Compression Fusion (LCF). To probe this phenomenon, we developed a classical toy model of a two-dimensional lattice on the surface of a three- dimensional sphere. Boron nuclei are used as point particles, in analogy to Proton-Boron (pB11) fusion, as they naturally form two-dimensional materials (Borophene lattice structures). To form a lattice, we initialize 𝑁 particles on the surface of the sphere, pushing the particles to equilibrium through strong Coulomb coupling with a viscous damping term, minimizing the Coulomb potential similar to the Thomson problem. To simulate a phase transition, we remove a single particle (or region of particles), forcing the system to rearrange itself into a new equilibrium. We develop a scaling relation for the peak kinetic energy attained by a single particle as a function of the total number of particles 𝑁 and the number of particles removed 𝑁rm. For certain values of 𝑁, we observe an order of magnitude gain in energy when increasing 𝑁rm from 1 to 6, indicating it may be possible to engineer a lattice to maximize the energy gain. We comment on the pB11 fusion cross section and the classical tunneling probability.