Particle acceleration during classical phase transitions on a spherical lattice

When compressed, certain lattices undergo phase transitions that may allow nuclei to gain significant kinetic energy. To explore the dynamics of this phenomenon, we develop a methodology to study Coulomb coupledN-body systems constrained to a sphere, as in the Thomson problem. We initializeNtotal Boron nuclei as point particles on the surface of the sphere, allowing them to equilibrate via Coulomb scattering with a viscous damping term. To simulate a phase transition, we removeNrmparticles, forcing the system to rearrange into a new equilibrium. With this model, we consider the Thomson problem as a dynamical system, providing a framework to explore how non-zero temperature affects structural imperfections in Thomson minima. We develop a scaling relation for the average peak kinetic energy attained by a single particle as a function ofNandNrm. For certain values ofN, we find an order of magnitude energy gain when increasingNrmfrom 1 to 6. The model may help to design a lattice that maximizes the energy output.