Crystalline beams

A beam of confined charged particles, that are cooled to the extreme of the space-charge dominated regime, where the relative motion of particles within the beam is small compared to their Coulomb potential energies, will crystallize in a unique form of condensed matter. Such a system of particles can be simulated using the method of Molecular Dynamics, which explicitly includes the interaction between all pairs of particles and uses repeating eels to simulate the effects of a long beam. Within the molecular dynamics simulations typically a few thousand particles are followed in time, allowed to equilibrate, and then the velocities are gradually scaled down while still allowing the system to maintain equilibrium. To reach a cold equilibrium value requires 10-100 thousand iterations, corresponding to real times on the order of a few thousand betatron periods