Development of a method for modeling the dynamics of many Coulomb particles

Abstract

An investigation is made of the properties of a new algorithm for numerically solving the Newton equations for many Coulomb particles, based on taking more accurate account of the time dependence of the interaction forces between nearest neighbors. It is shown that when the four nearest neighbors are taken into account the accuracy of the method is considerably increased over that of the previously used method where the two nearest neighbors were included. The accuracy is investigated by monitoring the conservation of energy and by the method of reversing the particle motion (the reversal method). It is shown that the reversibility of the numerical solution is maintained for times of the order of the transit time for the average interparticle distance, whereas the energy is conserved for much longer times with an accuracy of better than a tenth of one percent. A method for diagnosing bound states is proposed from the energy distribution of the mutually nearest neighbors in the center of mass system. A discussion is given of the relationship between the results obtained and the present ideas on the stochastic properties of dynamic systems. It is suggested that the effect of recombination being “frozen”, discovered from the modeling, results from the absence of Gibbs mixing of the free and bound states.