Simulation of Coulomb particles collisions and calculation of Lyapunov exponent for bound orbits

Abstract

The computer simulation from the first principles allows us to obtain results for systems consisting of
many particles and interacting according to the Coulomb law (plasma, star clusters and astrophysical
objects). In this work, the methodology of simulation for Coulomb systems is investigated. The influence
of rounding errors, integration errors of reversible Newton equations is studied on the characteristics of
Coulomb collisions on the basis of the consideration of several model problems. The trajectories of two
particles attracted to the positively charged force center are got for various initial coordinates and
velocities and also their energetic natures are researched. It is shown that the symmetries are broken and
the particle paths are destroyed due to rounding errors and calculation errors. The degree of deviation
from symmetry is described by the value of the Lyapunov exponent, which characterizes the chaos and
turbulence in plasmas for the system. The results can be also extended to the system of gravitating
masses.