Chaotic behaviour in PIC simulation and its relation to computational errors Original Research Article

For a parallelized one-dimensional electrostatic PIC simulation code, an increase of separation of test particle orbits has been observed between numerical results with a single node and multiple nodes under the same initial and boundary conditions. The PIC simulation treats the many body Hamiltonian system which is characterized by positive Lyapunov exponents. In order to check the accuracy of simulation results at microscopic level, we have evaluated the chaotic property of the dynamical system realized in these two calculations. By measuring the maximum Lyapunov exponent, it is shown that the separation of particle orbits is not caused by accumulation of numerical errors, but caused by the origin of chaos that the solution is sensitive to initial conditions. Therefore, both results obtained with the single node and the multiple nodes are considered as the realization of an ensemble and equally reliable.We also discuss the relation between breakdown of energy conservation and stochasticity in the particle simulation.