A Complementary Fluid Method in delta δf Particle Simulation

A new simulation method that improves the conservation properties of δ f particle simulation for the collisionless Boltzmann equation is presented. When the distribution function is divided into a reference distribution specifi ed in advance and a variation distribution, the time evolution of the variation distribution is described by an advection termin the phase space and a source term associated with the reference distribution. The time evolution of the Klimontovich distribution function of the δ f method was investigated. It is shown that the errors in the Monte Carlo estimate of the source term in the δ f method deteriorate the conservation properties. In the new simulation method, errors in the Monte Carlo estimate of the source term are corrected with a complementary fl uid model. An example of the complementary fl uid model is presented for bump-on-tail instability. The simulation results are compared with those of the conventional δ f method. It is demonstrated that particle, momentum, and energy are well conserved with the new simulation method.