ELSEVIER Computer Physics Communications 108 (1998) 159-179 Computer Physics Communications A numerical method for solving the one-dimensional Vlasov-Poisson equation in phase space Takayuki Utsumi 1 Tomoaki Kunugi, James Koga Japan Atomic EnergyResearchInstitute, Tokai-mura, Naka-gun, lbaraki-ken 319-11, Japan Received 2 July 1997; revised 9 October 1997 Abstract A new numerical method for solving the one-dimensional Vlasov-Poisson equation in phase space is proposed. The scheme advects the distribution function and its first derivatives in the x and v directions for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of standard problems; the recurrence effect for a free streaming distribution, linear Landau damping, strong nonlinear Landau damping, the two-stream instability, and the bump-on-tail instability. A method of smoothing filamentation is given. The method can be generalized in a straightforward way to treat the Fokker-Planck equation, the Boltzmann equation, and more complicated cases such as problems with nonperoiodic boundary conditions and higher dimensional problems. (~ 1998 Elsevier Science B.V. PACS: 52.65.-y Keywords: Vlasov-Poisson equation; Differential algebraic CIP scheme 1. Introduction The system we solve here is the single species one-dimensional Vlasov-Poisson equation with periodic boundary conditions. These are written throughout the text in dimensionless units as 3f 3f E Of O, (1) --- ÷ u - - - = 3t c)x Ov O0 8E 1 / f dv. (2) 3x --00 J E-mail: utsumi@popsvr.tokai.jaeri.go.jp 0010-4655/98/$19.00 (~) 1998 Elsevier Science B.V. All rights reserved. PII S0()10-4655 (97) 001 19-7