Evidence for second-order oscillations at the Best frequency in direct numerical simulations of the Vlasov equation

Quantitative evidence for second-order oscillations occurring at the freque ncy predicted by Best [Physica 74, 183 (1974)] and by Sedlacek and Nocera [ J. Plasma Phys. 48, 367 (1992)] is provided by direct, ab initio numerical simulations of the Vlasov equation. These oscillations are relevant both fo r their intrinsic connection to the more customary plasma echo (also retrie ved), for their diagnostic applications to the study of turbulence, and for the high accuracy needed to reproduce them. This latter fact is used as a sensitive test for the numerical integration, which indeed reproduces both known and new features of the oscillations, including nonlinear Landau damp ing, particle trapping, and the oscillations' frequencies, in excellent agr eement with theory. (C) 1999 American Institute of Physics. [S1070- 664X(99 )01312-9].