Whistler anisotropy instability: Spectral transfer in a three-dimensional particle-in-cell simulation

A three-dimensional (3-D) particle-in-cell (PIC) simulation of the whistler anisotropy instability is carried out for a collisionless, homogeneous, magnetized plasma with beta(e) = 0.10. This is the first 3-D PIC simulation of the evolution of enchanced fluctuations from this growing mode driven by an anisotropic electron velocity distribution with T-perpendicular to e/T-parallel to e > 1 where perpendicular to and parallel to represent directions perpendicular and parallel to the background magnetic field B-o, respectively. The early-time magnetic fluctuation spectrum grows with properties reflecting the predictions of linear theory with narrowband maxima at kc/omega(e) similar or equal to 1 and k x B-o = 0, and a wave vector anisotropy in the sense of k(perpendicular to) << k(parallel to) Here omega(e) represents the electron plasma frequency. At later times the fluctuations undergo both a forward transfer to shorter wavelengths, also with k(perpendicular to) << k(parallel to), and an inverse transfer to longer wavelengths with wave vector anisotropy k(perpendicular to) >> k(parallel to). The inverse transfer is consistent with a prediction of nonlinear three-wave coupling theory.