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 β 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 ⟂ e / T ∥ e >1 where ⟂ and ∥ 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 k c / ω e ≃ 1 and k × B o =0, and a wave vector anisotropy in the sense of k ⟂ << k ∥ . Here ω e represents the electron plasma frequency. At later times the fluctuations undergo both a forward transfer to shorter wavelengths, also with k ⟂ << k ∥ , and an inverse transfer to longer wavelengths with wave vector anisotropy k ⟂ >> k ∥ . The inverse transfer is consistent with a prediction of nonlinear three‐wave coupling theory.