A generalized Hasegawa–Mima equation in curved magnetic fields

Abstract

We derive a model equation describing electrostatic plasma turbulence in general (inhomogeneous and curved) magnetic fields by analysing the effect of curved geometry on the ion fluid polarization drift velocity. The derived nonlinear equation generalizes the Hasegawa–Mima equation governing drift wave turbulence in a straight homogeneous magnetic field, and may serve as a toy model for the description of turbulent plasmas. The equation is most appropriate for configurations with a small$\boldsymbol {E}\times \boldsymbol {B}$drift velocity divergence, or a mild spatial change in$\boldsymbol {E}\times \boldsymbol {B}$drift velocity. We identify the conserved energy of the system, and obtain conditions on magnetic field topology for conservation of generalized enstrophy. Through numerical examples, we further show how the curvature of the magnetic field reshapes self-organized steady turbulent states.