Global Non-Axisymmetric Whistler Instabilities in a Rotating Plasma

Flow-driven instabilities in magnetized, differentially rotating disk plasmas are studied as a potential mechanism of turbulent viscosity. In addition to the well-understood linear magneto-rotational instability, global eigenvalue calculations also observe large-scale modes that can be interpreted as over-reflected Alfven waves that are trapped either between resonances and/or the domain boundary (Ogilvie, et al. MNRAS 279 1995, Ebrahimi, et al. ApJ 936:145 2022). This work investigates local and global linear stability of non-axisymmetric perturbations in a differentially rotating disc threaded with axial and azimuthal magnetic fields in incompressible Hall-MHD. We find unstable whistler modes, and Alfvenic modes that are modified by a coupling with whistler waves. The Hall term introduces an asymmetry in the linear system based on the relative orientation of the magnetic field and the rotation axis, known in the axisymmetric case (Wardle MNRAS 307 1999, Balbus, et al. ApJ 552 2001). We show that this effect is more pronounced for non-axisymmetric modes. The whistler branch of instability exists in the electron-MHD limit, from which a single second ordinary differential equation for the radial structure of the eigenmodes is derived. Nonlinear Hall-MHD simulations of the differentially rotating system using the NIMROD code quantify the effect of non-axisymmetric whistler modes on angular momentum transport.