Whistler wave (${\omega }_{\pm }=\pm v_A{d}_i{k}_{\parallel }k$)

In the inertia-free, constant-density electron magnetohydrodynamics model with uniform guide field $B_0\hat{\mathbf{z}}$, a transverse magnetic plane wave obeys $\omega \mathbf{b}=i{v}_A{d}_i{k}_{\parallel }\mathbf{k}\times \mathbf{b}$. The helicity decomposition of a transverse Fourier mode gives the displayed dispersive branches with opposite circular polarizations. This electron-current mode is called a whistler wave; see Lyutikov's analysis of electron magnetohydrodynamics. Its pressure-free induction equation should not be identified with a general kinetic Alfvén model.