MHD wave coupling in the geomagnetic tail with field‐aligned density variations

Abstract

The normal MHD modes of the tail lobe are calculated for a simple model that is stratified in z. An important feature of our equilibrium field is that it may be tilted at an arbitrary angle (θ) to the antisunward direction, i.e., B = B(cosθ,0,sinθ). When θ = 0, the familiar singular second‐order equation of Southwood [1974] is recovered. When θ ≠ 0, the system is goverened by a nonsingular fourth‐order equation. Hansen and Harrold [1994] (hereafter HH) considered exactly this system and concluded that (for θ ≠ 0) energy was no longer absorbed by a singularity but rather over a thickened boundary layer across which the time‐averaged Poynting flux (〈Sz〉) changed. Our results are not in agreement with those of HH. We find (〈Sz〉) is independent of z and find no evidence of boundary layers, even for θ as small as 10−6 rad. Our solutions still demonstrate strong mode conversion from fast to Alfvén modes at the “resonant” position, but the small component of Alfvén speed in the ˆ direction permits the Alfvén waves to transport energy away from this location and prevents the continual accumulation of energy there. The implications for MHD wave coupling in realistic tail equilibria are discussed.