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

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 (theta) to the antisunward direction, i.e., B = B(cos theta, 0, sin theta). When theta = 0, the familiar singular second-order equation of Southwood [1974] is recovered. When theta not equal 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 theta not equal 0) energy was no longer absorbed by a singularity but rather over a thickened boundary layer across which the time-averaged Poynting flux ([S-z]) changed. Our results are pot in agreement with those of HH. We find [S-z] is independent of z and find no evidence of boundary layers, even for theta as small as 10(-6) rad. Our solutions still demonstrate strong mode conversion from fast to Alfven modes at the "resonant" position, but the small component of Alfven speed in the (z) over cap direction permits the Alfven 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.