Correction to “Pressure‐driven and ionosphere‐driven modes of magnetospheric interchange instability”

Abstract

[1] In the paper "Pressure-driven and ionosphere-driven modes of magnetospheric interchange instability" by A. Miura (Journal of Geophysical Research, 114, A02224, doi:10.1029/2008JA013663, 2009, there were substantial errors in the equations. These errors were made by the mistaken use of the wave number vector in the equatorial plane instead of the wave number vector at the ionosphere in evaluating an ionospheric destabilizing contribution to the potential energy variation. Owing to these errors, the ionospheric destabilizing contribution to the potential energy variation was underestimated. This Correction provides the accurate form of the potential energy variation and corrects a quantitative prediction in the paper about the range of the azimuthal mode number m of unstable ionosphere-driven interchange modes in an axisymmetric inner magnetospheric model with a dipole magnetic field.[2] From equation (106) through equation (120) in Miura [2009], terms arising from k ?I , which is the wave number vector at the ionosphere, were mistakenly calculated by using k ?eq , which is the wave number vector in the equatorial plane. Thus, from equation (106) through equation (120), those terms should be multiplied by˛, which is defined by˛=Equations (C1)-(C5), which are necessary for the calculation of the explicit form of k 2 ? at arbitrary r and  in the spherical coordinates (r,  , ), were newly added after equation (105) as shown below. One can calculate the correction factor˛by using equation (C4) asIt is obvious that˛ 1 and˛= 1 occurs at L = 1.©2013. American Geophysical Union. All Rights Reserved. 2169-9380/13/10.1002/jgra.50173In other words, k?eq for L > 1 owing to the geometrical constriction of a magnetic flux tube toward the ionosphere. Thus, the ionospheric destabilizing contribution ıW I to the potential energy variation ıW was underestimated in Miura [2009], because |ıW I | is proportional to k 2 ?I . Therefore, the following corrections due to the introduction of the correction factor˛do not cause any essential change in one of the conclusions of the paper, which indicates that a substantial region of the inner magnetosphere with the equatorial plasmaˇless than one may be unstable against the ionosphere-driven interchange instability, which is caused by a horizontal plasma displacement on the spherical ionospheric surface. As shown below, one will find by the following corrections that ionosphere-driven interchange modes with a wider range of the azimuthal mode number m than m . 2 predicted by mistakenly using k ?eq instead of k ?I become unstable in the inner magnetosphere.[3] Necessary modifications to Miura [2009], which are caused by the introduction of the correction factor˛, are as follows:[4] 1. In paragraph [1] (abstract) of Miura [2009], the second and last sentences from the bottom "For an axisymmetric, north-south symmetric and lowmagnetospheric model, in which the magnetic field is approximated by a dipole field, the m = 1 or m = 2 ionosphere-driven mode, where m is the azimuthal mode number,...