Magnetospheric interchange instability

It is shown that the conventional derivation of the MHD interchange instability criterion using an energy approach yields incorrect results. A special case involving straight, parallel flux tubes is considered in which the conventional energy argument should apply but disagrees with the result of an elementary dynamical argument. It is shown that the disagreement arises because the conventional derivation neglects the self-consistent changes in the magnetic field that result from the flux-tube interchange. When these self-consistent changes are included in the energy approach, a new interchange instability criterion is derived that agrees with the dynamical criterion. The new instability criterion is qualitatively different from the conventional one and suggests that the pressure gradient of energetic ions at Jupiter may not stabilize the Io torus against interchanges. The inner magnetospheres of earth, Jupiter, and Saturn may all be interchange unstable.