Theory of magnetospheric standing hydromagnetic waves with large azimuthal wave number: 4. Standing waves in the ring current region

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There is a rich variety of observations of long‐period pulsations in the ring current region. One class of such pulsations is characterized by large azimuthal wave numbers and close confinement to a field line. In this paper, computations are made of the eigenfrequencies and fields of standing oscillations which can exist in a realistic self‐consistent magnetohydrodynamic model of such a region. The model, which depends on a few simple parameters, allows for the shape of the field line to be distorted from a dipole. In this paper it is limited to isotropic pressure. The magnetic field and transverse gradient of pressure can be defined. It is assumed that growth and loss processes are small and in balance because the plasma has reached a quasi‐linear equilibrium state. The computations show that a rich variety of compressional modes can exist. They are much more complex than simple coupled Alfvén and magnetosonic modes which are often invoked in such circumstances. At some points along the field line, such modes may be closely coupled while at other points they are essentially uncoupled with different wavelengths. This leads to modes with complex nonharmonic structures. It is noted that the transverse pressure gradient allows an MHD instability, related to the flute instability, to exist in appropriate circumstances. Such calculations should allow good comparison of theory and observation.