On the existence of purely transverse field‐line oscillations

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Abstract
We have shown that transverse toroidal (or poloidal) oscillations are possible in a dipole field, provided they are sufficiently localized in radial (azimuthal) direction for the Hall current‐generated electric fields to be relevant. Explicit solutions are obtained for azimuthal oscillations and it is shown that these are localized in the radial direction with an exponential decay length in the equatorial plane; where L0 is the equatorial distance of the field line; ω and ωci are field line resonance and ion cyclotron frequencies, and k is the zonal wave number of the mode. It is also shown that a superposition of a continuum of such structures centered over a range of L values can generate the fluctuations that are observed.