Abstract:
An analytic solution has been formulated to study the role of ionospheric conductivity on
toroidal field line oscillations in the Earth’s magnetosphere. The effect of ionospheric conductivity is
addressed in two limits, viz, (a) when conductance of Alfvén wave is much different from ionospheric
Pedersen conductance and (b) when conductance of Alfvén wave is close to the ionospheric Pedersen
conductance. In the former case, the damping is not significant and standing wave structures are formed.
However, in the latter case, the damping is significant leading to mode translation. Conventionally,
“rigid-end” and “free-end” cases refer to eigenstructures for infinitely large and vanishingly small limit
of ionospheric conductivity, respectively. The present work shows that when the Pedersen conductance
overshoots (undershoots) the Alfvén wave conductance, a free-end (rigid-end) mode gets transformed
to rigid-end (free-end) mode with an increase (decrease) in harmonic number. This transformation takes
place within a small interval of ionospheric Pedersen conductance around Alfvén wave conductance,
beyond which the effect of conductivity on eigenstructures of field line oscillations is small. This regime of
conductivity limit (the difference between upper and lower limits of the interval) decreases with increase
in harmonic number. Present paper evaluates the damping effect for density index other than the standard
density index m = 6, using perturbation technique. It is found that for a small departure from m = 6, both
mode frequency and damping rate become a function of Pedersen conductivity.
