Role of finite ionospheric conductivity on toroidal field line oscillations in the Earth’s magnetosphere—Analytic Solutions

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.