Reinterpreting the Burton-McPherron-Russell Equation for Predicting Dst

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2722 Forecasting (7924, 7964), 2740 Magnetospheric Configuration And Dynamics, 2744 Magnetotail, 2778 Ring Current, 2788 Magnetic Storms And Substorms (7954)

Scientific paper

The simple equation proposed by Burton et al. [1975] and extensively applied with considerable success for predicting the time series of the geomagnetic storm index Dst is generally derived solely from conservation of energy: the total energy in the ring current plasma, related to Dst by the Dessler-Parker-Sckopke theorem, is calculated from a solar-wind-controlled energy input (source) rate and an effective loss rate, without describing the specific energization processes. More recently, numerical simulation models of ring current evolution have relied on the opposite approximation: they describe the energization (particle drifts under solar-wind-controlled electric fields) and loss processes, without imposing conservation of energy. The fact that, despite their different underlying assumptions, predictions of Dst by both methods agree reasonably well with each other and with observations suggests that some of the assumptions need to be reexamined. The Dessler-Parker-Sckopke theorem, in its generalized form, contains a magnetotail surface term proportional to the open magnetic flux, the time derivative of which equals the difference between the electric field integrals along the dayside and along the nightside reconnection lines. The dayside integral contributes a term to the equation for (d/dt)Dst that is identical in form and (within the uncertainties) consistent in magnitude with the empirically determined source term of the Burton-McPherron-Russell equation. The success of the empirical equation in predicting Dst then implies that the two remaining source terms in the theoretical equation, the contribution of the nightside integral in the magnetotail term and the rate of increase of plasma energy content, sum to zero (at least approximately); this is equivalent to the statement that the amount of kinetic energy being added to the ring current plasma equals a fraction X/ℒMT of the magnetic energy being removed from the magnetotail by nightside reconnection (X ~ 10 RE = distance between Earth and the inner edge of the magnetotail, ℒMT = effective length of the magnetotail). The simplest interpretation is that the energy of ring current plasma is indeed being supplied primarily from the magnetotail by processes that involve nightside reconnection in an essential way.

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