As all magnetospheric activity is powered by energy input from the solar wind, detailed understanding of the energy transfer processes and mechanisms is a key challenge for space weather applications. As described in the previous section, observationally we lack global measurements of the energy transfer and thus are limited to the use of proxies. However, global MHD simulations can be used to trace the energy transfer through the simulation magnetopause and through the magnetosphere-ionosphere system. In this section, we analyze the energy transfer using the GUMICS-4 global MHD simulation (Janhunen, 1996) and compare and contrast the results with those obtained using the empirical proxies.
In the MHD formulation applied in the global MHD simulations, the total energy flux is given byU = P∕(γ − 1) + ρV 2∕2 + B2∕2μ 0 is the total energy density, P the plasma pressure, and γ = 5∕3 is the ratio of specific heats. The total energy flux is a conserved quantity in the simulation, and thus it is possible to trace energy flow lines, and the energy transfer through the magnetopause can be evaluated by following the energy flux flow lines and computing its normal component at the boundary.
The challenge in this approach is the determination of the magnetopause surface in the simulation. Observationally, the magnetopause is a current layer (often a tangential discontinuity) that separates the solar wind and interplanetary field from the magnetospheric plasma and field. Thus, from in situ satellite observations, the magnetopause can be distinguished as the location of the current maximum or as the (often very sharp) discontinuity in the magnetic field and plasma density. After trying several methods, the chosen solution for finding the magnetopause in the GUMICS-4 simulation was to define the magnetosphere as a cavity carved by the solar wind plasma flow lines (Palmroth et al., 2003). The magnetopause is then the surface defined by the innermost plasma flow lines encircling the magnetosphere. This method has proven to be quite robust and consistent with other definitions of the magnetopause.
The energy entering from the solar wind into the magnetosphere is dominated by the Poynting flux, and is only modulated by the dominant energy source, solar wind kinetic energy flux. As the 𝜖 parameter essentially is the Poynting flux toward the magnetopause, it is a good proxy also for the energy transfer rate. The magnetospheric magnetic field topology and the electric field imposed by the solar wind flowing past the magnetosphere create a geometry where a large portion of the entering Poynting flux is focussed to the inner magnetotail (Papadopoulos et al., 1999). Figure 10 illustrates how the Poynting flux entering through the magnetopause is directed toward the central plasma sheet under the Earthward pointing magnetic field in the northern tail lobe and cross-tail (out of the plane of the figure) electric field. In the magnetotail, the energy is converted from magnetic to plasma energy at the cross-tail current sheet.
The amount of energy conversion in the magnetotail can be quantified by evaluating the integral of the Poynting flux divergence (∫ dV ∇⋅ S) in a region that encompasses most of the inner magnetosphere, and hence the region that is mostly affecting space weather phenomena (Laitinen et al., 2005). While this method does not exactly specify the region where the energy conversion takes place, selecting a suitably large region ensures that no major dissipation locations are left out, while the energy conversion outside the active regions is small enough not to produce errors in the evaluation.
Figure 11 shows three frames from a simulation showing the magnetopause size and shape as well as the locations of energy entry from the solar wind into the magnetosphere during the magnetic storm on April 6, 2000 (for observations see Figures 7 and 9). Energy transfer from the solar wind into the magnetosphere is shown in blue and energy escape from the magnetosphere to the magnetosheath is shown in red. Note also the highly variable size of the magnetosphere as the increasing solar wind dynamic pressure compresses the magnetosphere to almost half its original size. As shown previously, in this event the compression was strong enough to push the magnetopause inside the geostationary orbit for an extended period during the storm main phase (Huttunen et al., 2002).
Integration of the energy flow vector over the magnetopause surface yields a total energy input per unit time, i.e., power transfer through the boundary. The top panel of Figure 12 shows a comparison of the total energy computed from the simulation with the empirical 𝜖 parameter. Note that the scale for the empirical parameter is different from the simulation one: the two quantities do not agree in magnitude, which indeed is expected. While the energy input through the simulation boundary is a total energy entering the system, the scaling for the 𝜖 parameter was empirically obtained to match the inner magnetosphere and ionosphere energy dissipation (free scaling parameter 7 RE in Equation 3). Thus, the difference in the magnitudes is a measure of the amount of solar wind energy input that becomes geoeffective in the inner magnetosphere.
Detailed analysis of the energy input locations shows that most of the energy enters the magnetosphere through the magnetopause Earthward of about −10 RE, which gives two main regions of energy input, the dayside, and the nightside boundary in the inner magnetotail region. Further down the tail, the energy transfer through the boundary is very small, as the Poynting flux flows very closely parallel to the boundary. If one looks at the azimuthal sectors (in a plane perpendicular to the Sun-Earth line), it can be seen that the energy is mostly entering in sectors that are parallel or antiparallel to the IMF orientation. This means that for southward IMF, the energy is mainly gaining access through the high-latitude regions in both hemispheres. This is consistent with the conceptual picture of the reconnecting magnetopause where the reconnection occurs close to the subsolar point and the open flux is transported across the high-latitude regions (Dungey, 1961).
Mainly two processes consume energy in the ionosphere: Joule heating resulting from the ionospheric closure of field-aligned currents and precipitation of magnetospheric electrons causing the auroral displays. Both quantities can be computed from the ionospheric solution of the global simulation. Total integrated power from Joule heating is obtained from PJH = ∫ ΣP E2dS. The energy of the precipitating electrons is integrated from the innermagnetosphere plasma parameters as EPREC = neTe3∕2. The two bottom panels of Figure 12 show line plots of the values integrated over the polar cap and compared with the empirical proxies discussed in Section 4. Figures 13 and 14 show excerpts from two simulations showing the ionospheric Joule heating and the auroral Hall conductivity, which is enhanced in regions of auroral precipitation, and hence proportional to the precipitation energy.
It is obvious that the strong activity drives highly enhanced auroral precipitation to a wide and expanded auroral oval. Furthermore, the ionospheric Joule heating is large both in the auroral oval region and in the polar cap, due to the very strong electric fields in the polar cap region. The MHD precipitation tends to follow closely the solar wind driver, while the AE-based proxy shows lower level of variability. On the other hand, the MHD simulation produces a large peak at the time of a solar wind pressure pulse, which is not present in the AE-based proxy for the Joule heat. As solar wind pressure pulses are known to be associated with enhanced ionospheric Joule heating (Palmroth et al., 2004), it is not clear to what extent the discrepancies are associated with limitations of the simulation and to what extent they are caused by the use of index-based proxies that may miss large parts of the dissipation if the measuring stations are not suitably located to record the disturbances. This is clearly an area where more work, both simulation and observational, is required for enhanced understanding of the coupling of the solar wind and the ionospheric processes.
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