Physics
Scientific paper
Dec 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011agufmsm52a..01s&link_type=abstract
American Geophysical Union, Fall Meeting 2011, abstract #SM52A-01
Physics
[2730] Magnetospheric Physics / Magnetosphere: Inner, [2736] Magnetospheric Physics / Magnetosphere/Ionosphere Interactions, [2740] Magnetospheric Physics / Magnetospheric Configuration And Dynamics, [2753] Magnetospheric Physics / Numerical Modeling
Scientific paper
The frozen-in theorem of ideal magnetohydrodynamics (MHD) is a powerful theorem that allows the evolution of the magnetic field within an MHD fluid to be determined based on the motion of the plasma. It is often argued, however, that the frozen-in condition is invalid for the inner magnetosphere because the current densities are large, suggesting that j/ne (the equivalent flow velocity for the current) is larger than u, the flow velocity of the plasma. As we shall emphasize here, what matters for MHD is the curl of the electric field, that is the induction electric field, rather than that portion of the electric field that is related to the electrostatic potential. From an MHD perspective, providing the induction electric field is properly specified within the simulation domain, the electric field associated with the electrostatic potential is irrelevant. On considering the ion momentum equation, which includes the electric field, it can be shown that for barotropic flows, where the gradient in pressure and density are parallel, the quantity frozen to the fluid is a modified version of the magnetic induction that includes a term related to the fluid vorticity. Provided the fluid vorticity is much less than the ion gyro-frequency, the magnetic field is frozen to the fluid. This analysis also emphasizes that while the frozen-in condition has been invoked to suggest that diamagnetic drifts are absent in MHD, this is not the case. The MHD momentum equation does include the diamagnetic drift. Within MHD the frozen-in condition is used to determine the electric field from the flow, not the flow from the electric field. The issue then becomes whether or not the barotropic approximation applies. We have analyzed simulation results provided by the OpenGGCM model, run at the Community Coordinated Modeling Center. We find that there are cases where the pressure and density gradients are not aligned. Because MHD assumes adiabatic flows, and adjacent flux tubes would be expected to have very similar histories, any cross-flow gradients should be small. We suggest that non-MHD processes (e.g., reconnection) create regions within the inner magnetosphere were adjacent flux tubes have significantly different flow histories, resulting in non-aligned pressure and density gradients. Whether or not this significantly affects the induction electric field requires further analysis, but it does raise the question of how MHD, or convection models that require prescribed electric fields, can fully address the dynamics of the inner magnetosphere.
Raeder Joachim
Strangeway Robert J.
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