| The notion of frozen-in magnetic field originates from H. Alfvén, the result of a work on
electromagnetic-hydrodynamic waves published in 1942. After that, the notion
of frozen-in magnetic field, or ideal MHD, has become widely used in space plasma
physics. The controversy on the applicability of ideal MHD started in the
late 1950s and has continued ever since.
The applicability of ideal MHD is particularly interesting in regions where
solar wind plasma may cross the magnetopause and access the magnetosphere.
It is generally assumed that a macroscopic system can be described by ideal
MHD provided that the violations of ideal MHD are sufficiently small-sized near
magnetic x-points (magnetic reconnection). On the other hand, localized
departure from ideal MHD also enables other processes to take place, such
that plasma may cross the separatrix and access neighbouring magnetic flux
tubes. It is therefore important to be able to quantify from direct
measurements ideal MHD, a task that has turned out to be a major challenge.
An obvious test is to compare the perpendicular electric field with the
plasma drift, i.e. to test if E=–v×B.
Yet another aspect is to rule out the existence of parallel (to B) electric
fields. These two tests have been subject to extensive research for decades.
However, the ultimate test of the "frozen-in" condition, based on
measurement data, is yet to be identified. We combine Cluster CIS-data and
FGM-data, estimating the change in magnetic flux (δB/δt)
and the curl of plasma –v×B(∇×(v×B)), the terms in the "frozen-in equation".
Our test suggests that ideal MHD
applies in a macroscopic sense in major parts of the outer magnetosphere,
for instance, in the external cusp and in the high-latitude magnetosheath.
However, we also find significant departures from ideal MHD, as expected on
smaller scales, but also on larger scales, near the cusp and in the
magnetosphere-boundary layer. We discuss the importance of these findings.
Keywords. Magnetospheric physics (Magnetopause, cusp
and boundary layers; Solar wind-magnetosphere interactions)
– Space plasma physics |