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A rendering of the magnetic field lines of the magnetosphere of the Earth.. In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field.
Two pairs of gauge transformed potentials (φ, A) and (φ′, A′) are called gauge equivalent, and the freedom to select any pair of potentials in its gauge equivalence class is called gauge freedom. Again by the Poincaré lemma (and under its assumptions), gauge freedom is the only source of indeterminacy, so the field formulation is ...
Schematic of the Birkeland or Field-Aligned Currents and the ionospheric current systems they connect to, Pedersen and Hall currents. [1]A Birkeland current (also known as field-aligned current, FAC) is a set of electrical currents that flow along geomagnetic field lines connecting the Earth's magnetosphere to the Earth's high latitude ionosphere.
The wave modes derived using the MHD equations are called magnetohydrodynamic waves or MHD waves. There are three MHD wave modes that can be derived from the linearized ideal-MHD equations for a fluid with a uniform and constant magnetic field: Alfvén waves; Slow magnetosonic waves; Fast magnetosonic waves
Earth's ring current is responsible for shielding the lower latitudes of the Earth from magnetospheric electric fields. It therefore has a large effect on the electrodynamics of geomagnetic storms . The ring current system consists of a band, at a distance of 3 to 8 R E , [ 1 ] which lies in the equatorial plane and circulates clockwise around ...
Finally only in this case the superposition principle fully apply, i.e. the wave function in a point P can be expanded as a superposition of waves on a border surface enclosing P. Wave functions can be interpreted in the usual quantum mechanical sense as probability densities where the formalism of Green's functions and propagators apply. What ...
The phase velocity of an electromagnetic wave in such a medium is = = + For the case of an Alfvén wave = + where is the Alfvén wave group velocity. (The formula for the phase velocity assumes that the plasma particles are moving at non-relativistic speeds, the mass-weighted particle velocity is zero in the frame of reference, and the wave is ...
Artistic representation of Earth's magnetosphere. The plasma sheet is highlighted in yellow. In the magnetosphere, the plasma sheet is a sheet-like region of denser (0.3-0.5 ions/cm 3 versus 0.01-0.02 in the lobes) [citation needed] hot plasma and lower magnetic field located on the magnetotail and near the equatorial plane, between the magnetosphere's north and south lobes.