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If the pressure from particles within the magnetosphere is neglected, it is possible to estimate the distance to the part of the magnetosphere that faces the Sun.The condition governing this position is that the dynamic ram pressure from the solar wind is equal to the magnetic pressure from the Earth's magnetic field: [note 1] (()) where and are the density and velocity of the solar wind, and ...
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. [1] [2] It is created by a celestial body with an active interior dynamo.
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.
In the height region between about 85 and 200 km altitude on Earth, the ionospheric plasma is electrically conducting. Atmospheric tidal winds due to differential solar heating or due to gravitational lunar forcing move the ionospheric plasma against the geomagnetic field lines thus generating electric fields and currents just like a dynamo coil moving against magnetic field lines.
The dynamic pressure of the wind dominates over the magnetic pressure through most of the Solar System (or heliosphere), so that the magnetic field is pulled into an Archimedean spiral pattern (the Parker spiral [6]) by the combination of the outward motion and the Sun's rotation. In near-Earth space, the IMF nominally makes an angle of ...
The Navier-Stokes equation for conservation of momentum, again in the same approximation, with the magnetic force and gravitation force as the external forces: = + + ′ + + + , where is the kinematic viscosity, is the mean density and ′ is the relative density perturbation that provides buoyancy (for thermal convection ′ = where is ...
The Alfvén wave velocity in relativistic magnetohydrodynamics is [4] = + + where e is the total energy density of plasma particles, is the total plasma pressure, and = is the magnetic pressure. In the non-relativistic limit, where P ≪ e ≈ ρ c 2 {\displaystyle P\ll e\approx \rho c^{2}} , this formula reduces to the one given previously.
The beta of a plasma, symbolized by β, is the ratio of the plasma pressure (p = n k B T) to the magnetic pressure (p mag = B 2 /2μ 0).The term is commonly used in studies of the Sun and Earth's magnetic field, and in the field of fusion power designs.