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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.
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.
Given that the Troyon limit suggested a around 2.5 to 4%, and a practical reactor had to have a around 5%, the Troyon limit was a serious concern when it was introduced. However, it was found that β N {\displaystyle \beta _{N}} changed dramatically with the shape of the plasma, and non-circular systems would have much better performance.
This gives 2.7×10 −4 Tesla. The magnetic field of a magnetic dipole has an inverse cubic dependence in distance, so its order of magnitude at the earth surface can be approximated by multiplying the above result with ( R outer core ⁄ R Earth ) 3 = ( 2890 ⁄ 6370 ) 3 = 0.093 , giving 2.5×10 −5 Tesla, not far from the measured value of 3 ...
The two-stream instability is a very common instability in plasma physics. It can be induced by an energetic particle stream injected in a plasma, or setting a current along the plasma so different species (ions and electrons) can have different drift velocities.
Schematic view of the different current systems which shape the Earth's magnetosphere. In many MHD systems most of the electric current is compressed into thin nearly-two-dimensional ribbons termed current sheets. [10] These can divide the fluid into magnetic domains, inside of which the currents are relatively weak.
Magnetic reconnection is a breakdown of "ideal-magnetohydrodynamics" and so of "Alfvén's theorem" (also called the "frozen-in flux theorem") which applies to large-scale regions of a highly-conducting magnetoplasma, for which the Magnetic Reynolds Number is very large: this makes the convective term in the induction equation dominate in such regions.
The radial current in the circuit is on the order of 3 × 10 9 amperes. [2] As a comparison with other astrophysical electric currents, the Birkeland currents that supply the Earth's aurora are about a thousand times weaker at a million amperes. The maximum current density in the sheet is on the order of 10 −10 A/m 2 (10 −4 A/km 2).