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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.
The plasmasphere, or inner magnetosphere, is a region of the Earth's magnetosphere consisting of low-energy (cool) plasma. It is located above the ionosphere . The outer boundary of the plasmasphere is known as the plasmapause , which is defined by an order of magnitude drop in plasma density.
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.
Solutions for more general systems may be obtained in the high-temperature (weak coupling) limit ... 5: 10 −3: Magnetosphere 10 7: 10 7: 10 −8: ... with symbol κ ...
where is the Boltzmann constant, is the mass of the ion, is its charge, is the temperature of the electrons and is the temperature of the ions. Normally γ e is taken to be unity, on the grounds that the thermal conductivity of electrons is large enough to keep them isothermal on the time scale of ion acoustic waves, and γ i is taken to be 3 ...
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).
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 ...
It only holds for high temperatures and weak magnetic fields. As the derivations below show, the magnetization saturates in the opposite limit of low temperatures and strong fields. If the Curie constant is null, other magnetic effects dominate, like Langevin diamagnetism or Van Vleck paramagnetism.