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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.
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 quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance R xy exhibits steps that take on the quantized values
When the particles have an arbitrary spin (any number of spin states), the formula is a bit more complicated. At low magnetic fields or high temperature, the spin follows Curie's law, with [ 3 ] C = μ 0 μ B 2 3 k B n g 2 J ( J + 1 ) , {\displaystyle C={\frac {\mu _{0}\mu _{\text{B}}^{2}}{3k_{\rm {B}}}}ng^{2}J(J+1),}
The gauge-fixed potentials still have a gauge freedom under all gauge transformations that leave the gauge fixing equations invariant. Inspection of the potential equations suggests two natural choices. In the Coulomb gauge, we impose ∇ ⋅ A = 0, which is mostly used in the case of magneto statics when we can neglect the c −2 ∂ 2 A/∂t ...
With the numbers q ~ 2, and Φ co and τ co increasing with geomagnetic activity (e.g., Φ co ~ 17 and 65 kVolt, and τ co ~ 0 and 1 h, during geomagnetically quiet and slightly disturbed conditions, respectively), eq. valid at lower latitudes, (θ > θ m) and within the inner magnetosphere (r ≤ 10 a) is the Volland-Stern model (see Fig. 1 a)).
The magnetic field in the Sun's corona is often approximated as a force-free field.. In plasma physics, a force-free magnetic field is a magnetic field in which the Lorentz force is equal to zero and the magnetic pressure greatly exceeds the plasma pressure such that non-magnetic forces can be neglected.
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).