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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.
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 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.
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.
If the current density is identically zero, then the magnetic field is the gradient of a magnetic scalar potential: B = − ∇ ϕ . {\displaystyle \mathbf {B} =-\nabla \phi .} The substitution of this into ∇ ⋅ B = 0 {\displaystyle \nabla \cdot \mathbf {B} =0} results in Laplace's equation , ∇ 2 ϕ = 0 , {\displaystyle \nabla ^{2}\phi =0 ...
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 ...