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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.
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.
A transport equation, usually of heat (sometimes of light element concentration): = + where T is temperature, = / is the thermal diffusivity with k thermal conductivity, heat capacity, and density, and is an optional heat source. Often the pressure is the dynamic pressure, with the hydrostatic pressure and centripetal potential removed.
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 magnitude of Earth's magnetic field at its surface ranges from 25 to 65 μT (0.25 to 0.65 G). [3] As an approximation, it is represented by a field of a magnetic dipole currently tilted at an angle of about 11° with respect to Earth's rotational axis, as if there were an enormous bar magnet placed at that angle through the center of Earth.
For the limit , the magnetic diffusion equation = is just a vector-valued form of the heat equation. For a localized initial magnetic field (e.g. Gaussian distribution) within a conducting material, the maxima and minima will asymptotically decay to a value consistent with Laplace's equation for the given boundary conditions.
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.
As the temperature approaches 0 K, the entropy decreases to zero, that is, the disorder decreases and the material becomes ordered. This occurs without the presence of an applied magnetic field and obeys the third law of thermodynamics. [17] Both Curie's law and the Curie–Weiss law fail as the temperature approaches 0 K.