Spheromak - Theory

Theory

Force free plasma vortices have uniform magnetic helicity and therefore are stable against many instabilities. Typically, the current decays faster in the colder regions until the gradient in helicity is large enough to allow a turbulent redistribution of the current.

Force free vortices follow the following equations.

\begin{align} \vec{\nabla} \times \vec{B} &= \alpha\vec{B} \\ \vec{v} &= \pm\beta\vec{B} \end{align}

The first equation describes a Lorentz force-free fluid: the forces are everywhere zero. For a laboratory plasma α is a constant and β is a scalar function of spatial coordinates.

Note that, unlike most plasma structures, the Lorentz force and the Magnus force, play equivalent roles. is the mass density.

The magnetic flux surfaces in a spheromak are toroidal, with the current being totally toroidal at the core of the torus and totally poloidal at the surface of the torus. This is similar to the field configuration of a tokamak, except that the field-producing coils are simpler and do not penetrate the plasma torus.

Spheromaks are subject to external forces, notably the thermal gradient between the hot plasma and its cooler surroundings. Generally this leads to a loss of energy at the outer surface of the spheromak though black body radiation, leading to a thermal gradient in the spheromak itself. Electrical current travels slower in the cooler sections, eventually leading to a redistribution of energy inside, and turbulence eventually destroys the spheromak.

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