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 these 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 \vec{j} \times \vec{B} forces are everywhere zero. For a laboratory plasma α is a constant and β is a scalar function of spatial coordinates. The magnetic flux surfaces 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. Unlike most plasma structures, the
Lorentz force and the
Magnus force, \rho\vec{\nabla} \times \vec{v} , play equivalent roles. \rho is the mass density. == Project ==