Velocity fields which preserve cylindrically symmetric force-free magnetic fields

It is shown that constant-α force-free magnetic fields are very preserved by velocity fields satisfying an equation of the form ∇ × ξ = αξ, where $\text{ξ = ∇ × (}\text{v}\text{×}\text{B}\text{) = (}\text{∂}\text{∂}\text{t}\text{− λ∇}{}^2\text{)}\text{B}$, and $\text{λ =}\text{1}\text{μσ}$. Explicit expressions are derived for the velocity fields preserving cylindrically symmetric force-free magnetic fields of interest in controlled thermonuclear fusion studies as well as astrophysics. Such velocity fields include the form of observed astrophysical features reported in the literature as well as those invoked in other studies, thus lending them further support and a firm foundation.