Plasma torus dynamos versus laminar plasma dynamos

Abstract

Earlier Wang et al [Phys Plasmas (2002)] have estimated a growth rate for the magnetic field of ${\gamma}=0.055$ and flow ionization velocity of $51{km}/{s}$ in a laminar plasma slow dynamo mode for aspect ratio of ${r_{0}}/L\approx{0.6}$, where $r_{0}$ is the internal straight cylinder radius, and L is the length scale of the plasma cylinder. In this paper, fast dynamo modes in curved Riemannian heliotron are shown to be excited on a plasma flow yielding a growth rate of ${\gamma}=0.318$ for an aspect ratio of ${r_{0}}/L\approx{0.16}$. It is interesting to note that the first growth rate was obtained in the Wang et al slow dynamo, where the magnetic Reynolds number of $Re_{m}=210$, while in the second one considered in this paper one uses the limit of $Re_{m}\to{\infty}$. These growth rates ${\gamma}$ are computed by applying the fast dynamo limit $lim_{{\eta}\to{0}}{\gamma}(\eta)>0$. This limit is used in the self-induced equation, without the need to solve these equations to investigate the fast dynamo action of the flow. In this sense the fast dynamo seems to be excited by the elongation of the plasma device as suggested by Wang group. The Frenet curvature of the tube is given by ${\kappa}_{0}\approx{0.5 m^{-1}}$. It is suggested that the small Perm torus could be twisted [Dobler et al, Phys Rev E (2003)] in order to enhance even more the fast dynamo effect. By considering the stability of the plasma torus one obtains a value for the fast dynamo growth rate as high as ${\gamma}=1.712$ from a general expression ${\gamma}=0.16{\omega}$ and a toroidal oscillation of a chaotic flow of ${\omega}=\frac{2{\pi}}{6}$.