Slow dynamo modes in compact Riemannian plasma devices from Brazilian spherical tokamak data

TL;DR

This paper investigates the existence of slow dynamo modes in compact Riemannian plasma devices like tokamaks, providing numerical estimates for magnetic growth rates based on Brazilian spherical tokamak data.

Contribution

It demonstrates the possibility of slow dynamo action in boundary-less plasma devices and derives a formula for maximum magnetic growth rate using real tokamak parameters.

Findings

Slow dynamo modes can exist in compact Riemannian plasma devices.

The maximum magnetic growth rate is approximately 1.3 times the ratio of perturbed flow velocity to magnetic field.

Spherical tokamak plasma stability is indicated by a safety factor q<1.

Abstract

Anti-dynamo modes are usually found in spheromaks plasma devices experiments due to the fact that Cowling anti-dynamo theorem is naturally applied to axisymmetric devices and flows. In this paper full consideration is given to the existence of slow dynamo modes in the case of compact Riemannian plasma devices without boundaries, such as tokamaks, stellarators and torsatrons. It is shown that a perturbed untwisted flow given by a decaying mode magnetic field is able to generate a slow twisted dynamo plasma flow where the unperturbed flow is also a steady flow. When the slow dynamo limit is obtained for high Reynolds magnetic numbers $Rm$, the unperturbed plasma flow achieve equilibrium as in spheromaks. The data of aspect ratio and other data obtained from the Brazilian spherical tokamak at the National institute for space research are used to obtain a numerical estimate for the maximum magnetic growth rate of the magnetic field of the slow dynamo action as ${\gamma}_{1max}\approx{\frac{0.26}{a}{\times}\frac{v_{1{\theta}}}{B_{1s}}}$ for a toroidal initial magnetic field $B_{0}\approx{0.4T}$ and an aspect data tokamak of 1.5. For a tokamak internal radius of $a\approx{0.2m}$ one obtains a maximum growth rate for the slow dynamo as ${\gamma}_{1max}\approx{1.3{\times}\frac{v_{1{\theta}}}{B_{1s}}}$, where $v_{1{\theta}}$ is the poloidal perturbed diffusive flow. The safety factor is given by $q\approx{-1}$ which is $q<1$ implying stability of spherical tokamak plasma.