Fast magnetic and electric dynamos in flat Klein bottle plasma flows

Abstract

Recently Shukurov et al [Phys Rev \textbf{E} (2008)] presented a numerical solution of a Moebius strip dynamo flow, to investigate its use in modelling dynamo flows in Perm torus of liquid sodium dynamo experiments. Here, by analogy one presents an electric dynamo on a twisted torus or Klein bottle topology. An exact solution in the form of flat Klein bottle dynamo flow is obtained. It is shown that even in the absence of magnetic dynamos initial electric fields can be amplified in distinct points of the Klein bottle. In this case diffusion is taken as ${\eta}\approx{5.0{\times}10^{-3}{\Omega}-m}$ the electric potential is obtained. The difference of electric fields at the beginning of plasma flow profile is ${\Delta}E_{Dyn}\approx{468\frac{V}{m}}$, which is stronger than the electric dynamo field obtained in the magnetic axis of spheromaks, which is of the order of $E_{Dyn}\approx{200\frac{V}{m}}$. The potential of the dynamo at the surface of the Earth computed by Boozer [Phys Fluids \textbf{B} (1993)] of ${\Phi}\approx{160V}$, is used to obtain the magnetic vector constant $A_{0}\approx{10^{6}V}$. In general the associated magnetic dynamo is shown to be a fast dynamo in force-free plasmas in Klein bottle. Of course if the magnetic dynamo growth is turned on the electric dynamo shall be able to sustain itself along the Klein bottle.