  The relaxation of a helical magnetic field ${\bf B}({\bf x}, t)$ in a
high-conductivity plasma contained in the annulus between two perfectly
conducting coaxial cylinders is considered. The plasma is of low density and
its pressure is negligible compared with the magnetic pressure; the flow of the
plasma is driven by the Lorentz force and and energy is dissipated primarily by
the viscosity of the medium. The axial and toroidal fluxes of magnetic field
are conserved in the perfect-conductivity limit, as is the mass per unit axial
length. The magnetic field relaxes during a rapid initial stage to a force-free
state, and then decays slowly, due to the effect of weak resistivity $\eta$,
while constrained to remain approximately force-free. Interest centres on
whether the relaxed field may attain a Taylor state; but under the assumed
conditions with axial and toroidal flux conserved inside every cylindrical
Lagrangian surface, this is not possible. The effect of an additional
$\alpha$-effect associated with instabilities and turbulence in the plasma is
therefore investigated in exploratory manner. An assumed pseudo-scalar form of
$\alpha$ proportional to $q\,\eta\, ({\bf j}\cdot {\bf B})$ is adopted, where $
{\bf j}=\nabla\times {\bf B}$ and $q$ is an $\mathcal{O}(1)$ dimensionless
parameter. It is shown that, when $q$ is less that a critical value $q_c$, the
evolution remains smooth and similar to that for $q=0$; but that if $q>q_c$,
negative-diffusivity effects act on the axial component of $\bf B$, generating
high-frequency rapidly damped oscillations and an associated transitory
appearance of reversed axial field. However, the scalar quantity $\gamma={\bf
j}\cdot {\bf B}/B^2$ remains highly non-uniform, so that again the field shows
no sign of relaxing to a Taylor state for which $\gamma$ would have to be
constant.
