  We calculate the stability of a multiple relaxation region MHD (MRXMHD)
plasma, or stepped-Beltrami plasma, using both variational and tearing mode
treatments. The configuration studied is a periodic cylinder. In the
variational treatment, the problem reduces to an eigenvalue problem for the
interface displacements. For the tearing mode treatment, analytic expressions
for the tearing mode stability parameter $\Delta'$, being the jump in the
logarithm in the helical flux across the resonant surface, are found. The
stability of these treatments is compared for $m=1$ displacements of an
illustrative RFP-like configuration, comprising two distinct plasma regions.
For pressure-less configurations, we find the marginal stability conclusions of
each treatment to be identical, confirming analytic results in the literature.
The tearing mode treatment also resolves ideal MHD unstable solutions for which
$\Delta' \to \infty$: these correspond to displacement of a resonant interface.
Wall stabilisation scans resolve the internal and external ideal kink. Scans
with increasing pressure are also performed: these indicate that both
variational and tearing mode treatments have the same stability trends with
$\beta$, and show pressure stabilisation in configurations with increasing edge
pressure. Combined, our results suggest that MRXMHD configurations which are
stable to ideal perturbations plus tearing modes are automatically in a stable
state. Such configurations, and their stability properties, are of emerging
importance in the quest to find mathematically rigorous solutions of ideal MHD
force balance in 3D geometry.
