  It has been proposed that the million degree temperature of the corona is due
to the combined effect of barely-detectable energy releases, so called
nanoflares, that occur throughout the solar atmosphere. Alas, the nanoflare
density and brightness implied by this hypothesis means that conclusive
verification is beyond present observational abilities. Nevertheless, we
investigate the plausibility of the nanoflare hypothesis by constructing a
magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from
the nature of an ideal kink instability. The set of energy-releasing
instabilities is captured by an instability threshold for linear kink modes.
Each point on the threshold is associated with a unique energy release and so
we can predict a distribution of nanoflare energies. When the linear
instability threshold is crossed, the instability enters a nonlinear phase as
it is driven by current sheet reconnection. As the ensuing flare erupts and
declines, the field transitions to a lower energy state, which is modelled by
relaxation theory, i.e., helicity is conserved and the ratio of current to
field becomes invariant within the loop. We apply the model so that all the
loops within an ensemble achieve instability followed by energy-releasing
relaxation. The result is a nanoflare energy distribution. Furthermore, we
produce different distributions by varying the loop aspect ratio, the nature of
the path to instability taken by each loop and also the level of radial
expansion that may accompany loop relaxation. The heating rate obtained is just
sufficient for coronal heating. In addition, we also show that kink instability
cannot be associated with a critical magnetic twist value for every point along
the instability threshold.
