  The global magnetic field in the solar corona is known to contain free
magnetic energy and magnetic helicity above that of a current-free (potential)
state. But the strength of this non-potentiality and its evolution over the
solar cycle remain uncertain. Here we model the corona over Solar Cycle 24
using a simplified magneto-frictional model that retains the
magnetohydrodynamic induction equation but assumes relaxation towards
force-free equilibrium, driven by solar surface motions and flux emergence. The
model is relatively conservative compared to some others in the literature,
with free energy approximately 20-25% of the potential field energy. We find
that unsigned helicity is about a factor 10 higher at Maximum than Minimum,
while free magnetic energy shows an even greater increase. The cycle averages
of these two quantities are linearly correlated, extending a result found
previously for active regions. Also, we propose a practical measure of
eruptivity for these simulations, and show that this increases concurrently
with the sunspot number, in accordance with observed coronal mass ejection
rates. Whilst shearing by surface motions generates 50% or more of the free
energy and helicity in the corona, we show that active regions must emerge with
their own internal helicity otherwise the eruptivity is substantially reduced
and follows the wrong pattern over time.
