  We improve the current upper bound on the axion-photon coupling derived from
stellar evolution using the $R_2$ parameter, the ratio of stellar populations
on the Asymptotic Giant Branch to Horizontal Branch in Globular Clusters. We
compare this with data from simulations using the stellar evolution code MESA
which include the effects of axion production. Particular attention is given to
quantifying in detail the effects of uncertainties on the $R$ and $R_2$
parameters due to the modelling of convective core boundaries. Using a
semiconvective mixing scheme we constrain the axion-photon coupling to be
$g_{a\gamma\gamma} < 0.47 \times 10^{-10}~\mathrm{GeV}^{-1}$. This rules out
new regions of QCD axion and axion-like particle parameter space. Complementary
evidence from asteroseismology suggests that this could improve to as much as
$g_{a\gamma\gamma} < 0.34 \times 10^{-10}~\mathrm{GeV}^{-1}$ as the
uncertainties surrounding mixing across convective boundaries are better
understood.
