  The exponential growth (avalanching) of runaway electrons (REs) during a
tokamak disruption continues to be a large uncertainty in RE modeling. The
present work investigates the impact of tokamak geometry on the efficiency of
the avalanche mechanism across a broad range of disruption scenarios. It is
found that the parameter $\nu_{*, crit}$ describing the collisionality at the
critical energy to run away delineates how toroidal geometry impacts RE
formation. In particular, utilizing a reduced but self-consistent description
of plasma power balance, it is shown that for a high-density
deuterium-dominated plasma, $\nu_{*, crit}$ is robustly less than one,
resulting in a substantial decrease in the efficiency of the RE avalanche
compared to predictions from slab geometry. In contrast, for plasmas containing
a substantial quantity of neon or argon, $\nu_{*, crit} \gtrsim 1$, no
reduction of the avalanche is observed due to toroidal geometry. This sharp
contrast in the impact of low-versus high-Z material results primarily from the
relatively strong radiative cooling from high-Z impurities, enabling the plasma
to be radiatively pinned at low temperatures and thus large electric fields,
even for modest quantities of high-Z material.
