  Dynamo action in the Earth's outer core is expected to be controlled by a
balance between pressure, Coriolis, buoyancy and Lorentz forces, with marginal
contributions from inertia and viscous forces. Current numerical simulations of
the geodynamo, however, operate at much larger inertia and viscosity because of
computational limitations. This casts some doubt on the physical relevance of
these models. Our work aims at finding dynamo models in a moderate
computational regime which reproduce the leading-order force balance of the
Earth. By performing a systematic parameter space survey with Ekman numbers in
the range $10^{-6} \leq E \leq 10^{-4}$, we study the variations of the force
balance when changing the forcing (Rayleigh number, $Ra$) and the ratio between
viscous and magnetic diffusivities (magnetic Prandtl number, $Pm$). For
dipole-dominated dynamos, we observe that the force balance is structurally
robust throughout the investigated parameter space, exhibiting a
quasi-geostrophic (QG) balance (balance between Coriolis and pressure forces)
at zeroth order, followed by a first-order MAC balance between the ageostrophic
Coriolis, buoyancy and Lorentz forces. At second order this balance is
disturbed by contributions from inertia and viscous forces. Dynamos with a
different sequence of the forces, where inertia and/or viscosity replace the
Lorentz force in the first-order force balance, can only be found close to the
onset of dynamo action and in the multipolar regime. Our study illustrates that
most classical numerical dynamos are controlled by a QG-MAC balance, while
cases where viscosity and inertia play a dominant role are the exception rather
than the norm.
