  We report on discharge probability studies with a single Gas Electron
Multiplier (GEM) under irradiation with alpha particles in Ar- and Ne-based gas
mixtures. The discharge probability as a function of the GEM absolute gain is
measured for various distances between an alpha source and the GEM. We observe
that the discharge probability is the highest when the charge deposit occurs in
the closest vicinity of the GEM holes, and that the breakdown limit is lower
for argon mixtures than for neon mixtures.
  Our experimental findings are in line with the well-grounded hypothesis of
the charge density being the limiting factor of GEM stability against
discharges. A detailed comparison of the measurements with GEANT4 simulations
allowed us to extract the critical charge density leading to the formation of a
spark in a GEM hole. This number is found to be within the range of
$(5-9)\times10^6$ electrons after amplification, and it depends on the gas
mixture.
