A large Time Projection Chamber (TPC) is the main device for tracking and charged-particle identification in the ALICE experiment at the CERN LHC. After the second long shutdown in 2019-2020, the LHC will deliver Pb beams colliding at an interaction rate of up to 50 kHz, which is about a factor of 50 above the present readout rate of the TPC. To fully exploit the LHC potential, the TPC readout chambers will be upgraded with Gas Electron Multiplier (GEM) technology.
To assure stable behaviour of the upgraded chambers in the harsh LHC environment, a dedicated R\&D programme was launched in order to optimize GEM stack geometry and its high voltage configuration with respect to electric discharges. We present a summary of discharge probability measurements performed with 3- and 4-GEM prototypes irradiated with highly ionising alpha particles.