  We study the feedback of positive ions in triple and quadruple Gas Electron
Multiplier (GEM) detectors. The effects of GEM hole diameter, detector gain,
applied voltages, number of GEMs and other parameters on ion feedback are
investigated in detail. In particular, it was found that the ion feedback is
independent of the gas mixture and the pressure. In the optimized multi-GEM
structure, the ion feedback current can be suppressed down to 0.5% of the anode
current, at a drift field of 0.1 kV/cm and gain of 10^4. A simple model of ion
feedback in multi-GEM structures is suggested. The results obtained are
relevant to the performance of time projection chambers and gas
photomultipliers.
