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A systematic study of the behavior of the ATLAS monitored drift tubes (MDTs) under controlled irradiation by alpha particles has been performed. The aim of the study was two fold: to quantify the response of the tubes to alpha particles and consequence to heavily ionizing particles and to measure aging effects under the nominal operating conditions. A setup of a well controlled radium (226Ra) source was used in order to enrich the tube gas (Ar, CO2) with the alpha emitter 222Rn and irradiate the tubes internally. The ionization produced by an alpha particle with mean energy of 6.4 MeV has been measured. The energy deposition of the alpha and beta rays of the source inside the tube was computed by simulating the MDT geometry and the accumulated charge to the tube wire at operating conditions was calculated. The results of aging effects up to an accumulated charge of 41.5 mC are given by using the alpha-irradiation setup.