The ALICE experiment at the CERN LHC will upgrade its inner tracking detector. The newly designed tracker will consist of 7 layers of silicon Monolithic Active Pixel Sensors (altogether 12 G pixels). Related R&D studies require testing radiation hardness of various detector components (FPGAs, cables, etc.). For this purpose we use the cyclotron U-120M located at the Nuclear Physics Institute of AS CR at Rez. The machine can deliver proton beams up to energy of 35 MeV with currents up to 50 uA. The tests of radiation hardness, however, need to be performed with currents which are eight to nine orders of magnitude lower. In the talk we will discuss how to measure proton flux and dose at these extremely low beam intensities using the Timepix and commercial ionization chamber from PTW Freiburg. Special attention will be paid to the performance of the Timepix detector exposed to proton beams.