This paper reviews the search for light dark matter in beam dump experiments with a special emphasis on the necessity of beam purity for precise background rejection at the sensitivities aimed at these experiments. As a case study we cite the P348 experiment which has test beam time in Fall 2015 at the SPS H4 beam line at CERN and aims to search for the $U^{\prime }\left(1\right)$ gauge boson, $A^{\prime }$, which as per one model of dark matter mediates a weak interaction between ordinary matter and dark matter via mixing of these “dark photons” with ordinary photon. The experiment aims to probe the still unexplored area of mixing strength $10^{-5}\le ϵ\le 10^{-3}$ and masses $M_{A^{\prime }}\le 100$ MeV by using 10–300 GeV electron beam from the CERN SPS. This paper presents the simulation results for rejection of background due to beam impurity, by tracking the incoming particles with Micromegas detectors at a level <$10^{-10}$.