Numerical calculations based on a hybrid model of near-cathode plasma (negative glow) of a short glow discharge have been performed to describe processes occurring in a newly developed PLES (plasma electron spectroscopy) detector for gas chromatography. The formation of narrow peaks is demonstrated, which are the spectra of fast electrons generated by Penning ionization from atoms and molecules of helium impurities, such as Ar, N2, O2, and CO2.