In the paper the ionization state of molecular tritium and electric potentials in a Windowless Gas Tritium Source (WGTS) of tritium -decay experiment KATRIN are considered. The ionization processes in WGTS are sustained by -electrons and so-called "secondary electrons", arising from inelastic and ionization collisions of "primary" -electrons with tritium molecules. As a result in the WGTS tritium gas volume acts as a low-temperature and slightly ionized gas steady state close to quasi neutrality (the Debye length is small in comparison with the setup characteristical sizes). On the basis of an one-dimensional self-consistent model the WGTS plasma steady state is described and the influence of plasma phenomena on neutrino mass measuring process is discussed. It is found that electric potentials in a main plasma volume can not significantly make worse the measurement process. At the same time the nonequilibrium electron spectrum and fast plasma flow at the end of the tube can result in instabilities which are able to spoil slightly the -electron spectrum endpoint. This problem must be carefully investigated further. For more reliable conclusions more detailed consideration is required that will include kinetic effects in the WGTS plasma.