The electrical discharge in dense plasmas such as those obtained in shock tube experiments is investigated theoretically. Assuming that the positive ion saturation current density is of the order of the positive ion random current density, it is shown that quite high current densities are possible in dense plasmas, without an electron emission at the cathode being required. For instance, current densities up to 1000 A/cm2are possible in argon at a temperature of 15 000°K and a pressure of 1 atm. It is then shown that the positive ion mean free path is in general much larger than the positive space charge sheet near the cathode. Hence the positive ions may be accelerated by the cathode voltage drop. Since their accommodation coefficient is smaller than 1, they keep part of their kinetic energy after neutralization, and they additionally can heat up the plasma in the vicinity of the cathode. This self‐sustained discharge mechanism, which represents a thermal breakdown of the plasma layer near the cathode, reduces the cathode voltage drop and limits the current density to a higher value.