PLASMA PRE-SHEATH IN LOW-PRESSURE DISCHARGES CONTAINING BEAM ELECTRONS OF FINITE-TEMPERATURE

The pre-sheath potential and ion flux to the sheath have been solved in the case of beam-plasma interaction. A finite temperature is assumed for the beam. The breakdown in the space-charge sheath formation and the uncertainty of the floating potential appearing on the assumption of monoenergetic beams are avoided. The monoenergetic case is treated consistently as a limit of the present theory. The potential of the pre-sheath boundary increases with the beam density ratio and shows an abrupt jump to a higher value above a critical ratio. The floating potential increases from the usual value as the beam density ratio increases and tends to a value above the potential equivalent of the beam energy. The abrupt jump of the pre-sheath, however, causes only a small discontinuity in the floating potential. The results are also relevant to Langmuir probe studies in beam-plasma systems.