TONKS-LANGMUIR PROBLEM FOR A BI-MAXWELLIAN PLASMA

An analytical solution of the Tonks-Langmuir (T-L) problem with a bi-M axwellian electron energy distribution function (EEDF) is obtained for a plasma slab, The solution shows that the ambipolar potential; the p lasma density distribution, and the ion flux to the wall are mainly go verned by the cold electrons, while the ionization rate and voltage dr op across the waif sheath are governed by the hot electrons. The ioniz ation rate by direct electron impact is found to be spatially rather u niform, contrary td the T-L solution where it is proportional to the p lasma density distribution, The temperature of hot electrons defined b y the ionization balance is found to be close to that of the T-L solut ion for a mono-Maxwellian EEDF, and is in reasonable agreement with ex periments carried out in a low pressure capacitance RF discharge, The energy balance for cold electrons in this discharge shows that their h eating by hot electrons via Coulomb interaction is equalized by the co ld electrons' escape to the RF electrodes during collapse of the RF sh eath.