Theory of a wall sheath in a gas-discharge plasma

An integro-differential equation is proposed that generalizes the plasma-sh eath (Langmuir-Tonks) equation to include charge. exchange between ions and neutrals in a discharge plasma and makes it possible to correctly analyze how the discharge evolves from the regime of collisionless ion motion to th e diffusive regime in pure gases with allowance for the space charge in the sheath at the plasma boundary. The integro-differential equation is solved numerically, and the ionization rate is calculated as a function of the ra tio between the ion mean free path and the characteristic discharge dimensi on. The ion energy distribution function in the positive column of a discha rge plasma is computed. The parameter range in which the positive column ca n exist is examined, and the limits of applicability of different discharge models are: analyzed depending on the relations between the ion mean free path, Debye length, and discharge dimension.