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Strongly damped surface waves in plasmas. I. The WKB approximation

The propagation of highly damped surface waves in plasmas, i.e. plasmas with large axial electron density gradients is dealt with. The WKB approximation adopted in previous models of surface wave discharges is not applicable in this situation. A key parameter of discharge behaviour is v/ omega , where v is the electron-atom collision frequency and omega is the excitation frequency of the wave. Discharges in which v/ omega <<1 are generally referred to as 'weakly collisional'. However, the range of validity of the WKB approximation depends also on the local value of the electron density. Even if v/ omega <<1, this approximation breaks down for sufficiently low electron densities (e.g. near the end of the discharge), while in some cases WKB may adequately model discharges in which v/ omega >>1. The limits of validity of the WKB approximation are examined, both for published experimental results and parameters relevant to the authors' experiments on fluorescent lamps. In a second paper they show solutions for cases where the axial density gradients are high, using formalism developed previously for electrostatic surface waves.