Instabilities and pattern formation in low-temperature plasmas

D. Mackey, L. Plantie and M.M. Turner

This paper is concerned with a dynamical systems analysis of an instability occurring in a cylindrical high-frequency plasma discharge. Stationary, spatially periodic modulations of the plasma density and temperature have been observed in experiments and reproduced in kinetic simulations. A macroscopic model is proposed here in order to determine parameter ranges for which these plasma ``striations'', which are extremely undesirable in industrial applications, may form. The model consists of two nonlinear, coupled partial differential equations which describe ambipolar diffusion of electrons and ions and electron energy transport. We emphasise the importance of a particular thermoelectric transport coefficient, usually neglected in fluid models of plasma discharges, which proves essential in describing the pattern formation mechanism.

This has appeared as Applied Mathematics Letters 18(8), 865-873, 2005

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