The formation of orderly, steady, spatial structures in rf-heated plasmas that have metastable states is studied as the development of an instability of the solution to the reaction-diffusion equations for the plasma species. Plasma-species (electrons, ions, and metastable atoms) source functions are given in terms of the electron energy distribution in strong electric fields and of the various collision cross sections. The methods of two-time expansions and bifurcation theory are used to calculate the nonuniform states that bifurcate from the unstable uniform steady state for straight and toroidal tubes. The sinusoidal density variations give the discharge the appearance of glowing balls of gas. This pattern formation is analogous to the morphogenesis found in certain chemical reactions and biological processes.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics