Collisional radiative models with multiple transport-sensitivelevels - application to high electron density mercury discharges

Abstract

In this paper some of the basic concepts in collisional radiativemodelling of plasmas will be generalized. A mathematical framework ispresented which is suitable for systems with an arbitrary number oftransport sensitive and quasi-steady or local chemistrystates.The mathematical formulation presented here leads to straightforwardextensions of quantities which have been previously introduced for systems inwhich only the atom and ion ground states were dealt with explicitly. Theseare the net coefficients of ionization and recombination, theeffective specific emission coefficients, and the relativeoverpopulation coefficients. For a given set of transport-sensitivedensities these quantities can be used to calculate the particle and radiationsource terms and the atomic state distribution function.Furthermore the use of matrix-vector calculus has led to concise, insightfull,yet general expressions. And although some explicit referenceswill be made to plasmas which are governed primarily by processes involvingelectrons, most of the theory presented here can be carried over to othersystems without great difficulty.As an example, a collisional radiative model for mercury will be presented fordischarges with electron temperatures between 0.75 eV and 2 eV and electrondensities between 1018 m-3 and 1020 m-3. In the currentmodel six transport-sensitive levels have been assumed. Another 13 excitedmercury states are taken into account implicitly; ladderlike excitation andionization will be shown to be of major importance for discharges in thisparameter range. The model allows the incorporation of heavy-particlereactions and a full treatment of the transfer of resonant radiation.