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

In this paper some of the basic concepts in collisional radiative modelling of plasmas will be generalized. A mathematical framework is presented whic h is suitable for systems with an arbitrary number of transport sensitive a nd quasi-steady or local chemistry states. The mathematical formulation presented here leads to straightforward extens ions of quantities which have been previously introduced for systems in whi ch only the atom and ion ground states were dealt with explicitly. These ar e the net coefficients of ionization and recombination, the effective speci fic emission coefficients, and the relative overpopulation coefficients. Fo r a given set of transport-sensitive densities these quantities can be used to calculate the particle and radiation source terms and the atomic state distribution function. Furthermore the use of matrix-vector calculus has led to concise, insightfu ll, yet general expressions. And although some explicit references will be made to plasmas which are governed primarily by processes involving electro ns, most of the theory presented here can be carried over to other systems without great difficulty. As an example, a collisional radiative model for mercury will be presented for discharges with electron temperatures between 0.75 eV and 2 eV and electron densities between 10(18) m(-3) and 10(20) m( -3). In the current model six transport-sensitive levels have been assumed. Another 13 excited mercury states are taken into account implicitly; ladde rlike excitation and ionization will be shown to be of major importance for discharges in this parameter range. The model allows the incorporation of heavy-particle reactions and a full treatment of the transfer of resonant r adiation.