Electron cross sections for rare gases used for discharge light sources modelling

SWARM CALCULATIONS The way to verify the validity of a set of cross sections is to compare calculated and measured swarm parameters. These swarm quantities, such as drift velocity or mobility, are directly connected to the power deposition; ionisation coefficient is related to the ionisation balance; the other data are diffusion coefficients and excitation coefficients which are less frequently measured. They are obtained with a precision higher than the precision for cross sections determination. The swarm are used directly in most plasma models. The calculations are based on the solution of the Boltzmann&s;s equation which describes very well the transport of electrons under the influence of an electric field. The cross sections set which correctly reproduces the observable macroscopic phenomena relevant to real plasmas, is inserted in the collisional terms of this equation. This equation is solved under the assumption of the so-called hydrodynamic regime [2] and provides the energy distribution function. Swarm parameters are then obtained by integration. Electron cross sections invoked are the momentum transfer cross sections and the set of inelastic cross sections from transition between the ground state to the various excited and ionized states. Results of cross sections from different laboratories can be discordant and data sets may be fragmentary. It is necessary to collect as many sets of data as possible from the literature to assess their reliability and determine the most trust worthy set of data to be recommended for use in applications. In fact, when data coming from different sources (experimental and calculations) are assembled in a set and then used in models, the agreement between calculated and measured values may be poor. Moreover, the change of individual cross sections inside a set can generated differences in the calculations greater than the errors in the cross sections determination. There are two reasons of such disagreements: first of all, individual and independent errors (in magnitude and energy) can provide a sizable error, and including all known cross sections does not necessary mean including all possible processes. An example of swarm parameters calculation using cross sections, coming from different recent sources, and comparison with the corresponding measured values will be presented for Xenon. It has been found that small changes in these cross sections induce considerable changes in the swarm parameters. It is also possible to use the calculation of swarm parameters to derive a set of electron cross sections by comparison of calculated and measured swarm data [3] in the low energy range (below 100 eV). The cross sections are modified until there is a good agreement between these macroscopic data. This process can provide 2 types of needed data: data to replace existing cross sections judged uncertain or incorrect and those which are not available.