Inversion formalism for the Boltzmann high-energy operator in particle-beam-sustained molecular or atomic plasma discharges

Abstract

We derive a general formalism for the inversion of the Boltzmann high-energy operator in any particle-beam-sustained molecular or atomic plasma discharge, including all excitation transitions: ionisation, electronic, vibrational and rotational with the possibility of de-excitation from molecules excited in the first vibrational state. The final formulation predicts strong departures from Maxwellian in the 'tail' of the electron distribution function. Use of the present analysis together with measurements of the high-energy distribution provides a means for obtaining information about cross sections for vibrational excitations in molecules. Essential scaling laws are also derived from this formalism. Applications are made in the case of low-pressure molecular nitrogen lasers and to long-distance energy transport in a nitrogen atmosphere.

Analysis of the Boltzmann low- and medium-energy equation in particle-beam-sustained molecular or atomic plasma discharges. Application to O2

“…Generally (see Peyraud (1985b) for atomic species, and A for molecular species), the electron distribution is strongly decreasing after we cross the potential barrier U? (respectively U,, for atomic species, and uvI for molecular species case ( a ) or U:, for case ( b ) ) .…”

“…The medium-energy electron distribution function in molecular gases will be the result of the resolution of the differential equation ( 18) which has exactly the same structure as those used for atomic gases in Peyraud (1985a). Then all the analytic developments of this paper have been retained.…”

“…However, the complete kinetics of particle-beam-generated plasmas requires also an investigation of the low-and mediumenergy electron distribution, hereafter called 'bulk', leading to the calculation of the macroscopic values such as electron density n, and 'temperature' T, . This investigation was attempted for atomic rare gases with a generalization for all atomic species (see Peyraud 1985a, b, Peyraud-Cuenca 1987. However some problems arising from the compatibility between the conservation equations and Maxwellian modelling for the very small energy distribution need to be clarified (see appendix A8 of Peyraud 1986).…”

The role of low threshold metastable excitations in the kinetics of a molecular oxygen plasma generated by a particle beam

“…Referring to the scaling laws derived from the kinetic formalism detailed in Peyraud-Cuenca (1988), it can be easily established that the separation between 'bulk' and 'tail' of the distribution function is not sudden as in usual molecular (N,) or atomic gases. Indeed, the quantitative investigation leading to the scaling laws obtained in Peyraud-Cuenca (1988) shows that the electron distribution function must be divided into three parts (instead of two); this discussion is based on experimental conditions existing in the gun jet electrons studied by Pointu and Zeller (1986) at Orsay. The 5 cm2 electron beam established in oxygen, for pressures between 0.1 and 1.5 Torr, has an energy between 1 and 5 keV and a current limited to 150 mA by the available alimentation.…”

“…In a previous paper (Peyraud-Cuenca 1988) we have derived a general formalism for the inversion of the Boltzmann high-energy operator in any particle-beam-sustained molecular or atomic plasma discharge.…”