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

The author derives 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.