Vibrational Kinetics in Plasma as a Functional Problem: A Flux-Matching Approach

Abstract

A new approach to calculate the vibrational distribution function of molecules in a medium providing energy for vibrational excitation is proposed and demonstrated. The approach is an improvement of solution methods based on the drift-diffusion Fokker-Planck (FP) equation for a double differentiable function representing the vibrational populations on a continuum internal energy scale. A self-consistent numerical solution avoids approximations used in previous analytical solutions. The dissociation flux, a key parameter in the FP equation, is fixed using the kinetics of molecular dissociation from near-continuum levels, so that the vibrational kinetics becomes a functional problem. The approach is demonstrated for the kinetics of asymmetric stretching of CO, showing that it represents an alternative, potentially much more efficient in computational terms, to the presently usual state-to-state approach which is based on the kinetics of the populations of individual levels, and gives complementary insight into the dissociation process.

The behavior and modelling of the vibrational-to-translational temperature ratio at long time scales in CO2 vibrational kinetics

“…Recently, the reduction methodology has been used in a two-step modelling approach to model a surface wave microwave plasma reactor 25 . The importance of this temperature ratio has also been discussed in other works 15,16,26 , where it is mentioned that the non-equilibrium effect leading to the vibrationally enhanced dissociation of CO2 is better exploited at high values of this ratio. Higher values of the temperature ratio lower the energy level for the point of no return, beyond which vibrationally excited molecules most likely increase their vibrational energy and dissociate.…”

“…Different modelling approaches have been used to get insights into the plasma processes and the reactor performance [12][13][14][15][16][17][18][19][20][21][22] . The detailed study of vibrational kinetics requires the calculation of population densities for different vibrational energy levels, usually the full span, from ground state to dissociation limit.…”

“…In this approach the energy levels are considered discrete and a large number of species and reactions are not rare. A more recent approach 15,16 replaces the discrete energy levels by a continuous vibrational energy function.…”

Plasma Modeling and Prebiotic Chemistry: A Review of the State-of-the-Art and Perspectives

“…In the last few years, many researchers, including two authors of the present paper, aimed to achieve a better understanding of this mechanism using computer simulations. For example, a recent scheme is based on the characterization of the upwards flux in energy space, J [ 76 , 77 , 78 ]. J is a functional of the function , which is the distribution of molecules according to their internal energy .…”

“…It has been shown [ 76 , 77 , 78 ] that the two transport coefficients in Equation ( 5 ), namely the two jump moments and , can be calculated starting from the rate coefficients of the chemical reactions involving the different vibrational states. The calculation is not simple and the use of formulas requires the evaluation of numerous data; nevertheless the calculation is possible and produces results that are reliable and comparable with those based on the explicit discretization of the internal energy.…”