## Kinetic Modelling of Collisional De-excitation

Many advanced propulsion concepts are based on rarefied plasmas, e.g. Applied-Field Magneto-Plasma-Dynamic (AFMPD) thrusters, Mini-Magnetospheric Plasma Probes (M2P2), and Inertial Electrostatic Confinement (IEC) thrusters.

Those plasmas are often assumed to be optically thin. This implies the dominance of two processes – collisional electron excitation (forward reaction) and spontaneous emission (backward reaction). The latter is also known as non-collisional de-excitation and led to the introduction of so-called CR (Collision-Radiative) models. These models contain two inherent assumptions: First, collisional de-excitation processes are negligible. Second, the coupling between bound and free electrons is strong enough to maintain an excitation temperature equal to the temperature of the free electrons.

This project aims for identifying validity limits of CR models with respect to the first assumption. Therefore, the collisional de-excitation process is modelled kinetically in order to be free and flexible in the choice of the plasma state. This concerns essentially the electron energy distribution and relaxation processes in the plasma as a function of electron density and plasma perturbation. In a previous study [1] a high fidelity cross section model for the kinetic treatment of highly rarefied plasmas was presented. Due to its relevance for kinetic discharge simulations of pulsed plasma thrusters, the electron – atom/ion interaction cross section data base has been coded on basis of Carbon [2]. Despite the fact that the data in [2] is of high fidelity, it cannot be readily used for verification purposes of the collisional de-excitation modelling. Currently, it is very difficult to characterise that process accurately enough. We apply the “Detailed Balancing” principle for the cross section generation. That principle needs additional information (statistical weight) in order to describe transitions between energy levels. Reference [2] does not provide statistical weights, and NIST provides statistical weights but no proper (forward) reaction cross sections. Hence, we derived a consistent data base which contains both: cross sections for the electron impact induced excitation of atomic species and statistical weights, both for individual transitions between different energy levels. Given this data it is possible to consistently identify high fidelity cross sections for the backward reaction process – electron impact induced de-excitation of excited atoms. This new database was evaluated (reproduction of correct values under thermal equilibrium conditions).

Preliminary results were very promising. Cross sections and rate coefficients for the collisional de-excitations between individual energy levels were computed. That data might be of relevance in the fields of e.g. spectroscopy (evaluation of spectra with respect to the gas/plasma properties of the background media), and flow simulations (application to flow regimes where CR models loose validity). Also, the newly derived rate coefficients directly from high fidelity cross section data might lead to new insights regarding the classical approach of the generation of those coefficients (via equilibrium constants). Even more, the numerical tools generated within this project allow for non-equilibrium energy distribution functions in both reaction directions. Those distribution functions in turn allow for advanced rate coefficients applicable to non-continuum conditions. If embedded in e.g. DSMC codes, simulation problems can be selected regardless of the expected type of energy distribution.

## References

- Petkow, D., Herdrich, G., Fasoulas, S., and Auweter-Kurtz, M.,”
*On the kinetic modelling of collisional effects relevant for non-stationary magnetoplasmadynamic thrusters*”, IEPC-2011-307, International Electric Propulsion Conference 2011, Wiesbaden. - Suno, H. and Kato, T., “
*Cross section database for carbon atoms and ions: Electron impact ionization, excitation, and charge exchange in collisions with hydrogen atoms*”, Atomic Data and Nuclear Data Tables 92 (2006), Vol. 4, pp. 407–455.

## Outcome

Herdrich, G., D. Petkow, C. Syring, and M. Pfeiffer. 2013. “Kinetic Modelling of the Jet Extraction Mechanism in Spherical IEC Devices.” 12-3201 European Space Agency, the Advanced Concepts Team. [link]