Advances in Aerospace Engineering

Volume 2014, Article ID 847097, 17 pages

http://dx.doi.org/10.1155/2014/847097

## Global Modeling of CO_{2} Discharges with Aerospace Applications

DEDALOS Ltd., Vassilissis Olgas 128, 54645 Thessaloniki, Greece

Received 14 July 2014; Accepted 4 November 2014; Published 18 December 2014

Academic Editor: Martin Tajmar

Copyright © 2014 Chloe Berenguer and Konstantinos Katsonis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We developed a global model aiming to study discharges in CO_{2} under various conditions, pertaining to a large spectrum of pressure, absorbed energy, and feeding values. Various physical conditions and form factors have been investigated. The model was applied to a case of radiofrequency discharge and to helicon type devices functioning in low and high feed conditions. In general, main charged species were found to be for sufficiently low pressure cases and O^{−} for higher pressure ones, followed by , CO^{+}, and in the latter case. Dominant reaction is dissociation of CO_{2} resulting into CO production. Electronegativity, important for radiofrequency discharges, increases with pressure, arriving up to 3 for high flow rates for absorbed power of 250 W, and diminishes with increasing absorbed power. Model results pertaining to radiofrequency type plasma discharges are found in satisfactory agreement with those available from an existing experiment. Application to low and high flow rates feedings cases of helicon thruster allowed for evaluation of thruster functioning conditions pertaining to absorbed powers from 50 W to 1.8 kW. The model allows for a detailed evaluation of the CO_{2} potential to be used as propellant in electric propulsion devices.

#### 1. Introduction

Global Modeling (GM) has been lately extensively used for theoretical study of various types of plasma discharges in view of their applications. Reviews of GM applications including references to older publications can be found elsewhere; see, for example, [1, 2], for an extensive bibliography on the subject. GM allowed for successful investigation of plasmas of various compositions addressing natural conditions and specifically physical conditions and form factors with various applications in mind. In what concerns CO_{2}, to which focuses the present study, its presence in the atmosphere of Earth is of paramount importance for the environment [3], being a main greenhouse gas. Besides, CO_{2} is a constituent of various atmospheres in the solar system planets and satellites [4–6]. Carbon oxides are also present in the composition of asteroids and comets [7]. Moreover, various laboratory and industrial applications call for the study of CO_{2} plasmas, such as various types of plasma reactors. In this domain, we compare our theoretical results with experimental ones obtained in a radiofrequency discharge [3] meant to investigate the efficiency of CO_{2} dissociation in view of reducing the CO_{2} emissions. We also address here specifically Electric Propulsion (EP) applications using CO_{2} as propellant, because of its important presence in various space environments. Noteworthy, EP devices dedicated to low Mars orbit satellites propulsion are of paramount importance in this context. Also, as was the case with previous GM studies [2, 8–10] the present GM of CO_{2} discharges can be used as a basis of atmospheric entrance studies, notably in the case of Mars (typically 95% of CO_{2} plus N_{2} and Ar), provided the important hydrodynamic constraints are taken into consideration.

Functioning Diagrams (FD) and the corresponding Plasma Components Composition (PCC) diagrams which are obtained in the present study are important to monitor experimentally EP devices, mainly by optical emission spectroscopy and also theoretically by comparison with corresponding results (electron temperature , line intensities) obtained from “zero-dimensional” collisional-radiative models. The latter are also useful for calculating the resonant vacuum ultraviolet (VUV) line intensities and so evaluate the radiative plasma cooling and the erosion of the plasma facing components in thrusters. With increasing absorbed energy and functioning time, erosion evaluation becomes particularly important.

In Section 2 of the present paper, the essentials of a GM are reported summarily, together with the necessary atomic and molecular parameters, notably those used in the CO_{2} case. Atomic and molecular data being of interest to our GM are specifically addressed. Description of the GM elaboration techniques is not reported here, as it is available elsewhere (see e.g., [1, 2, 11] and references therein). Also, sensitivity of the used parameters is not specifically investigated, because previous GM studies of various plasmas compositions showed in general a smooth variation [12]. In Section 3, theoretical results obtained from our model and general considerations concerning CO_{2} discharges in higher pressures, pertaining to lower electron temperatures (), are given and commented. They are compared in Section 4 with GM results obtained for plasmas of various compositions including mixtures with Ar and with the aforementioned experimental results for CO_{2} from [3]. In Section 5, our GM results pertaining to lower pressures are given. They are of specific interest to EP because ionization is a key parameter for thrust. In general, these sufficiently ionized plasmas are characterized by quite high . These results can be compared with previously obtained ones for EP applications using a common propellant such as Ar but also in case of feeding with N_{2}O, N_{2}, and O_{2} and with mixtures of the two latter ones, hence with the air in various altitudes. An overview of such results is given in [2]. In Section 5 FDs giving the total ionization percentage as a function of pressure , for various absorbed power and values and occasionally the corresponding PCCs, are presented for each EP case investigated. Concomitant and variations are also discussed in Section 5. Conclusions are given in Section 6.

#### 2. GM Equations and CO_{2} Atomic and Molecular Data

In this section, after giving a short description of the GM construction, necessary for the introduction of the basic definitions, we review the CO_{2} atomic and molecular data which we had used in our model.

##### 2.1. Summary Model Description

The GM is essentially composed of one power balance equation and of a system of particle balance equations [10]. The power balance equation, giving the power dependence of the electron density, can be written in a condensed form as follows:
represents here each of the main Ground Level (GL) species, with and the corresponding ionization rate and the wall recombination rate. The total energy loss is essentially composed of three terms, and being the mean kinetic energy lost per electron and per ion, respectively, and the energy lost to collisions of electrons with heavy particles . All have to be calculated for the main considered heavy particles , namely, CO_{2}, CO, O, and O_{2}. Moreover, represents the plasma volume and and are the densities of electrons and of the species , respectively, as usually. The area for effective loss included in the term of (1) is given by with and the radius and length of the plasma and and the axial and radial edge to center ratios of positive ion density. These are modified Godyak factors that can be extended to high pressure, as derived in [13] or to electronegative discharges [14]. The plasma sheath depends strongly on the Bohm velocity , which for CO_{2} is , where is the electron charge and is the mass of the CO_{2} molecule. An example of sheath calculation has been given in [10]. For the plasma reactor case, we use a combined cross section value of 285 Å^{2} for the ionic momentum transfer corresponding to an ionic sheath composition of 40% , 40% of CO^{+}, and 20% of .

Each of the particle balance equations is constituted by the sum of all the creation and destruction terms for a given species and can be written: where denotes the sum of all and terms. For an equation pertaining to , each term includes production or loss rates involving the species . Production and loss reaction rates are given by the product of the reactant densities with the corresponding rate coefficient :

##### 2.2. Atomic and Molecular Data Description

A list of the considered CO_{2} states with their energies is given in Table 1. Inelastic reactions considered in the model are given in Tables 2 to 4 including occasionally references where they have been previously reported. Table 1, containing structure data of CO_{2}, includes the energies of the excited states, both electronic and vibrational. Excitation of all those states is taken into account by the collisional energy loss term . The character of each electronic transition, allowed or forbidden, is indicated following [15]. Energy values were taken from [16, 17] and excitation cross sections used in from [15, 16]. The list of the 20 processes included in the GM, involving the CO_{2} and CO species and their ions, is given in Table 2. Note that CO_{2} elastic scattering rate is introduced only in the power balance equation under in order to determine the entirety of energy losses, including those coming from various types of GL excitation, dissociation, and ionization. Reaction rates are separately included in the respective particle balance equations and participate in the determination of the populations provided by the set of the statistical equations. Table 3 gives the list of the 20 processes involving oxygen species included in the GM. Processes involving carbon species are contained in Table 4.