Thi-Thoi Tran
email: thi-thoi.tran@ifpen.fr

Delphine Sinoquet
email: delphine.sinoquet@ifpen.fr

Sébastien Da Veiga
email: sebastien.da-veiga@safran.fr

Marcel Mongeau
email: mongeau@recherche.enac.fr

An adapted derivative-free optimization method for an optimal design application with mixed binary and continuous variables

Keywords: Mixed integer non-linear programming, black-box simulation, derivative free trust region method, necklace distance

Numerous optimal design applications are black-box mixed integer nonlinear optimization problems: with objective function and constraints that are outputs of a black-box simulator involving mixed continuous and integer (discrete) variables. In this paper, we address an optimal design application for bladed disks of turbo-machines in aircraft. We discuss the formulation of an appropriate distance with respect to discrete variables which can deal with the cyclic symmetry property of the system under study. The necklace concept is introduced to characterize similar blade configurations and an adapted distance is proposed for discrete space exploration of a derivative-free optimization method. The results obtained with this method on a simplified industrial application are compared with results of state-of-the-art black-box optimization methods.

Motivation

Air traffic is one of the most important means of transportation, especially in Europe. Besides, it is connected with very high costs of fuel [START_REF]Air transport action group (atag[END_REF][START_REF]International air transport association, iata price analysis[END_REF], and also with high costs of maintenance and of manufacturing. Thus, reducing fuel consumption by increasing engine efficiency and maintenance savings by decreasing vibrations are two major concerns of the aviation industry.

There are several ways to optimize costs in aircraft: optimal trajectories, optimal seat arrangement designs, optimal cargo arrangements . . . In our case, we want to optimize the design of turbo-machines, precisely, by maximizing the efficiency of compressor and minimizing the vibrations.

In the concrete application proposed by SAFRAN, the optimization variables are of 2 types: continuous shape parameters, x, e.g. thickness, length of blades and binary variables y associated to each blade, with the value 0 for a reference shape and 1 for the other predefined shape (mistuning shape). Binary variables are used to locate these reference blade shapes on the disk. This parameterization provides the distribution of the two shapes around the turbine disk.

There is a strong symmetry in this problem that should be taken into account. Two bladed disks that differ only by a rotation of the blade pattern around the disk will lead to the same simulation outputs, such arrangements are considered as the same solution or called redundant solution : e.g. 001101001101 and 010011010011. Note that the number of identical solutions increases rapidly with the number of blades (see Table 1).

In practice, engineers try to overcome this difficulty in practical optimization by using Reduce Order Modeling Technique (ROMT), detailed in [START_REF] Han | Optimization of Intentional Mistuning Patterns for the Mitigation of the Effects of Random Mistuning[END_REF][START_REF] Choi | Optimization of intentional mistuning patterns for the reduction of the forced response effects of unintentional mistuning: Formulation and assessment[END_REF][START_REF] Choi | Optimization of intentional mistuning for bladed disk : Intentional mistuning intensity effect[END_REF][START_REF] Choi | Pattern optimization of intentional blade mistuning for the reduction of the forced response using genetic algorithm[END_REF]. Briefly, grouping blades by sectors of 2 patterns -00 or 11 and 10 or 01 -tends to reduce the number of discrete variables from n to n/2.

In general these mixed problems are NP-hard and difficult to solve. Especially, for real applications, the difficulty lies in evaluating computationally expensive cost function: it can take several hours or even days to compute the functions to be optimized. Moreover, the derivatives are often not available. Most of algorithms for solving black-box Mixed Integer Nonlinear Problem are based on genetic algorithms which require a lot of function evaluations which are particularly costly in our application. In the next section, we motivate the use of derivative-free trust-region method. adaptations to hope to converge to a global optimal solution (e.g., a multi-start approach with several initial points). We focus on surrogate DFO methods [START_REF] Conn | Introduction to Derivative-Free Optimization[END_REF][START_REF] Audet | Derivative-Free and Blackbox Optimization[END_REF]. These methods aim to explore the optimization variable space by replacing the costly-to-evaluate functions by response surfaces, with a choice of the points to simulate based on a compromise between exploration (points far from points simulated at previous iterations) and exploitation of information captured by the response surface (points around potential optima). Most popular response surfaces for surrogate optimization are Radial Basis Functions (RBF) and Gaussian processes [START_REF] Jones | Efficient global optimization of expensive black-box functions[END_REF][START_REF] Gutmann | A radial basis function method for global optimization[END_REF][START_REF] Costa | Rbfopt: an open-source library for black-box optimization with costly function evaluations[END_REF].

Besides, derivative-free trust-region algorithm is based on local quadratic models defined inside a trust region

m(z) = α + g T z + 1 2 z T Hz,
whose coefficients are determined as the solution of minimal Frobenius norm problem

   min α,g,H=H T 1 2 H 2 F m(z i ) = f i , i = 0, . . . , p.
where Z = (z 0 , . . . , z p ) is the interpolation set for both continuous and binary variables z = (x, y), f i the associated objective function evaluations and . F the Frobenius norm. The interpolation set is assumed to be poised, see details in [START_REF] Conn | Introduction to Derivative-Free Optimization[END_REF][START_REF] Audet | Derivative-Free and Blackbox Optimization[END_REF]. The brief idea of the algorithm is to replace the initial problem, which involves the expensive simulations with quadratic optimization problem, simple to optimize. At the first step, we fix the binary variables to the best current solution and solve the quadratic sub-problem within the trust region with respect to continuous variables only. When a better point is obtained in this first step (a smaller objective function), the second step consists in minimizing the quadratic model with respect to both continuous and binary variables, thus solving a mixed binary continuous quadratic problem.

The model is built in order to efficiently approximate the function and fulfills the fully-linear or fully-quadratic model properties to ensure the local convergence of the algorithm. Thus, model improvement steps are performed in order to optimize the geometry of the interpolation set, see details in [START_REF] Conn | Introduction to Derivative-Free Optimization[END_REF][START_REF] Conn | A trust region method for solving grey-box mixed integer nonlinear problems with industrial applications[END_REF][START_REF] Audet | Derivative-Free and Blackbox Optimization[END_REF].

The introduction of binary (or integer) variables requires an adapted trust region definition. In [START_REF] Conn | A trust region method for solving grey-box mixed integer nonlinear problems with industrial applications[END_REF], the authors introduce a l 1 -norm trust region for continuous variables and the Hamming distance trust region for binary variables defined as

j:yc j =0 y j + j:yc j =1 (1 -y j ) ≤ ∆ y , (1)
with ∆ y , the size of the trust region for binary variables. When the algorithm reaches a "local solution" (no further improvement), an exploration phase is necessary in binary variable domain. It is performed by adding a "no-good-cut" constraint to escape from this local solution y * , defined as

j:y * j =0 y j + j:y * j =1 (1 -y j ) > ∆ * y , (2)
where (y * , ∆ * y ) are respectively the local solution and the current radius of the "sufficiently explored" area around this solution. Note that this approach leads to a bunch of constraints, one for each explored local solution.

In the next section, we propose an adapted distance that will be used for the trust region associated with binary variables for our application.

Adapted distance for blade design application

To avoid the solution redundancy (illustrated in Table 1), engineers use ROMT which reduces the optimization problem size but has the disadvantage of removing a large number of feasible solutions. Safran's application with 12 blades has 352 distinct arrangements but only 28 distinct arrangements for the two subproblems of ROMT, limiting a lot the explored configuration set with a high probability to remove "good" candidates.

Therefore, we attempt to define a new distance which can avoid the redundant solutions without arbitrary removal of configurations. The new distance should lead to simple constraints as the Hamming distance which leads to linear constraints [START_REF]Air transport action group (atag[END_REF].

In order to detect similar blade arrangements, we introduce the concept of "necklace" [START_REF] Fredricksen | An algorithm for generating necklaces of beads in two colors[END_REF][START_REF] Gabric | Constructing de bruijn sequences by concatenating smaller universal cycles[END_REF]. In combinatorics, a k-ary necklace of length n is an equivalence class of n-character strings over an alphabet k = {a 1 , . . . , a k } of size k, taking all rotations as equivalent. It represents a structure with n circularly connected beads which have k available colors. Our blade design application can be seen as a 2-color necklace optimization with a fixed number of beads.

Using the concept of necklace gives an exact formula of the number of distinct arrangements which is the number of necklace for given n beads : 1/n d|n φ(d)2 n/d , where φ is Euler's totient function, the summation is taken over all divisors d of n.

There are numerous applications based on "necklace" concept and various distances, e.g. geometry distance for music, swap distance [START_REF] Toussaint | A mathematical analysis of african, brazilian, and cuban clave rhythms[END_REF][START_REF] Toussaint | The geometry of musical rhythm[END_REF][START_REF] Toussaint | Computational geometric aspects of rhythm, melody, and voice-leading[END_REF], Hamming distance with shift [START_REF] Jiang | On the sum of distances along a circle[END_REF], and necklace alignment distance (NAD) [START_REF] Bremner | Necklaces, convolutions, and X+Y[END_REF].

Following the idea of NAD, we propose a new distance, that we call in the following the necklace distance, Besides these metric properties, d neck has one important property

d neck (y, y ) = min r d H (y, Rot r (y )), (3)
d neck (y, y ) = 0 ⇐⇒ y ∈ Rot(y ) (4)
which ensures to detect all the necklaces in the set. The definition of the necklace distance is not linear because of "min" operator. We propose in the next section an adaptation of this distance for the trust region and no-good-cut constraints used in the trust region algorithm.

Reformulating the distance for trust region DFO algorithm

The mixed binary continuous sub-problem associated with the minimization of the quadratic model is written as

       min x,y m(x, y) min(g 1 (y, y c ), . . . , g n (y, y c )) ≤ ∆ y x -x c l1 ≤ ∆ x , x ∈ R n , y ∈ {0, 1} n , (5)
with x c and y c the current centers of the two trust regions in continuous and binary variable space with ∆ x and ∆ y , the size of the trust region for respectively the continuous and binary variables and g i (y, y c ) = d H (y, Rot i (y c )), i = 1, . . . , n.

To deal with "min" operator in the constraints, we add slack variables t, integer, and y n+1 , y n+2 , . . . , y n+n , binaries, and propose an exact reformulation,

                       min x,y,t m µ (x, y, t) = min x,y,t m(x, y) + µt t ≥ g 1 (y, y c ) -M y n+1 . . . t ≥ g n (y, y c ) -M y n+n n i=1 y ni = n -1 t ≤ ∆ y x -x c l1 ≤ ∆ x , x ∈ R n , y ∈ {0, 1} 2n , t ∈ Z + , (6)
with a real parameter µ > 0 and an integer parameter M > n.

As explained before, the exploration phase uses "no-good-cut" constraints (2) to enforce to explore new values for binary variables. The maximum number of constraints is 2 n -1. If we apply the same trick as in [START_REF] Choi | Optimization of intentional mistuning patterns for the reduction of the forced response effects of unintentional mistuning: Formulation and assessment[END_REF] for exploration phase, we highly increase the dimension of the problem due to the additional slack variables, n + 1 for each "no-good-cut" constraint. We use instead the equivalence min(g 1 , g 2 , . . . , g n ) ≥ ∆ * y ⇐⇒ g i ≥ ∆ * y , i = 1, . . . , n, and thus replace no-good-cut constraints by at most n linear constraints

Toy problem

The problem of determining the best-case (or worst-case) mistuning pattern and maximizing the forced response vibration amplification by the addition of a small mistuning to a perfectly cyclical bladed disk is mentioned in literature [START_REF] Liao | Mistuning Forced Response Characteristics Analysis of Mistuned Bladed Disks[END_REF][START_REF] Óttarsson | Dynamic modeling and vibration analysis of mistuned bladed disks[END_REF][START_REF] Han | Optimization of Intentional Mistuning Patterns for the Mitigation of the Effects of Random Mistuning[END_REF][START_REF] Choi | Optimization of intentional mistuning patterns for the reduction of the forced response effects of unintentional mistuning: Formulation and assessment[END_REF][START_REF] Choi | Optimization of intentional mistuning for bladed disk : Intentional mistuning intensity effect[END_REF][START_REF] Choi | Pattern optimization of intentional blade mistuning for the reduction of the forced response using genetic algorithm[END_REF][START_REF] Schonlau | Conception robuste en vibration et aéroélasticité des roues aubagées de turbomachines[END_REF]. We use a single degree-of-freedom (DOF) per blade disk model (see Figure 1).

y i ∈ {0, 1}, (7)
where

A = T -1 F, Fi = F 0 e jφi , T =      T 0 -k c 0 . . . 0 -k c -k c T 1 -k c . . . 0 0 . . . . . . . . . . . . . . . . . . -k c 0 0 . . . -k c T N -1      , T i = -m i ω 2 + jωc + 2k c + (1 + δ i )k b .
The nomenclature is detailed in [START_REF] Choi | Pattern optimization of intentional blade mistuning for the reduction of the forced response using genetic algorithm[END_REF].

Preliminary numerical results

We present some preliminary results of our trust-region method, called DFOb in the following, applied to the toy problem and to a simplified application provided by SAFRAN.

Results for the Toy problem

In general, optimization researchers ideally seek for an algorithm which provides the smallest objective function value comparing to alternative algorithms. But, for derivative free optimization methods dealing with expensive-to-evaluate simulations, the efficiency of an optimization algorithm is generally measured by comparing the objective function value for a given budget of simulations (fixed number of simulations). On this toy example, we run 10 times our method DFOb with different initial random points with two different distances for binary variables : Hamming distance and the necklace distance proposed in previous section (equation 3). The new implementation allows to reach a better point than the Hamming distance implementation as shown in Figure 2. The number of simulations to reach the same objective value, 9.68272e -04, is larger with Hamming distance (90 simulations) than with the necklace distance (60 simulations).

Results on SAFRAN application

We apply our method DFOb on the two sub-problems of ROMT and compare the results with NOMAD, [START_REF] Abramson | The NOMAD project[END_REF][START_REF] Digabel | Algorithm 909: NOMAD: Nonlinear optimization with the MADS algorithm[END_REF] and RBFopt [START_REF] Costa | Rbfopt: an open-source library for black-box optimization with costly function evaluations[END_REF] optimization methods with a fixed budget of 100 simulations:

1. ROMT sub-problem 1 with patterns 00 -11, 2. ROMT sub-problem 2 with patterns 10 -01.

DFOb and RBFOpt share the same initial points (random choice from RBFOpt method). NOMAD's initial point is chosen as the best point of the initial set with regard to objective function value. Some constraints are added in order to avoid trivial solutions with only one type of patterns : only zero or one values in vector of binaries y. 4), DFOb method coupled with necklace distance has very good performance compared to RBFopt and NOMAD. NOMAD and RBFopt provide infeasible points during the exploration phasis (with small objective function values), the constraints being handled as soft constraints. In DFOb, the constraints are taken into account explicitely. For the second ROMT sub-problem (see Figure 5), DFOb finds good points rapidly after less than 10 simulations, nevertheless, it does not reach the best objective function value obtained by NOMAD and RBFopt within the fixed budget of simulations (100). With a different initial set, DFOb is able to find the global solution within 100 simulations. A future study will focus on the sensitivity of the results of our method to the initial set and of its size.

Conclusions

In this study we address black-box optimization problems with costly-to-evaluate objective functions. A trust region derivative free optimization method adapted to mixed binary and continuous variables is presented. In order to improve the

  where d H denotes the Hamming distance, Rot r (y) is the rotation of r positions from y. It is clear that this distance satisfies the non-negativity property: d neck (y, y ) ≥ 0, the reflexivity property : d neck (y, y) = 0, the commutativity property: d neck (y, y ) = d neck (y , y), the triangle inequality property: d neck (y, y ) ≤ d neck (y, y ) + d neck (y , y ).

d

  H (y, Rot(y * )) ≥ ∆ * y , . . . , d H (y, Rot n (y * )) ≥ ∆ * y . Note that, in practice, we use ∆ * y = 1.

Fig. 1 :

 1 Fig. 1: Single DOF per blade disk model ([7])

Fig. 2 :

 2 Fig. 2: Mean best average objective function obtained with 10 random initial datasets with Hamming distance and with the proposed distance.

Figure 3

 3 illustrates the efficiency of DFOb coupled with the necklace distance compared to Hamming distance for binary variables for

Fig. 3 :

 3 Fig. 3: Comparing results obtained with Hamming and necklace distances for the two ROMT sub-problems with patterns 00 -11 (left) and 10 -01 (right) of Safran application

Fig. 4 :

 4 Fig. 4: Compare DFOb, Nomad and RBFOpt results obtained for sub-problem with patterns 00 -11 of Safran application. Square black symbols indicate infeasible points.

Fig. 5 :

 5 Fig. 5: Compare DFOb, Nomad and RBFOpt results obtained for sub-problem with patterns 10 -01 of Safran application.

Table 1 :

 1 Number of distinct and total arrangements for a given number of blades

	Total number of	Number of distinct	Total number of
	blades on the disk (N ) arrangements ( 2 N /N ) arrangements (2 N )
	2	3	4
	3	4	8
	5	8	32
	10	108	1024
	12	352	4096
	20	52488	1048576
	2 Derivative free trust-region method
	Among Derivative-free optimization (DFO) methods, one distinguishes direct
	search methods (e.g., directional or Nelder Mead simplex) and trust region meth-
	ods based on simple interpolation or regression models (linear or quadratic). The
	direct search methods require a large number of simulations, whereas the second
	type of methods is generally more efficient to converge to a local solution. Con-
	vergence results to local minima are proved for the later methods but it requires


Sean D Mcguire
email: sean.mc-guire@centralesupelec.fr

Augustin C Tibère-Inglesse

Pierre B Mariotto

Brett A Cruden

Christophe O Laux

Measurements and modeling of CO 4th positive (A -X) radiation

We present absolute intensity measurements of CO 4th positive emission from a CO 2 /Ar plasma jet produced using an atmospheric pressure plasma torch facility. The centerline temperature of the plasma jet is approximately 6300 K. A VUV emission spectroscopy system was adapted to the plasma torch facility to measure spectrally resolved emission down to 140 nm. The emission from the plasma in the VUV, UV and near IR is consistent with thermochemical equilibrium. Carbon lines in the UV and VUV are found to be optically thick and their amplitude is therefore substantially affected by the line broadening parameters used for the calculation. For the CO 4th positive emission, these measurements test the performance of various models for the electronic transition moment function (ETMF). These ETMFs are used to calculate sets of Einstein coefficients that are used by SPECAIR to calculate the spectrally resolved emission of the plasma for comparison with experiments. We find that the EMTF of Kirby and Cooper and Spielfiedel accurately reproduce the measured emission from 150 -215 nm.

Introduction

Radiative heat flux is expected to be an important contributor for manned space missions beyond Earth orbit, due to the large capsule size and high entry velocity associated with such missions. [START_REF] Pitts | Performance of entry heat shields on Pioneer Venus probes[END_REF][START_REF] Cruden | Absolute radiation measurement in Venus and Mars entry conditions[END_REF][START_REF] Bose | Shock Layer Radiation Measurements and Analysis for Mars Entry[END_REF][START_REF] Grinstead | Shock radiation measurements for Mars aerocapture radiative heating analysis[END_REF] The radiative heat flux is expected to become significant for Mars and Venus entries at speeds above 7.5 km/s. The Pioneer Venus missions entered at velocities in excess of 11 km/s. For Mars entry scenarios, Johnston, Brandis and Sutton [START_REF] Johnston | Shock Layer Radiation Modeling and Uncertainty for Mars Entry[END_REF] provide simulated values of the convective and radiative heat fluxes for the Mars Pathfinder and hypersonic inflatable aerodynamic decelerator (HIAD) missions. They provide estimates of the radiative heat flux that fall between 25 -37 % of the total heat flux for the HIAD mission. Beyond direct entry scenarios, there is significant interest in using aerocapture maneuvers for missions to Mars and Venus in order to increase the percentage of useful payload. [START_REF] Lockwood | Systems analysis for a Venus aerocapture mission[END_REF][START_REF] Lockwood | Aerocapture Systems Analysis for a Titan Mission[END_REF][START_REF] Hall | Cost-benefit analysis of the aerocapture mission set[END_REF][START_REF] Bose | Shock Layer Radiation Measurements and Analysis for Mars Entry[END_REF] Depending upon the specific parameters of this maneuver, the radiative heat flux can represent an important portion of the total heat flux. For Venus and Mars atmospheres, composed primarily of CO 2 , the CO(A 1 Π → X 1 Σ + ) transition, called the CO fourth positive system and denoted CO(4+), represents either a significant or dominant portion of the radiative heat flux [START_REF] Brandis | Validation of CO 4th positive radiation for Mars entry[END_REF][START_REF] Cruden | Absolute radiation measurement in Venus and Mars entry conditions[END_REF]. Cruden, Prabhu and Martinez [START_REF] Cruden | Absolute radiation measurement in Venus and Mars entry conditions[END_REF] measured the CO(4+) contribution to be between 54 -64% of the total radiance from measurements in the electric arc shock tube (EAST) facility for Mars and Venus entry test conditions. It is therefore important to validate the radiation models used for this system and to reduce the corresponding uncertainty. Accurate values of the Einstein coefficients are also necessary to correctly scale the rates of CO recombination. [START_REF] Johnston | Shock Layer Radiation Modeling and Uncertainty for Mars Entry[END_REF][START_REF] Brandis | Investigation of Nonequilibrium Radiation for Mars Entry[END_REF][START_REF] Cruden | Compositional Dependence of Radiance in CO 2 /N 2 /Ar Systems[END_REF][START_REF] Johnston | Modeling of nonequilibrium CO fourth-positive and CN violet emission in CO 2 -N 2 gases[END_REF][START_REF] Macdonald | Nonequilibrium radiation and dissociation of CO molecules in shock-heated flows[END_REF] In 2013, researchers at NASA Ames studied the radiation of CO(4+) in the EAST facility [START_REF] Brandis | Validation of CO 4th positive radiation for Mars entry[END_REF][START_REF] Cruden | Absolute radiation measurement in Venus and Mars entry conditions[END_REF] to characterize the radiative heat flux under Venus and Mars entry conditions. They compared measurements of CO(4+) radiation with predictions made with the HARA [START_REF] Johnston | Non-Boltzmann modeling for air shock-layer radiation at lunar-return conditions[END_REF][START_REF] Johnston | Spectrum modeling for air shock-layer radiation at lunar-return conditions[END_REF], HyperRad [START_REF] Liu | Electron Stark broadening database for atomic N, O, and C lines[END_REF] and NEQAIR [START_REF] Arnold | Nonequilibrium and equilibrium radiative transport and spectra program: user manual[END_REF] radiation codes. When the equilibrium post-shock temperature was used, the models underestimated the measured radiation by a factor of 2. They noted that a large portion of the CO(4+) spectrum was blackbody limited. Fitting a blackbody curve to this portion of the spectrum yielded a second estimate of temperature, found to be 2 -9 % higher than the equilibrium shock calculation. By using this second temperature, they achieved better agreement between the radiation models and the measurements, yet discrepancies remained at certain wavelengths. The purpose of this work is to evaluate and validate the radiative models for CO(4+) emission. The plasma torch facility at laboratoire EM2C operates at atmospheric pressure and provides a plasma in chemical and thermal equilibrium. This enables more definitive tests of the radiation models because the population distribution and concentration of the emitting species are accurately known. Specifically, this paper compares the performance of five CO(4+) radiation models against the experimental data obtained in the VUV and identifies which models work best. The transition probabilities tested here are based on the electronic transition moment functions of DeLeon [START_REF] Deleon | CO (A-X) electric dipole transition moment[END_REF][START_REF] Deleon | Erratum: CO (A-X) electric dipole transition moment[END_REF], Kirby and Cooper [START_REF] Kirby | Theoretical study of low-lying 1 Σ + and 1 Π states of CO. II. Transition dipole moments, oscillator strengths, and radiative lifetimes[END_REF], Spielfiedel et al [START_REF] Spielfiedel | Ab-initio calculation of the dipole transition moment and band oscillator strengths of the CO (A-X) transition[END_REF], Chantranupong et al [START_REF] Lek Chantranupong | A configuration interaction study of the oscillator strengths for various low-lying transitions of the co molecule[END_REF] and Cheng et al [START_REF] Cheng | Spectral Study of A 1 Π -X 1 Σ + Transitions of CO Relevant to Interstellar Clouds[END_REF]. Spielfiedel et al [START_REF] Spielfiedel | Ab-initio calculation of the dipole transition moment and band oscillator strengths of the CO (A-X) transition[END_REF], Chantranupong et al [START_REF] Lek Chantranupong | A configuration interaction study of the oscillator strengths for various low-lying transitions of the co molecule[END_REF] and Cheng et al [START_REF] Cheng | Spectral Study of A 1 Π -X 1 Σ + Transitions of CO Relevant to Interstellar Clouds[END_REF] For the analysis presented here, all experimental results are compared with simulations obtained using SPECAIR. [START_REF] Laux | Optical Diagnostics and Radiative Emission of Air Plasmas[END_REF][START_REF] Laux | Optical diagnostics of atmospheric pressure air plasmas[END_REF][START_REF] Specair | Software Package, Ver. 3.0[END_REF] The spectral positions of the CO(4+) lines are calculated with the Dunham expansion coefficients of Farrenq et al [START_REF] Farrenq | Improved Dunham coefficients for CO from infrared solar lines of high rotational excitation[END_REF] and Simmons et al [START_REF] Simmons | The fourth positive system of carbon monoxide observed in absorption at high resolution in the vacuum ultraviolet region[END_REF]. Transitions between levels ν = 0, 23 of the excited state and ν = 0, 41 of the ground state are included in the calculation. The Einstein coefficients for each rovibrational transition are calculated using the method outlined in Laux and Kruger [START_REF] Laux | Arrays of radiative transition probabilities for the N 2 first and second positive, NO beta and gamma, N + 2 first negative, and O 2 Schumann-Runge band systems[END_REF]:

Radiation transition probabilities of CO(4+)

A ν ν = 64π 4 ν 3 3hc 3 (2 -δ 0,Λ +Λ ) (2 -δ 0,Λ ) Re 2 ν ν (1)
where:

Re 2 ν ν = ∞ 0 ψ ν (r) Re(r) ψ ν (r)dr 2 (2)
Re ν ν is the electronic-vibrational transition moment, ψ ν and ψ ν represent the vibrational wavefunctions of the upper and lower states respectively, Λ and Λ represent the projection of the orbital angular momentum of the upper and lower states respectively and δ is the Kronecker delta function. The above expressions are taken from Schadee [START_REF] Schadee | Unique definitions for the band strength and the electronic-vibrational dipole moment of diatomic molecular radiative transitions[END_REF]. Additional relations are contained in Appendix C. For these calculations, the Rydberg-Klein-Rees (RKR) method was first used to determine the potential energy curves for the X and A states of CO. The vibrational wavefunctions were then calculated. Finally, the electronic transition moment Re(r) was taken from one of five datasets reported in the literature: DeLeon [START_REF] Deleon | CO (A-X) electric dipole transition moment[END_REF][START_REF] Deleon | Erratum: CO (A-X) electric dipole transition moment[END_REF], Kirby and Cooper [START_REF] Kirby | Theoretical study of low-lying 1 Σ + and 1 Π states of CO. II. Transition dipole moments, oscillator strengths, and radiative lifetimes[END_REF], Spielfiedel et al [START_REF] Spielfiedel | Ab-initio calculation of the dipole transition moment and band oscillator strengths of the CO (A-X) transition[END_REF], Chantranupong et al [START_REF] Lek Chantranupong | A configuration interaction study of the oscillator strengths for various low-lying transitions of the co molecule[END_REF] and Cheng et al [START_REF] Cheng | Spectral Study of A 1 Π -X 1 Σ + Transitions of CO Relevant to Interstellar Clouds[END_REF]. DeLeon supplies an interpolation based on his experimental data and those previously reported by Field et al [START_REF] Field | Radiative decay rates from deperturbed v=0-7 vibrational levels of CO A 1 Π measured using synchrotron radiation[END_REF]. The ETMF of Kirby and Cooper [START_REF] Kirby | Theoretical study of low-lying 1 Σ + and 1 Π states of CO. II. Transition dipole moments, oscillator strengths, and radiative lifetimes[END_REF], Chantranupong et al [START_REF] Lek Chantranupong | A configuration interaction study of the oscillator strengths for various low-lying transitions of the co molecule[END_REF], Cheng et al [START_REF] Cheng | Spectral Study of A 1 Π -X 1 Σ + Transitions of CO Relevant to Interstellar Clouds[END_REF] and Spielfiedel et al [START_REF] Spielfiedel | Ab-initio calculation of the dipole transition moment and band oscillator strengths of the CO (A-X) transition[END_REF] are ab initio calculations. Figure 1 shows a comparison of the electronic transition moments. To comply with the convention outlined by Whiting [START_REF] Whiting | Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra[END_REF], the data of Kirby and Cooper have been divided by a factor of √ 2. The ab initio calculations of Kirby and Spielfiedel are close -to within 5%. In the sections that follow, we will therefore use the ETMF of Kirby and Cooper for the calculations and treat these ETMFs as identical.

Appendix A shows some of the most important vibrational bands present in the spectrum for the conditions studied. Figure 2 shows the band origin wavelengths associated with each r-centroid for the observed transitions. All r-centroids fall between 2 and 3 bohr. In looking at Fig. 1, we note that this is where there is a large discrepancy between the various models for Re(r). Note we do not use the r-centroid approximation in the calculation of the Einstein coefficients. However, this approximation proves useful in visualizing where on the Re(r) curve the vibrational bands are located. Finally, Appendix B includes a discussion of line broadening for the modeling of optically thick atomic lines in the VUV/UV portions of the spectrum.

Experiment

Plasma torch facility

The plasma torch facility is a TAFA Model 66 inductively coupled plasma (ICP) torch powered by a 120 kVA radio frequency LEPEL Model T-50-3 power supply. The power supply operates at 4 MHz and provides a maximum of 12 kV DC and 7.5 A to the oscillator plates. Details of the plasma torch facility are provided in previous publications [START_REF] Laux | Optical Diagnostics and Radiative Emission of Air Plasmas[END_REF][START_REF] Macdonald | Measurements of air plasma/ablator interactions in an inductively coupled plasma torch[END_REF]. For the experiments presented here, a 5-cm diameter exit nozzle was used. The plasma at the exit of the torch is at atmospheric pressure. Figure 3 shows a schematic of the facility. Radial, swirl and axial gas injectors can be used for gas injection. Calibrated flow meters from Bronkhorst (F-202AV, F-201AC, F-201CV) are used to control the mass flow rate of each gas through the system.

A significant effort was invested in determining a suitable mixture and injection procedure for introducing the flow into the torch in order to obtain an axisymmetric plasma with a smooth temperature profile. This torch has been previously operated with either air or mixtures containing comparatively small quantities of argon. For such mixtures, smooth and axisymmetric temperature profiles are quite easily obtained and are not sensitive to the method of injection -i.e. the relative values of radial, swirl and axial injection. In the present experiments, argon was the predominant species. In many cases, the temperature profiles obtained with an argon rich mixture were experimentally observed to be asymmetric about the centerline axis. However, a symmetric profile was necessary for the Abel inversion used in the calculation of the temperature profile. To ensure that the profile was axisymmetric, we found that increasing the swirl helped and chose the relative level of radial and swirl axial injection accordingly. Axisymmetry was checked by comparing left/right half profiles. The large majority of the mixture injected (∼ 91%) passed via the radial and swirl injectors and was premixed. As a percentage of the total flow rate, approximately 54% was injected via the radial injector and 37% via the swirl injector. A small amount of axial injection (∼ 10%) of pure argon was also used. This small amount of argon axial injection was found to enhance the plasma stability during operation. The reported value of 3.79 g/s argon injected includes this axial component.

The torch could not be operated with large quantities of CO 2 as it could not sustain the level of ionization necessary for preserving the plasma. Argon is comparatively easy to ionize and its emission does not significantly interfere with the emission from the CO(4+) band in the plasma. It is included in the SPECAIR calculations to account for any argon lines that appear in the spectra. For the results presented in this paper, 3.79 g/s of Ar (≥ 99.99% purity) and 0.352 g/s of CO 2 (≥ 99.9% purity) were injected into the torch. The uncertainties on these mass flow rates are both on the order of ± 2 %. This combination provided a stable plasma with a relatively hot centerline temperature.

Temperature measurements were obtained from the absolute intensity of emission lines of atomic carbon (833 nm), oxygen (777 nm) and argon (764 nm). These measurements were made using a UV-VIS spectrometer (Acton SpectraPro 500i), intensified PI-MAX camera and imaging setup. A longpass filter was installed in the optical path to suppress higher order diffraction interferences. The imaging system is comprised of two parabolic mirrors and a periscope to image the spectrometer slit across the jet profile. Intensity measurements are Abel-inverted to provide spatially resolved intensity measurements. The procedure for these emission-based temperature measurements is documented in Refs. [START_REF] Laux | Optical Diagnostics and Radiative Emission of Air Plasmas[END_REF][START_REF] Tibère-Inglesse | Validation cases for recombining nitrogen and air plasmas[END_REF]. The analysis relies upon the assumption of thermochemical equilibrium and rotational symmetry of the plasma jet. It also assumes that the atomic emission used for the temperature analysis is optically thin.

VUV spectrometer

The spectrometer and imaging system used for VUV measurements are shown in Figure 4a. The spectrometer is a McPherson VUV spectrometer (Model 218). An imaging box made of steel is attached to the spectrometer. Two spherical mirrors of 50 cm focal length inserted into this box are used to image the slit onto the torch -the spectrometer slit and torch are located at the focus of each mirror and therefore there is no image magnification. These mirrors are coated with the Acton Optics #1200 coating for 120 nm. The VUV system provides line-of-sight measurements along the chord intersecting the plasma centerline, 2.5 cm downstream of the nozzle exit.

For comparing measurements with SPECAIR calculations, the radiative transport equation is solved along the line-of-sight using the temperature profile measured using the UV-VIS spectrometer. Figure 11 shows the slit function of the VUV system for the CO(4+) measurements below 300 nm.

An overview of the VUV emission system is shown in Fig. 4a. The optical layout for the VUV system is shown in Fig. 4b. Through the use of a rotary vane roughing pump and a turbopump (80 liters/sec), the system was pumped down to a pressure of approximately 5.0×10 -5 Torr for all tests. The rotary vane pump was equipped with a zeolite adsorbent filter to prevent oil backstreaming into the optical system. An argon purge (AirLiquide, Argon Alphagaz 2, ≥ 99.9999% pure) was used to remove oxygen from the final 10 cm of the optical path that is not under vacuum. A MgF 2 window separated this argon purged section from the primary section under vacuum. A diagram of this final 10 cm section is shown in Fig. 4c. The portion in green is under vacuum and was manufactured out of PEEK, a vacuum compatible material. The portions in red and orange are under an argon purge. The portion highlighted in orange is water-cooled copper, whereas the portion highlighed in red is manufactured out of Teflon. The materials PEEK and Teflon were chosen in order to provide electrical isolation from the torch head which rests at 10 kV. A continuous argon purge was run at a pressure slightly above 1 atm to prevent oxygen from leaking into the system. Pressure relief ports were drilled in the red teflon piece to permit a portion of the argon flush to exit via these holes, rather than entirely into the plasma. The remaining portion exited through the final viewing hole, directly entering the plasma jet. Tests were conducted to verify that this purge did not affect the measured radiation (section 4.2). The final viewing hole in the water-cooled copper piece is 2 mm in diameter. The optical system was focused in the center of the plasma jet, 2.5 cm from the copper surface.

For calibration in absolute intensity an Optronics OL550 Tungsten ribbon lamp was used for wavelengths above 400 nm. An argon mini-arc discharge, with calibration traceable to NIST standards between 120 and 400 nm [START_REF] Klose | Radiometric calibrations of portable sources in the vacuum ultraviolet[END_REF], was used for wavelengths below 400 nm. In order to calibrate the system using the argon discharge, a modification of the VUV system was required. The final 10 cm of the imaging line was replaced with an adaptor to mount the system directly to the discharge housing. The sliding tube protruding from the imaging box and holding this entire assembly was adjusted so that the argon discharge emission was located at the system focus. A diaphragm placed in the imaging box served as the limiting aperture of the system so that the collection solid angle was the same for both the measurements made in the plasma torch and the calibration measurements. For these VUV/UV calibration measurements, we found that the level of stray light was too large to make calibrations below approximately 160 nm. To address this problem, a VUV transmission filter (eSource Optics 50150FBB) with a peak transmission wavelength of 146 nm and bandwidth of 62.5 nm was employed. This significantly cut down on the stray light which was mostly due to emission from the argon discharge in the UV and visible spectral regions. The reported transmissivity of this filter was verified by performing calibrations with and without the filter. For the wavelengths above 160 nm, for which it was possible to compare the two calibrations, the reported filter transmission was found to be accurate. Therefore, this filter was only put in place for the calibration between 140 and 300 nm. It was not installed for measurements of the plasma emission as it would have significantly and unnecessarily reduced the available signal. Figure 5 shows the temperature measurements for the mixture studied here. The difference in the nominal temperatures between the argon, carbon and oxygen lines is approximately 85 K.

We therefore treat the plasma to be in equilibrium and apply the maximum uncertainty range, highlighted in Fig. 5. This range will be used later in the SPECAIR calculations to determine maximum and minimum emission spectra. Figure 6 shows the chemical composition of the plasma determined with NASA CEA [START_REF] Mcbride | Computer program for calculating and fitting thermodynamic functions[END_REF] and using the nominal temperature from the argon 764 nm line. Wavelength (nm) Intensity (mW/cm 2 /nm/sr) Figure 7: Comparison between measured C 2 Swan emission (blue) and the SPECAIR calculation (red). The SPECAIR calculation is bounded by the maximum and minimum intensities possible given the uncertainties in the temperature measurements. An offset of 0.07 mW/cm 2 /nm/sr was added to the SPECAIR spectrum.

As an additional confirmation that the plasma is in thermochemical equilibrium, we measured C 2 d 3 Π ga 3 Π u (Swan system) emission using the UV/VIS spectrometer setup. A grating of 600 grooves/mm blazed at 300 nm was used and the slit function had a FWHM of approximately 0.2 nm. A long pass filter (λ > 350 nm) was also used to suppress higher order interferences within the spectrometer. These measurements were compared with SPECAIR predictions based upon the measured temperature profiles of Fig. 5. SPECAIR modeling of C 2 Swan radiation has been previously validated by Caillault et al. [START_REF] Caillault | Modeling the spectral radiation of a methane/nitrogen plasma test case 4[END_REF] An offset of 0.07 mW/cm 2 /nm/sr was added to the SPECAIR spectrum to compensate for a small continuum that is not modeled. The mole fraction of C 2 is on the order of 5 -10 × 10 -6 (Figure 6). Figure 7 shows a comparison between the measured and computed spectra. The good agreement is consistent with the plasma being in thermochemical equilibrium. O ( 7Wavelength (nm) Intensity (mW/cm 2 /nm/sr) Figure 8: Measurements of the C 2 Swan bands (450 -650 nm) using the VUV system in its final configuration. The SPECAIR calculation is bounded by the maximum and minimum intensities given the uncertainties in the temperature measurements. Two experimental measurements are included on this plot and overlap between approximately 440 and 520 nm.

To verify that the VUV system did not perturb the central portion of the plasma responsible for the measured emission, measurements were made in the UV/VIS region of the spectrum but using the VUV spectrometer. For these measurements, a low resolution grating of 180 grooves/mm was used. These measurements were compared with SPECAIR calculations that have been shown to reproduce the unperturbed torch signal in Fig. 7. Figure 8 shows the comparison with SPECAIR to be good. Again, a constant background of 0.07 mW/cm 2 /sr/nm was added to the SPECAIR calculation to account for continuum radiation not modeled in SPECAIR. Aside from features at 400 nm, believed to be the C 2 Deslandres-d'Azambuja system not modeled in SPECAIR, the good agreement confirms that the presence of the water-cooled copper piece and argon purge adjacent to the plasma are not perturbing the central region of the plasma responsible for the emission.

VUV measurements

Figure 9 shows a SPECAIR calculation of the CO 2 /Ar plasma emission at the exit of the torch with and without self-absorption. The calculation was done by assuming thermochemical equilibrium and by solving the radiative transport equation across the profile defined by the measured temperatures reported in Fig. 5. It is worth noting that the CO(4+) emission becomes heavily optically thick in the VUV below 180 nm. All carbon lines, including the one at 248 nm, are also heavily optically thick. The optically thin and optically thick calculations presented in Fig. 9 differ by several orders of magnitude for the lines below 200 nm, indicating the extent of optical thickness. Figure 10 shows a zoom on the calculated 193 nm carbon line to illustrate the severe impact of self-absorption on the line profile.

For the VUV measurements, a high-resolution 2400 grooves/mm grating was used in the VUV spectrometer. The slit function has an approximate FWHM of 0.08 nm and is shown in Figure 11 for reference. Figures 12a -12d show the comparison between the measured spectrum and SPECAIR calculations based upon the ETMFs from Kirby [START_REF] Kirby | Theoretical study of low-lying 1 Σ + and 1 Π states of CO. II. Transition dipole moments, oscillator strengths, and radiative lifetimes[END_REF], Chantranupong [START_REF] Lek Chantranupong | A configuration interaction study of the oscillator strengths for various low-lying transitions of the co molecule[END_REF], Cheng [START_REF] Cheng | Spectral Study of A 1 Π -X 1 Σ + Transitions of CO Relevant to Interstellar Clouds[END_REF] /nm/sr) Figure 10: Zoom on the calculated 193 nm C line structure from the calculation in Fig. 9 and DeLeon [START_REF] Deleon | CO (A-X) electric dipole transition moment[END_REF][START_REF] Deleon | Erratum: CO (A-X) electric dipole transition moment[END_REF]. Note that the C 2 D 1 Σ + u -X 1 Σ + g (Mulliken system) is included in SPECAIR calculations and appears at 230 nm. We used the model of Bruna and Wright for this molecular system. [START_REF] Bruna | Theoretical study of the transition probabilities of the doubly-excited states E 1 Σ + g of C 2 and 2 2 Σ + g of C + 2[END_REF] For these plots, the uncertainty in the temperature measurements is carried through the SPECAIR calculation. The bounds on the SPECAIR calculation correspond to the minimum and maximum possible temperature based upon the measured temperature profile shown in Fig. 5. The Kirby ETMF agrees within the error bars from between 162 -210 nm. Chantranupong is on the lower end of the error from 162-175 nm, outside the range from 175-218nm, and in agreement above 218 nm. Cheng agrees well from 162-180 nm, and is too high at longer wavelengths. DeLeon is in agreement only from 162-170nm, and too high everywhere else. These differences stem from the corresponding differences in the ETMF's shown in Fig. 1 for radii between 2 and 3 bohr. Concerning the Kirby ETMF calculations, the discrepancy with the experimental measurements below 162 nm can be accounted for by cold gas absorption in the shear layer. This is discussed below. Sources of radiation that could cause the discrepancy above 210 nm were checked, including O 2 Schumann-Runge from entrained oxygen and carbon bound-free, though neither were strong enough to account for the difference. Thus, the discrepancy above 210 nm may indicate that Kirby's ETMF should be reevaluated at larger separation distances (see Fig. 2) that impact this region of the spectrum.

None of the curves reproduce the spectra accurately below approximately 165 nm. This is attributed to absorption from cold gases in the VUV. CO 2 is present in the shear layer of the jet, where temperatures are cold enough that it remains undissociated. To evaluate the potential impact of CO 2 on the spectra, the cross-sections for cold CO 2 absorption from Thompson, Harteck and Reeves [START_REF] Thompson | Ultraviolet absorption coefficients of CO 2 , CO, O 2 , H 2 O, N 2 O, NH 3 , NO, SO 2 , and CH 4 between 1850 and 4000 Å[END_REF] were used. This dataset includes data from Watanabe, Zelikoff and Inn [START_REF] Watanabe | Absorption coefficients of several atmospheric gases[END_REF]. Given the injection mixture used for these measurements a CO 2 mole fraction of x CO2 ≈ 0.078 is calculated at room temperature. Adding about 0.5 cm of cold gas absorption to the measurement reproduces nicely the experimental data (see Figs. 13a -13d). This would be consistent with local cooling of the gas mixture near the water-cooled copper piece (Fig. 5). Another possible species for absorption of the signal would be O 2 due to air entrainment around the boundaries of the jet. Adding about 50 µm of cold O 2 absorption also produces the level of absorption needed to match the profile produced by CO 2 absorption. Note that this equivalent path length of O 2 would not be consistent oxygen levels associated with the level of vacuum in the system or the purity of the argon purge. Rather, it would have to come from cold air entrainment into the edges of the jet. The absorption profiles of O 2 and CO 2 are quite similar in shape over the wavelength range 145 -160 nm and thus produce a similar result using either molecule as the absorber. Therefore, while CO 2 is a likely absorber given that it is known to be present, it is possible that some amount of O 2 is also contributing to the reduced signal at low wavelengths. Based upon the comparison with SPECAIR predictions, the measurements appear to be free from cold gas absorption down to about 165 nm. Table 1 shows how the integral of the measured spectrum, from 165 -220 nm, compares with the model predictions.

Atomic carbon has several lines that emit in the VUV and UV. Figure 14 shows zooms on the Figure 12 193 and 248 nm carbon lines that were not visible in the previous figures. The calculation for the underlying CO bands was done with the Kirby ETMF. The Einstein coefficients for these carbon lines were taken from the NIST atomic spectral database [START_REF] Kramida | NIST Atomic Spectra Database (version 5.6.1)[END_REF] which, in turn, cites Fischer [START_REF] Fischer | Some improved transition probabilities for neutral carbon[END_REF] as the source for these coefficients. As discussed in Appendix B, Doppler broadening is the dominant line broadening mechanism. However, for these atomic lines of carbon, van der Waals broadening also plays an important role. The Einstein coefficient accuracy for the 193 nm line is quoted to be within 3%. The Einstein coefficient accuracy for the 248 nm line is quoted to be 18%. Both lines appear to be well captured. Table 1: Integrals of the measured/theoretical spectra between 165 and 220 nm in mW/cm 2 /sr. The theoretical spectra used for the calculation correspond to those in Figs. 13a-13d and include CO 2 absorption. However, the impact of this absorption is minimal given the wavelength bounds of the integral. The uncertainty bounds on the SPECAIR calculations correspond to the minimum and maximum values based upon the uncertainty in the temperature measurement.

The uncertainty for the experimental value is estimated to be primarily from the reported uncertainty of the calibration source (±5%, [START_REF] Klose | Radiometric calibrations of portable sources in the vacuum ultraviolet[END_REF]). The total uncertainty for the experimental value is estimated at ±6% or ± 36 mW/cm 2 /sr. /nm/sr) Figure 14: Zoom on the 193 nm C feature (left) and 248 nm C feature (right). Experiment is blue and SPECAIR calculation is in red. For reference, the SPECAIR calculation shown here used the Kirby ETMF for the underlying CO(4+) emission. The apparent shift in the location of the carbon 193 feature relative to the SPECAIR calculation is believed to be an artifact of the wavelength calibration rather than a real shift in the feature.

Conclusion

This paper presents VUV experimental data of CO(4+) emission and assesses the performance of radiation transition probabilities obtained from various ETMFs available in the literature. A McPherson VUV spectrometer was used to spectrally the emission coming from an atmospheric pressure plasma torch facility. To avoid oxygen absorption from the surrounding air, a specially designed system was put in place to make measurements down to 140 nm.

The temperature of the plasma was measured using atomic emission lines. These temperature measurements were used to predict the C 2 Swan emission and found to be consistent with measured emission spectra, suggesting the plasma to be in chemical and thermal equilibrium. The Swan band was also shown to be reproduced with the VUV spectrometer, indicating that the vacuum system attachments, with its cooling and argon purge, did not significantly alter the plasma properties.

At lower wavelengths (< 165 nm), absorption from cold gas (likely some combination of CO 2 and O 2 ) causes the signal to drop off. At these lower wavelengths, the spectra are also heavily optically thick and thus the calculations are insensitive to the ETMF employed. We find that the ETMFs of Kirby and Cooper or Spielfiedel predict the measured emission coming from the CO(4+) bands between 162-210 nm. The other ETMF's examined in this paper could be said to plausibly match the data over some narrower range centered around 160 nm, but deviate beyond the error bounds at higher wavelengths. One notable exception is the ETMF of Chatranupong, which comes into agreement with the measured data above 220 nm, while the Kirby ETMF overpredicts emission in this range. Based on the relationship of the r-centroid to wavelength (Figure 2), this suggests that the ETMF of Chatranupong may be more accurate for larger separations (>2.7 Bohr) than that of Kirby. Presently, however, SPECAIR retains the transition moments obtained from the ETMF of Kirby -see Appendix C for the conventions used in the calculation of these transition moments. The spectroscopic data based on the ETMF of Kirby, as well as the measured temperature profile and CO(4+) spectrum, are available for download and linked to this article on the journal website.

Figures A. 15 and A.16 show CO(4+) spectra calculated in the optically thin limit for a temperature of 6300 K, which corresponds approximately to the centerline temperature of the jet. Figure A.15 identifies the bands coming from various vibrational levels of the A electronic state. Note that emission from v = 0 is responsible for the central portion of emission centered around 160 nm, whereas the higher vibrational levels emit mostly on the wings.

Appendix B. Line broadening calculations

The majority of the atomic lines measured in the VUV/UV spectrum, as well as a portion of the CO(4+) spectrum, are optically thick to varying degrees. To account for self-absorption along the line-of-sight, it is necessary to take into account the appropriate line broadening mechanisms. These include Doppler, Stark, resonance, van der Waals and natural line broadening. All of these are calculated in SPECAIR. The dominant mechanism is found to be Doppler broadening, which is described by a Gaussian lineshape of full width at half maximum (FWHM) given by: ∆λ Doppler = λ ul 8kT ln 2 mc 2 (B.1)

For atoms, van der Waals broadening is also found to be important and is estimated based upon the approach detailed by Griem. [START_REF] Griem | Spectral Line Broadening by Plasmas[END_REF][START_REF] Griem | Principles of Plasma Spectroscopy[END_REF] We use the following formula, adapted from Griem [START_REF] Griem | Principles of Plasma Spectroscopy[END_REF], for the Lorentzian FWHM of carbon lines: where all values are in SI units. m e is the mass of the electron, X p the mole fraction of the perturber, E p the energy of the excited state of the perturber connected to its ground state by an allowed transition and m rp the reduced mass of the radiator and the perturber. The formula for the parameter R is taken from Griem:

∆λ vdw = p
R 2 = 1 2 E H E ∞ -E i 5 E H E ∞ -E i + 1 -3l i (l i + 1) (B.3)
where E H is the ionization energy of the hydrogen atom, E ∞ is the ionization energy of the radiating atom and E i is the excited state energy of the radiator. l i is the orbital angular momentum quantum number of the radiating state. We increased the FWHM calculated by Eqn. B.2 by a multiplicative factor of n 2/5 e , where n e is the number of valence electrons of the perturber. This is done based upon a remark by Griem in section 4.8 of his text. [START_REF] Griem | Principles of Plasma Spectroscopy[END_REF] Table B.2 shows the parameters used in Eqn. B.3 for the van der Waals calculation. Argon is the perturber present in the highest quantities (X p ∼ 0.84) and, for this perturber, we used E p = 11.6 eV , m rp = 9.2 amu and n e = 6. Table B.3 shows the Doppler and van der Waals FWHMs calculated with the equations above for the conditions at the center of the plasma jet (T = 6300 K, p = 1 atm). These are used for the SPECAIR calculation of the carbon lines at 193 and 248 nm.

Figure 1 :

 1 Figure1: Electronic transition moment function (Re(r)) taken from DeLeon[START_REF] Deleon | CO (A-X) electric dipole transition moment[END_REF][START_REF] Deleon | Erratum: CO (A-X) electric dipole transition moment[END_REF], Kirby and Cooper[START_REF] Kirby | Theoretical study of low-lying 1 Σ + and 1 Π states of CO. II. Transition dipole moments, oscillator strengths, and radiative lifetimes[END_REF], Spielfiedel et al[START_REF] Spielfiedel | Ab-initio calculation of the dipole transition moment and band oscillator strengths of the CO (A-X) transition[END_REF], Chantranupong et al[START_REF] Lek Chantranupong | A configuration interaction study of the oscillator strengths for various low-lying transitions of the co molecule[END_REF] and Cheng et al[START_REF] Cheng | Spectral Study of A 1 Π -X 1 Σ + Transitions of CO Relevant to Interstellar Clouds[END_REF]

Figure 2 :

 2 Figure 2: Band origin wavelength versus r-centroid for the observed bands (see Fig. A.16).

Figure 3 :

 3 Figure 3: Plasma torch head and nozzle assembly. The gas injectors include radial, swirl and axial injectors.

  (a) VUV spectrometer and imaging system used for measurements of CO(4+). (b) Optical layout of the VUV system showing the mirrors, diaphragm, adapting tube and their relative locations with respect to the spectrometer. The adapting tube is color-coded as in Fig. 4c to illustrate where the various components fall. The optical path is indicated by the dashed violet line. (c) Diagram showing the final tube protruding from the imaging box and coming into contact with the plasma.

Figure 4

 4 Figure 4

Figure 5 :

 5 Figure 5: Temperatures obtained by measuring absolute emission from several atomic features. Uncertainty bars are included in the figure. The grey region is bounded by the maximum and minimum temperature profiles based upon the atomic measurements. Note that the water-cooled copper piece is located at a radial distance of 2.5 cm.

2 Figure 6 : 4 . 2 .

 2642 Figure6: Equilibrium mole fractions as a function of radial distance. The calculations were done using NASA CEA[START_REF] Mcbride | Computer program for calculating and fitting thermodynamic functions[END_REF] based upon the temperature profile measured using the argon 764 nm line. The electron mole fraction is approximately equal to the C + mole fraction.

Figure 9 :

 9 Figure 9: SPECAIR calculation with and without self-absorption to illustrate the optically thick nature of the emission in the VUV. The Kirby electronic transition moment function was used for the calculation of the CO(4+) bands. This calculation was done without a slit function.

Figure 11 :

 11 Figure 11: Measured slit function of the VUV system.

  Experiment (blue) and SPECAIR calculations (red) based upon the Kirby electronic transition moment function. Experiment (blue) and SPECAIR calculations (red) based upon the Chantranupong electronic transition moment function. Experiment (blue) and SPECAIR calculations (red) based upon the Cheng electronic transition moment function. 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 Experiment (blue) and SPECAIR calculations (red) based upon the electronic transition moment functions of DeLeon et al.

2 / 2 / 2 / 2 /

 2222 nm/sr) (a) Experiment (blue) and SPECAIR calculations (red) using Kirby electronic transition moment function with a 0.5 cm absorption path length of cold CO 2 (x CO2 = 0.078). nm/sr) (b) Experiment (blue) and SPECAIR calculations (red) using Chantranupong electronic transition moment function with a 0.5 cm absorption path length of cold CO 2 (x CO2 = 0.078). nm/sr) (c) Experiment (blue) and SPECAIR calculations (red) using Cheng electronic transition moment function with a 0.5 cm absorption path length of cold CO 2 (x CO2 = 0.078). nm/sr) (d) Experiment (blue) and SPECAIR calculations using DeLeon electronic transition moment function with a 0.5 cm absorption path length of cold CO 2 (x CO2 = 0.078).

  Figure 13

4 Figure A. 15 :

 415 Figures A.[START_REF] Johnston | Spectrum modeling for air shock-layer radiation at lunar-return conditions[END_REF] and A.[START_REF] Liu | Electron Stark broadening database for atomic N, O, and C lines[END_REF] show CO(4+) spectra calculated in the optically thin limit for a temperature of 6300 K, which corresponds approximately to the centerline temperature of the jet. Figure A.15 identifies the bands coming from various vibrational levels of the A electronic state. Note that emission from v = 0 is responsible for the central portion of emission centered around 160 nm, whereas the higher vibrational levels emit mostly on the wings. Figure A.16 identifies the main vibrational bands in the range 140-240 nm.

Table B .

 B 2: Parameters used in Eqn. B.3 for the line broadening calculation for the 193 and 248 nm carbon lines.E H (eV ) E ∞ (eV ) E i (eV ) l i

	13.6	11.3	7.68	0
		21

Table B .

 B 3: Dominant broadening linewidths for two of the atomic carbon lines in the VUV.

		Doppler (FWHM, pm) van der Waals (FWHM, pm)
	C I (193 nm)	3.17	0.38
	C I (248 nm)	4.07	0.63

Acknowledgments

We would like to acknowledge the contributions of Carolyn Jacobs, Umar A Sheikh, Richard Morgan and Victor Gondret who participated in the development of this VUV system. The VUV spectrometer was obtained as part of an International NASA Space Act Agreement for Equilibrium radiation measurements. Augustin Tibère-Inglesse was supported by a CIFRE doctoral grant (number 42701092/20160218/JSE) with ArianeGroup (technical monitor: Laurent Visconti).

 188 190 192 194 196 198 200(2,0) [START_REF] Pitts | Performance of entry heat shields on Pioneer Venus probes[END_REF]0) (2,1) (0,0) [START_REF] Pitts | Performance of entry heat shields on Pioneer Venus probes[END_REF][START_REF] Pitts | Performance of entry heat shields on Pioneer Venus probes[END_REF] (2,2) (0,1) Appendix C.

The spectroscopic data for the CO(4+) transition based on the ETMF of Kirby (Ref. [START_REF] Kirby | Theoretical study of low-lying 1 Σ + and 1 Π states of CO. II. Transition dipole moments, oscillator strengths, and radiative lifetimes[END_REF]) are available for download as an Excel file on the journal website. This data was found to yield the best agreement with experimental data as shown in Fig. 12a and are now used in the SPECAIR radiation code. The conventions outlined in Refs. [START_REF] Schadee | Unique definitions for the band strength and the electronic-vibrational dipole moment of diatomic molecular radiative transitions[END_REF][START_REF] Laux | Optical Diagnostics and Radiative Emission of Air Plasmas[END_REF] were used. These lead to a set of equations linking the square of the electronic-vibrational transition moment (R ν ,ν e ) 2 to the values reported in Table C.1. These are as follows:

where (R ν ,ν e ) 2 represents the sum of the electronic-vibrational transition moment across all electronic subtransitions. In the above expressions, ν ν ,ν is the wavenumber of the transition in cm -1 and R ν ,ν e is in atomic units (ea 0 , where a 0 is the Bohr radius). Λ and Λ are the projected orbital angular momentum quantum numbers of the upper and lower states respectively. δ i,j represents the Kronecker delta function.