1646 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 37, NO. 8, AUGUST 2009

Kinetic Description of MartianAtmospheric Entry Plasma

D. Janette Drake, Svetozar Popovic, Leposava Vuškovic, and Thao Dinh

Abstract—A kinetic model for Martian atmospheric entryplasma (MAEP) is presented. The model was calculated based ondata from Viking, Pathfinder, and the Mars Exploration RoversOpportunity and Spirit. Calculations of the density, temperature,and electron density across the shock front were made. We em-ployed steady-state and nonsteady-state kinetic models to describethe rate of dissociation of CO2 in the Martian atmosphere as wellas the production of O2. Water vapor was included in the modelssince it represents 0.03% of the surface atmospheric composition.With the addition of small amounts of water vapor, we found adecrease in the dissociation of CO2 in the Martian air as well asan increase in the production of O2. This paper is to report ananalysis of MAEP and its interactions with the shock front whichforms in the front of the Martian Landers.

Index Terms—Kinetic modeling, Martian atmospheric entry,oxygen production, plasma production.

I. INTRODUCTION

NASA’S MARS exploration program seeks to understandMars as a dynamic system, including measuring the struc-

ture of the upper atmosphere and ionosphere, understandingthe past and present climate, and its potential habitability. Inkeeping with these goals, many satellites and landers have beensent to Mars [1]. Each of these Martian probes and satellitesfaced numerous challenges on their long missions. For thesatellites, one of the most challenging phases is the aerobrakingphase. First used by the Magellan spacecraft while orbitingVenus in 1993 [2] and then by the Mars Global Surveyor in1997 [3], the satellites skimmed the atmosphere of the planetusing the friction between the atmosphere and the probes toslow their velocity. This subsequently led to a decrease in theorbital radius for the satellite. The major benefit of this processis that the naturally occurring forces were used to decrease thealtitude of the orbit as opposed to a deorbital burn which wouldinvolve the use of fuel to ignite the engines. Since less fuel wasneeded for the mission to get the satellite into orbit, the cost waslower. This friction also caused heating and ionization of thesurrounding atmosphere, generating Martian atmospheric entryplasma (MAEP), which is relatively poorly understood.

The first report on hypersonic aerodynamic problems duringterrestrial reentry was apparently by Hermann [4]. He reportedhow the changes in the altitude and the strong heating at the

Manuscript received March 5, 2009. First published July 7, 2009; currentversion published August 12, 2009. This work was supported in part by theNASA’s Graduate student research’s program through Marshall Space FlightCenter and NASA Langley Research Center.

D. J. Drake, S. Popovic, and L. Vuškovic are with the Departmentof Physics, Old Dominion University, Norfolk, VA 23529 USA (e-mail:ddrak002@odu.edu).

T. Dinh is with Berriehill Research Corporation, Dayton, OH 45459 USA.Digital Object Identifier 10.1109/TPS.2009.2023846

stagnation point would affect the chemical composition of theair flowing around the probe and eventually cause ionization. Inaddition, he described the interactions of the ionized gas with ashock wave formed by a circular cylinder, sphere, and circularcone. Although this paper was concerned with reentry, it helpedto define the types of obstacles that the Mars exploration landerswould face during entry. A more comprehensive review of theeffects of planetary atmospheric entry at Mach numbers greaterthan 20 for Earth, Mars, and Jupiter was given by Gnoffo [5].

Martian entry plasma is a complex mixture consisting ofnumerous atomic and molecular gases (CO2, O2, O, CO, NO,N2, CN, C2, N, C, and Ar), ions (C+, O+

2 , Ar+, O−, CN+,O+, CO+, and NO+), and electrons. Modeling of these typesof plasmas is very computationally intensive. Gorelov et al. [6]showed, through a comparison of experiments and numericalsimulations at shock speeds of 4–9 km/s, that to model thistype of discharge, a weaker dissociation rate for CO2 moleculeshas to be included in the model. In addition, they showed that,for nonequilibrium ionization behind the shock fronts, a slowerionization rate for C and O atoms by electron impact and thenonequilibrium distribution of the free electron temperaturemust also be included. In an earlier work by Park et al. [7],a thermochemical model using the previously identified mole-cular, atomic, and ionic species was used to show that the vi-brational temperature approaches the translational temperaturequickly behind the shock front.

In recent years, there have been many models and experi-ments of CO2/N2 hypersonic flows in a convergent–divergentnozzle for application to Martian atmospheric entry [8]–[10].By using a thermochemical nonequilibrium Navier–Stokessolver, these researchers have shown how the rotational tem-perature, vibrational temperature, number density, and molarfractions of the gases vary in a plasma arcjet under specificlaboratory conditions. The main problem with these models andexperiments is that they do not include argon as a key speciesin the discharges. In addition, they do not take into account thecorrect geometry for the Martian Landers.

This paper is to report an analysis of MAEP and its in-teractions with the shock front which forms in the front ofthe Martian Landers. This paper is organized as follows. InSection II, we describe the free stream density measurementsfrom Viking Landers 1 and 2, and Pathfinder. In Section III,we describe the entry trajectory data and the calculations forthe shock-wave jump parameters for these probes as well as forthe Mars Exploration Rovers (MERs) Opportunity and Spirit.In Section IV, we describe the electron energy distributionfunctions (EEDFs) for CO2 under Martian entry conditions. Weshow the changes in the electron temperature and dissociation

0093-3813/$26.00 © 2009 IEEE

DRAKE et al.: KINETIC DESCRIPTION OF MARTIAN ATMOSPHERIC ENTRY PLASMA 1647

TABLE IMARTIAN ATMOSPHERIC COMPOSITION AT THE SURFACE

TABLE IIMARTIAN UPPER ATMOSPHERIC COMPOSITION FOR VIKING LANDER 2

rate coefficients for CO2 and O2. Section V describes thecalculation of the electron density under jump conditions forthree Martian probes, given that the dominant neutral speciesin the MAEP will be CO2, O2, O, CO, NO, N2, and Ar. InSection VI, we discuss steady-state and nonsteady-state chem-ical kinetic models used for the simulation of MAEP. Finally,in Section VII, we discuss the inclusion of water vapor in themodel and how it impacts the dissociation rate of CO2 in theMartian atmosphere.

II. CHARACTERISTICS OF THE MARTIAN ATMOSPHERE

Observations made by several Martian probes and satellitessuggest that the atmosphere at the surface is primarily com-posed of CO2 with minor components of N2 and Ar (seeTable I) [11].

The Viking Landers contained two diagnostic tools. The firstof these is the Viking Upper Atmospheric Mass Spectrometer(VUAMS), which took measurements of the free stream at-mospheric density, pressure, and temperature between 160 and130 km [12]. The second is the Viking Atmospheric StructureInstrument, which provided data from 120 to 9 km. In the upperatmosphere, the VUAMS provided data about the compositionchanges from 200 to 110 km. Based on these results, Nier andMcElroy [13] created a simple model for the number density ofthe species for each of the Viking Landers. In Table II, we showthe composition changes for the upper atmosphere from VikingLander 2. From the table, we observe that composition changesgreatly with altitude. At 125 km, the composition is comparablewith the composition at the surface. Therefore, we will use thesurface atmospheric composition for altitudes below 100 km.Above this altitude, we will use the results from the VikingLanders.

Beyond the basic composition of the atmosphere, there ismuch information from the Pathfinder and Viking Landersabout the free stream density and temperature during the entryphase into the atmosphere. This phase begins at approximately160 km above the surface and lasts until the parachutes aredeployed for landing, around 9 km, with a total elapsed time of

Fig. 1. Atmospheric free stream density distribution for the Martian at-mosphere. The Pathfinder Lander had three sensors in the upper atmosphereto measure the density as indicated by the data points about 140 km.

approximately 120 s. The Pathfinder probe had three diagnostictools, one set in each plane, during entry [14]. Each of thesetools collected data for the density, pressure, and temperaturefor the entire entry phase. The free stream density measure-ments for the Martian atmosphere are shown in Fig. 1.

From this figure, we observe that the Viking measurementsare higher than the Pathfinder measurements at higher altitudes.This difference is due to seasonal density changes and diurnalvariations within the thermosphere [15]. Two models wereconstructed for the Pathfinder data using the altitudinal densitydistribution

ρ = ρoe−C1h (1)

where ρ is the atmospheric free stream density, C1 is a constantdetermined by calculation, and h is the height in kilometers.

Free stream temperature measurements were made duringentry by the Pathfinder and Viking (VL1 and VL2) Landers.From Fig. 2, we observe that the temperature is very high in theupper atmosphere which most likely is caused by solar radia-tion. The temperature then decreases, with decreasing altitudereaching a minimum at 80 km. According to Schofield et al.[14], this temperature minimum may be due to a superpositionof waves, such as thermal tides. These tides will propagatefrom the lower atmosphere to higher altitudes with increasingamplitude. After 80 km, the temperature once again beginsto increase until it reaches an average of about 220 K at thesurface.

A comparison of the data from the three probes showsthat temperature measurements were less precise than the freestream density measurements in Fig. 1. Two models have beenemployed to estimate the temperature: the Glenn model and theLangley Atmospheric Upwind Relaxation Algorithm (LAURA)[16]. Neither of these was able to accurately describe the trendsin the data. All of the data were collected at relatively the sametime of year and same distance from the equator. The onlyknown difference in the data is from the fact that the Vikingdata were taken 20 years before the Pathfinder data. For ourresearch, we have estimated the average temperature over allsets of current Mars data; the resulting curve is labeled Present

1648 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 37, NO. 8, AUGUST 2009

Fig. 2. Temperature distributions in the Martian atmosphere from VikingLanders 1 and 2, Pathfinder Lander, the Glenn model, LAURA model, and ourpresent model.

Fig. 3. Velocity measurements for Pathfinder, Viking, MER Spirit, and MEROpportunity Landers.

Model in Fig. 2. In addition, we have constructed an upperand lower limit for the temperatures, which can be seen asthe shading in the calculations which involve these temperaturemeasurements.

III. MARTIAN PROBE ENTRY TRAJECTORY

AND SHOCK PARAMETERS

By reconstructing the entry trajectory of the Martian probes,when we use the present model, we are able to develop an accu-rate portrait of all the atmospheric phenomena faced by them.In Fig. 3, we have reconstructed the velocity measurements foreach of the listed probes. We note that the velocity was constantdown to an altitude of 60 km. The velocity then dropped sharplyover the next 50 km. At an altitude of approximately 10 km, asmentioned earlier, the parachutes for each of the probes weredeployed. Due to the closeness of the MER Spirit and MEROpportunity data, we will use the MER Opportunity data forthe remainder of this paper. These data will have error barsto take into account the velocity measurements of the MER

Fig. 4. Calculated values of the Mach number for the Viking, Pathfinder, andMER Opportunity Landers.

Spirit probe. It is important to note that, although there aresufficient velocity data for reconstruction of the trajectory of theMER Landers, there are no free stream temperature or densitymeasurements for these landers.

The Mach number (M) for each probe was determined byusing M = v/cs, where v is the velocity of the probe and cs isthe speed of sound in the medium determined by

cs =√

γRT

mm. (2)

Here, γ is the specific heat ratio, R is the universal gasconstant, mm is the molecular mass, and T is the temperaturefrom Fig. 2, and we present these results in Fig. 4. Fromthe figure, we observe that the Mach number increases as theprobes enter the atmosphere with peak values of 42, 31, and25 for the Pathfinder, MER Opportunity, and Viking Landers,respectively. Then, the Mach number begins to decrease sharplydue to an increase in atmospheric density.

In order to accurately estimate electron density and gascomposition for MAEP, we must construct a simple model forthe shock region in front of each probe during entry. For thismodel, certain assumptions must be made: 1) The gas mixturesgenerated during entry are thermodynamically perfect gases;2) ionization occurs instantly behind the shock front; 3) the gasmixtures are constant in the boundary layer behind the shockfront; and 4) gas parameters are defined by the free streamparameters and the relations across the shock. From theseassumptions, we are able to calculate the shock parameters

ρ2 = ρ(γ + 1)AM

AM (γ − 1) + 2(3)

T2 = T

{1 +

2(γ − 1)(γ + 1)2

AM − 1AM

[γAM + 1]}

(4)

where γ is the specific heat ratio, AM = M(T )2 sin2 β, β isthe oblique shock angle, T is the atmospheric temperature fromFig. 2, and ρ is the atmospheric density from Fig. 1.

The calculated density across the shock layer, or jump den-sity, is given in Fig. 5. We calculated these values from (3) in

DRAKE et al.: KINETIC DESCRIPTION OF MARTIAN ATMOSPHERIC ENTRY PLASMA 1649

Fig. 5. Jump density for the MAEP as a function of the altitude.

Fig. 6. Temperature across the shock layer in the MAEP. The shaded regionis due to the uncertainties of the measured free stream temperature data.

which the specific heat ratio of the Martian atmosphere is 1.29and the oblique shock angle for all three probes was 78.9◦.

The jump temperature was calculated from (4) and is shownin Fig. 6. We observe that the temperature reaches a peakaverage value of about 36 000 K, 19 000 K, and 13 000 Kfor the Pathfinder, MER Opportunity, and Viking Landers,respectively. These maximum values occurred between 50 and60 km above the surface. The shaded regions give us a range ofvalues for the temperature. For example, the Pathfinder Landerhas a peak temperature of 36 000 K ± 2500 around 60 km. Athigher altitudes, all the distributions become wider since theatmosphere becomes less dense.

IV. EVALUATION OF THE EEDF

In the absence of a magnetic field, the flow of electronsthrough a unit velocity phase space is described by theBoltzmann transport equation [17]

∂f(�r,�v, t)∂t

+�v ·�∇f(�r,�v, t)−e �E

m·�∇f(�r,�v, t)=

(∂f(�r,�v, t)

∂t

)coll

.

(5)

Here, the distribution of electrons in their velocity space �v atthe space coordinate �r and at time t is given by the electron

velocity distribution function f(�r,�v, t), me is the mass of theelectron, and e is the charge of the electron. In the case of aweakly ionized gas, the right-hand side of (5) will take intoaccount the elastic and inelastic collisions between electronsand neutral atoms or molecules.

Due to the complexity of (5), solutions can only be deter-mined for selected cases. We have employed three approx-imations for our model: 1) the homogenous approximation;2) the steady-state approximation, where the electron collisionfrequency in the ionized gas is approximately two or threeorders of magnitude larger than the driving frequency; and3) symmetry along an axis of symmetry for the Martian probes.By applying these approximations, a steady-state isotropic so-lution can be obtained for a monatomic gas [18]

13

(eE

N

)2d

dε

(ε

Qm

df

dε

)+

2mekBT

M

d

dε

(ε2Qm

df

dε

)

+2me

M

d

dε(ε2Qmf) − εf(ε)

∑j

Qj(ε)

+∑

j

(ε + εj)f(ε + εj)Qj(ε + εj) = 0. (6)

Here, we have expressed, by convention, the solution in termsof the electron energy ε = mv2/2 and have neglected super-elastic collisions. In (6), Qm is the momentum transfer crosssection; Qj is the cross section of the jth inelastic collision; Eis the electric field; M , N , and T are the mass, density, andtemperature of the neutral gas molecules; kB is the Boltzmannconstant; and f is the isotropic EEDF.

For a gas mixture, an appropriate modification to the crosssections of all gas species in (6) should be made: Qm =∑

n QnmGn in the first term and Qm =

∑n MQn

mGn/Mn andM =

∑n MnGn in the second and third terms. Here, Qn

m isthe momentum transfer cross section, Gn is the mole fraction,and Mn is the mass of the molecule of the nth species.

We calculated the EEDF by employing a commercial nu-merical Boltzmann solver, Bolsig, for weakly ionized gasesunder steady-state conditions [19]. Bolsig provides numericalsolutions for the EEDF at different values of the reducedelectric field (E/N). An upgraded version of Bolsig, known asBolsig+ [20], provides similar results as the old Bolsig programbut allows for more species to be included in the calculation ofthe discharge parameters and EEDF.

From the EEDF values, we are able to calculate the averageelectron temperature (Te) of the distribution and rate constants(kj) for certain processes

Te =23

∞∫0

ε3/2f(ε) dε (7)

kj =(

2e

m

)1/2∞∫

0

εQj(ε)f(ε) dε. (8)

To verify the accuracy of the numerical results, we present inFig. 7 a comparison of the results from Bolsig for pure carbondioxide with calculated values from Nighan [21]. We found that

1650 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 37, NO. 8, AUGUST 2009

Fig. 7. EEDF values in a carbon dioxide plasma.

Fig. 8. Calculated values of the average electron temperature in terrestrial andMartian air plasmas.

the Bolsig data agreed fairly well with the calculated values,±20%.

By applying (7), we calculated the average electron tempera-ture at various values of E/N for terrestrial air and Martian airand present these results in Fig. 8. We observe that Te increasesalmost linearly with E/N values greater than 4 × 10−16 V ·cm2. Below this point, the values for terrestrial air increase veryslowly and are almost constant, while the values for Martian aircontinue to increase linearly.

The dissociation rate coefficients for CO2 and O2 were calcu-lated by employing (8) and are shown in Fig. 9. We note that thecoefficients increased strongly with the reduced electric field.

V. EVALUATION OF THE ELECTRON DENSITY

The electron density was evaluated by using the Saha equa-tion [22]

logNeNik

Nk − Nik= −5040

εk

Te− 1.5 log

5040Te

+ 26.9366 + log2gki

gk0(9)

Fig. 9. Calculated values of the dissociation rate coefficients for CO2 and O2

in MAEP.

where Nik is the number density of ions from species k, Nk

is the neutral species density, εk is the ionization potential ofspecies k, gki is the statistical weight of the ion species k,and gk0 is the statistical weight of the neutral species k. Inthis model, we have assumed that the electron temperature (Te)equilibrates to the gas temperature obtained in Fig. 6. We mustalso assume that the gas temperature is still high enough thatwe can neglect the effects of ion chemistry. In addition, we arenot including the free stream electron density in this calcula-tion [23].

Since Martian air is composed of many constituents, thiscalculation is very complex. Looking at Table I, we see that themain constituents of the Martian atmosphere are CO2, N2, andAr. During ionization, the major additional neutral species, dueto the dissociation of CO2 and N2, will be O2, O, CO, and NO.The number densities of the other neutral species mentionedin the introduction will be negligible in comparison with thedensities of the other seven species. As such, we have reducedthe number of equations needed to find the electron density byassuming that these will be the seven dominant species in thedischarge.

We start with an assumed electron density and then calculateNik from (9). Then, we apply

Ne =∑

k

Nik (10)

to recalculate the electron density and repeat this process. Dueto the fast convergence of this method, we are able to calculatethe electron density fairly quickly (see Fig. 10). From thefigure, we observe that above 50 km, the electron density isconsistent for each probe. Below there, the Pathfinder resultsare orders of magnitude different from the Viking and MEROpportunity data. It is important to note that the distributionof the electron densities was due to the irregularity in the freestream temperature measurements.

Although we have considered that the plasma formed duringatmospheric entry will be in thermal equilibrium with the gastemperature (Te ∼ Tg), there have been many recent papers

DRAKE et al.: KINETIC DESCRIPTION OF MARTIAN ATMOSPHERIC ENTRY PLASMA 1651

Fig. 10. Calculated values of electron density for MAEP. The shaded regionsare due to deviations in the measurement of the free stream temperature data.

Fig. 11. Calculated values of electron density for MAEP when Te = Tg ,Te = 2Tg , and Te = 1/2Tg .

discussing the possibility that it is nonthermal equilibriumplasma [6], [9], [10]. As such, for a first approximation, wehave set Te = 2 ∗ Tg and Te = 1/2 ∗ Tg in our model to de-termine the effect this will have on the electron density. FromFig. 11, we observe that at high altitudes, the change in electrontemperature in the model had little effect on the calculatedelectron density. However, at altitudes below 40 km, the changeis significant, with the electron density decreasing sharply.

VI. GAS COMPOSITION

The most probable gas reactions that affect the productionand destruction of the neutral species in MAEP are listed inTable III. A more comprehensive list of the reactions can befound in a paper by Park et al. [7]. For our model, we haveexcluded all the carbonic and oxygen-containing ions, alongwith CN+, C+

2 , Ar+, N+, and N+2 , since their concentrations

will be very small in comparison to their neutral counterparts[23]. As such, they will not play a significant role in the rateprocesses. The only ion which will play any part is the O− ionwhich has an active role in the production and loss of the neutralspecies.

The gas composition can be obtained by solving a systemof rate and mass conservation equations. In a time-dependentmodel, the system reduces to a set of combined differentialequations and algebraic equations. Based on the discussion byDinh [35], the minimal system of rate and mass conservationequations is given by

d[CO2]dt

= −k1Ne[CO2] + k4[O−][CO] (11)

d[O3]dt

=(k6[CO2]o[O] + k9[O−]

)[O2] − (k3Ne+ k4[O]) [O3]

(12)

d[O]dt

= (k1[CO2] + 2k2[O2]) Ne

−(2k5[O][CO2]o + k4[O3]

+ k6[O2][CO2]o + k8[O−])[O] (13)

d[O−]dt

= k3Ne[O3] − (k7[CO] + k8[O] + k9[O2]) [O−] (14)

[CO2] + [CO] = [CO2]o (15)

2[CO2] + [CO] + [O] + 2[O2] + 3[O3] = 2[CO2]o (16)

where [X] is the concentration of species X , [CO2]o is theinitial concentration of neutral CO2, kn is the rate coefficientfor nth reaction, and Ne is the electron density calculated from(9). Equations (15) and (16) represent the mass conservation ofcarbon and oxygen atoms in the plasma, respectively. In (15),we have neglected the carbonic ions since they have negligiblenumber densities in comparison with their neutral counterparts.Similarly, in (16), we have neglected the oxygen ions.

The steady-state solution for this system can be found by set-ting the time differentials in (11)–(14) equal to zero. Including(15) and (16), this set of nonlinear coupled equations can nowbe solved for the six unknown concentrations: [CO], [CO2],[O], [O2], [O3], and [O−]. Fig. 12 shows the dissociation ofCO2 into CO, O, and O2 under these steady-state conditions.We observe from the figure that, as the reduced electric fieldincreases to 8.0 × 10−16 V · cm2, over 80}% of the CO2 hasbeen dissociated.

The reduced electric field (E/N) was estimated as follows.In Fig. 6, we observed that, for the Pathfinder data from 10to 100 km, the total change in jump temperature was approx-imately 36 000 K or 3 eV. We estimate that the total thicknessof the shock front is about 5λ, where λ is the mean free path, orabout 0.3 cm. Thus, the total electric field E is approximately10 V/cm. We determined that the number density N wasbetween 2 × 1016 and 1 × 1017cm−3. Therefore, we estimatedthe reduced electric field to be in the range of 1 × 10−16–6 ×10−16 V · cm2.

To calculate the time evolution of the species concentrations,we employed a fourth-order Runge–Kutta method. This methodpropagates a solution over an interval h by combining informa-tion from several Euler-style steps and then uses this informa-tion to match a Taylor series expansion up to O(h4). By usingfixed dissociation rate coefficients, we made these calculations.In Fig. 13, we observe that about 95% of the CO2 dissociation

1652 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 37, NO. 8, AUGUST 2009

TABLE IIIMAJOR GAS REACTIONS IN MAEP

Fig. 12. Dissociation of CO2 into CO, O, and O2 in MAEP at an altitude of40 km.

Fig. 13. MAEP composition at E/N = 5.0 × 10−16 V · cm2 and an alti-tude of 40 km as a function of time.

was achieved within 6.0 × 10−7 s, which is practically instan-taneous even in the time frame of an M = 20 flow. This resultis consistent with a previous work done by Park et al. [7],who showed that the dissociation rate for CO2 is very quickbehind the shock front during Martian atmospheric entry.

Changes in gas composition were looked at for variousconcentrations of CO2, CO, and O2 in the mixture. The EEDF

Fig. 14. EEDF of different compositions of CO2:CO:O2.

was calculated, and the results are shown in Fig. 14. Fromthis figure, we can observe how the concentration of CO andO2 in the mixture changes the distribution function. Therefore,we can conclude that changes in the composition will affectthe values of the rate coefficients and concentration of CO2

over time.To calculate the composition changes, we started with the

initial mixture and then calculate a new EEDF and corre-sponding rate coefficients after a selected length of time. Anew composition was computed, and the corresponding EEDFand rate coefficients were calculated. We used time steps of0.25 × 10−7 s. The values for the dissociation rate coefficientfor carbon dioxide are shown in Fig. 15. For constant kCO2,a straight line would appear across the page. As a result ofthe change in the mixture composition, we observe a decreasein kCO2 values over time. This corresponds to a change inthe dissociation rate of CO2 over time, as shown in Fig. 16where the solid line represents the values that were obtainedfor constant rate coefficients. Over the same time interval, thepercentage of CO2 dissociation was 15% less.

VII. EFFECT OF WATER VAPOR

In the previous sections of this paper, a water-free modelwas presented. From Table I, we observe that there is a smallamount of water vapor in the atmosphere, 0.03%. The effect ofOH radicals from water vapor in the MAEP is summarized inTable IV.

DRAKE et al.: KINETIC DESCRIPTION OF MARTIAN ATMOSPHERIC ENTRY PLASMA 1653

Fig. 15. Calculated dissociation rate coefficients for CO2 as a functionof time.

Fig. 16. Percentage of CO2 at E/N = 5.0 × 10−16 V · cm2 at an altitudeof 40 km as a function of time for constant and variable dissociation ratecoefficient k.

TABLE IVMAJOR REACTIONS DUE TO OH RADICALS IN MAEP

To date, the altitudinal changes in the concentration of watervapor have not been measured. McElroy et al. [36] constructeda photochemical model to compute the concentration for var-ious products of water vapor dissociation in the Martian at-mosphere. They found that the concentration of OH moleculespeaked at an altitude of about 40 km. However, the calculateddensity of OH was still less than 0.1% of the total free steamatmospheric density.

From the last reaction, we observe that the generation rateof OH radicals from the dissociation of water molecules isrelatively fast. This indicates that with an electron density of

Fig. 17. Percentage of CO2 in MAEP as a function of time with the amountof water added to the system indicated. The 0.003% curve cannot be seen in thefigure since it coincides with the 0.03% curve.

Fig. 18. Percentage of O2 in MAEP using the Pathfinder Lander data as afunction of time.

1010 cm−3, the concentration of OH radicals is about 10%of the initial water concentration in the system [35]. The firstreaction has a direct effect on the dissociation of CO2 inthe air. Since the amount of water vapor reduces the rate ofdissociation, we must take the OH radicals into account in ourmodel. Thus, we included an amount of water vapor equivalentto 0.03% of the total gas volume in our model.

As before, we observed the changes in the concentrationof CO2 in the atmosphere due to dissociation. In Fig. 17, weobserve that with small amounts of water vapor added to themodel, the dissociation of CO2 was not effected. However, asmore water vapor is included in the model, the amount of CO2

in the MAEP decreased at a slower rate.Another interesting phenomenon that occurs when water

vapor is added to our model is that the production of O2 inthe system increases. As calculated for the Pathfinder Lander,in Fig. 18, we estimated that the amount of O2 in the dischargewill increase by about 20% due to the presence of 0.03% ofwater vapor.

1654 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 37, NO. 8, AUGUST 2009

VIII. CONCLUSION

We have described the results of a kinetic model createdbased on free stream gas temperature, density, and velocity datafrom the Viking, Pathfinder, and MER Opportunity Landers.Altitudinal distribution of atmospheric composition was takenfrom the Viking data. The density and temperature across theshock front were calculated for each probe. A temperaturespread was observed due to the imprecision in the atmosphericmodels and data for the free stream temperature. The calculateddata rely upon the fact that the changes in the composition withaltitude are negligible up to 100 km and vary at higher altitudes.

The EEDF was calculated for the Martian atmosphere bysolving the Boltzmann transport equation. For atmospheric gasmixtures, electron temperature and dissociation rate coefficientswere then calculated as shown in Figs. 8 and 9. The electrondensity was determined from the Saha equation for a simplemodel with the main species for the ionized gas. From Fig. 10,we saw that above 50 km, the electron density was consistentfor each probe. At lower altitudes, the Pathfinder results wereorders of magnitude different from the Viking and MER Op-portunity data. In addition, we have shown the variations inelectron density when the electron temperature was assumedto be higher or lower than the gas temperature by a factorof two. In Fig. 11, we showed that at higher altitudes, thechange in electron temperature in the model had little effect onthe calculated electron density. On the other hand, at altitudesbelow 30 km, the change was considerable.

A gas composition model was then used to estimate thedissociation of CO2 in the Martian atmosphere for steady-stateand nonsteady-state conditions, and a comparison was made.We observed that 95% of the CO2 was dissociated within6.0 × 10−7 s, assuming that the dissociation rate coefficientswere constant in time. However, upon analysis of the changein the rate coefficient with composition, we determined that theamount of CO2 in the model would be 15% greater in the sametime period. By introducing a small amount of water vapor tothe model, we found that the rate of dissociation increased withconcentrations of water vapor above 0.03% for nonsteady-stateconditions. We also observed an increase in production of O2

by about 20% due to the presence of 0.03% of water vapor.

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D. Janette Drake, photograph and biography not available at the time ofpublication.

Svetozar Popovic, photograph and biography not available at the time ofpublication.

Leposava Vuškovic, photograph and biography not available at the time ofpublication.

Thao Dinh, photograph and biography not available at the time of publication.