Ablation and Ionization Phenomenon in a Teflon Pulsed Plasma Thruster

Transcription

1 Ablation and Ionization Phenomenon in a Teflon Pulsed Plasma Thruster IEPC Presented at Joint Conference of 3th International Symposium on Space Technology and Science 34th International Electric Propulsion Conference and 6th Nano-satellite Symposium, Hyogo-Kobe, Japan Lei Yang, Yuping Huang Beijing Research Institute of Precise Mechatronic Controls, Beijing, 76, China Haibin Tang 3 Beihang University, Beijing, 9, China and Xiangyang Liu 4 Beijing Institute of Technology, Beijing, 8, China Abstract: To reveal overlooked physics governing the ablation process in pulse plasma thrusters (PPT), a modified model that taken into account the effects of thermochemical reaction of Teflon propellant on the characters of wall ablation mechanism was derived and presented. The law of ablation and ionization phenomenon in the LES-6 PPT prototype was quantitatively clarified by this model. Results of wall-plasma interactions were closer to the practical situation, which accurately describe the essential relationship between ablating boundary layers and reflected the dynamic changes of inflow parameters during discharge. Furthermore, the temporal and spatial variations of the different plasma species in the discharge channel were numerically studied. It showed that plasma was mainly composed of monovalent ions, of which carbon ions and fluorine ions were focused on the upstream and downstream discharge channel, respectively. Good agreement with experimental measurements of the formation times of the various plasma species was found. A large number of short-lived and highly ionized carbon and fluorine species (divalent and trivalent ions) were created at the exit during initial discharge. And those considered more fully ionized species came out shorter. C q c L R p p = electric capacitance = electric quantity of capacitance = inductance = plasma resistance = plasma conductivity Nomenclature Postdoctoral Fellow, R&D center, ylforeverbit@6.com. Research Fellow, Institute Office, huangyp@8.sina.com. 3 Professor, School of Astronautics, thb@buaa.edu.cn. 4 Associate Research fellow, School of Aerospace Engineering, liuxy@bit.edu.cn.

2 I = discharge current j = current density k = Boltzmann constant m = mean molecule mass = Anisimov ratio = adiabatic exponent T = temperature n = number density K = coefficient of heat conduction Q = Joule thermal energy per unit area h = height of discharge channel, electrode to electrode w = width of electrodes l = length of electrodes Subscript = wall surface or initial = outer boundary of ablation boundary layer = outer boundary of plasma layer e = electron i = ion p = plasma x = axial direction I. Introduction ulsed plasma thruster (PPT) is the first application of electric propulsion on any spacecraft. The PPT has some P features superior to other kinds of electric propulsion. It has no sealing part, low power requirements, simple structure and high reliability, which are benefits of using a solid propellant, mainly Teflon (polytetrafluoroethylene: PTFE). By virtue of its advantages, PPT thus becomes a highlight on micro/nano-satellites technology research and application in many countries. On September 9,, PROITERES nano satellite launched by Japan used two groups of PPT as thruster units for attitude control and orbit hoisting,3. While in this area, the development of micro/nano-satellites and their networking technology in China also put forward the corresponding application requirements for PPT 4. However, PPT s controversial inefficiency has always hindered its development and space applications 5. According to experimental studies, PPT s low thrust efficiency effectiveness is caused by its ablation and ionization process of a solid propellant, which is quite different from the operating mode of other electrical thrusters. To be specific, when PPT works, only a small portion of propellant consumed is ionized and ejected outside via electromagnetic acceleration during discharge; while the rest is composed of neutral gas from ablation at the end of pulse discharge, and is moved out at a low speed via thermal expansion. In return, this less ionized and slow-moving late-time ablation gas will slow down the specific impulse of PPT 6. Therefore, based on the evolution of wall ablation, we can make quantitative analysis of ablation process, especially the temporal and spatial distribution characteristics of plasma species. A further research in this aspect will be of great value in theoretically studying discharge energy distribution and loss mechanism in PPT. Also, it may be a breakthrough in developing highperformance PPT. There are many efforts devoted to simulate the wall ablation mechanism in PPT. The famous Mikellides model is such an effort in this area 7. Assuming that saturated vapor exists in the surface of solid propellant, this model is a pioneer in combining ablation with magnetic fluid dynamics to determine the thermodynamic state relationship of the ablation boundary layer between the wall and the plasma layer, so as to describe wall-plasma interactions. For ablation boundary layer, the wall temperature is assumed to be the same as ablation vapor; while the vapor pressure and density of its outer layer is half of that in inner layer. In terms of the above simple assumptions, Mikellides model is very similar to the early Langmuir model, which was first developed to investigate the vaporization of metallic tungsten 8. However, these models feature simple boundary transient relations, which can only roughly describe the ablation and flow coupling state. In addition, the vapor speed at the vapor or plasma interface of Mikellides model or Langmuir model is limited to a value being a function of certain wall surface temperature.

3 To consider details of the ablation and vapor flow for the propellant exposed to discharge current, Keidar and Boyd applied the Knudsen layer formed near the ablated surface to describe the wall-plasma transition region (i.e. K-B model) 9,. However, developed from Anisimov s one-dimensional equilibrium evaporation theory, the K-B model ignores by nature the influence of propellant s thermally chemical reaction on the correlation between ablation boundary layer and plasma layer. For this reason, it has some innate defects in its own. On the other hand, studies have found that thermally chemical reaction of solid propellant is reflected on the complex diversity of ionizing components. These thermal controlled components vary widely and have a direct impact on the key parameters of heat transfer between ablation boundary layer and plasma layer. Thus, we can t afford to ignore such factors if we want to accurately simulate ablation and ionization phenomenon in PPT. In our work, given the defects of the above models, a new approach is carried out to describe PPT s ablation and ionization. The rest of the paper is organized as follows: Section is about the establishment of the modified K-B model by taking thermally chemical reaction into account and describes its coupled models and relevant calculations; Section takes LES-6 PPT as an example to make corresponding numerical calculation. Specifically, we firstly compare parameter variation relations of different models based on the wall-plasma interaction, then quantitatively obtain the temporal and spatial variation of the different plasma species in the discharge chamber, and finally discuss ablation and ionization phenomena in PPT; and Section concludes the major results of our research. II. Physical Model and Calculation A. Modified K-B Model By spatial position, PPT discharge chamber is divided into ablation boundary layer and plasma layer, as shown in Fig. Wherein the ablation boundary layer (also called Knudsen layer, vapor layer or power layer) is used to describe the transition layer of ablation between wall surface (Position ) of PTFE (commonly used as PPT propellant) and flow inlet (Position ), and the outer boundary parameters of this layer can characterize the ablation characteristics of PTFE; while the plasma layer describes the plasma Figure. Schematic representation of the layer structure generation and flow process, which reflects the PPT near the ablated surface. discharge ionization characteristics. Based on the Knudsen theory, this paper revises K-B model, and builds an modified model applicable to PPT s ablation boundary layer characteristics: mn mn = mnv { ( ) β exp α απ erfc.5 ( α) } () ( πd) ( πd) mn mn = {( + α ) ( ) ( ) ( ) } β.5 + α erfc α αexp α / π.5 () 4d d mn 4( γ ) mn γ γ γ.5 π α α β.5.5 ( ) ( ) ( ) α α erfc ( α) + = α exp ( α )/ π π d γ d (3) + γ γ ( γ ) where di = mi / kti( i =,) m and m refers to the mean molecule mass of Position and Position, reflecting the effect of mass distribution of components generated by thermally chemical reaction of PTFE; α = V / kt / m erf refers to error function, erfc refers to complementary error function ( ).5 with erf ( α) erfc( α) = ; β is Anisimov ratio ( ) γ = λ+ 5 /( λ+ 3) is heat insulation index, and λ is internal degree of freedom, reflecting the effect of the structure of components generated by thermally chemical reaction of PTFE. In this paper, Saha Equation is applied to calculate the compositions generated by the thermally chemical reaction of PTFE. In PPT discharge pulses, as relaxation times (< - s) for ionization and compound is smaller than the characteristic time (s) of discharging process, then it can be assumed that the plasma in PPT discharge chamber is in locally thermodynamic equilibrium, it satisfies the following Saha Equation : 3

4 ( r + ) ( r) 3/ ( r ) e εi π e + = exp ( r) ( r) nn mkt Z (4) n kt h Z where n is electron number density, n ( r) is number density of r-order ionized atoms, Z ( r) is atom distribution e ( r) function of r-order ionization atoms, m is electron mass, and e ε refers to the ionization energy required from r- i order to (r+)-order ionization. Equation ()(3) describe the relations among thermodynamic state parameters in ablation boundary layer (the temperature T, density n and velocity V in Position and density n and temperature T in Position ). If T and V are known parameters, we can figure out other thermodynamic state parameters such as T and n. Figure shows the model of heat fluxes from plasma to PTFE surface in these two layers. T can be obtained by heat transfer model in Eq.(5), namely, semi-infinite solid material non-steadystate heat transfer model, PTFE gasification decomposition conditions and the net heat Q s transferred to the propellant surface 3. T T =a t T K = Q = Q m Δh x= s i (5) where Q= I Rp /( h w) ; Δ h refers to the energy consumed in i raising the initial temperature ( T ) of the PTFE to the average Figure. Heat transfer between ablation temperature of plasma via gasification, decomposition, ionization boundary layer and plasma layer.. and heating. n is calculated by PTFE s equilibrium vapor pressure formula 4 p pc n = exp( Tc / T) kt = kt (6) 5 where pc =.847 pa, Tc = 85K. Furthermore, the outer boundary velocity V is particular critical for the calculation of Eq. () (3). For the sake of simplifying calculations, traditional K-B model usually assumes V as the local speed of sound or near the speed of sound. Whereas in this paper, we combine the mass and momentum conservation equations of particles in plasma layer (i.e, boundary and boundary, see Figure ) to establish the theoretical analysis model for boundary velocity V, see Eq. (7). Compared to the traditional methods, Eq. (7) considers the differences in average molecular mass of components between boundaries caused by the thermally chemical reaction of the plasma, i.e., effect of m /m variations on V. ( ) Tn / μ I w 3 m n V /( kt/ m) = / (7) Tn 4 nkt mn where n, T and m describe plasma layer s outer boundary, i.e., the density, temperature and the average molecular mass of the particles in Position. B. Calculation Procedure and Conditions In order to reveal the ablation and ionization characteristics of microsecond magnitude operation process of PPT, we need to combine the above model with PPT discharge and plasma flow dynamically, thus building a systematic numerical framework. PPT discharge can be described as a typical RLC circuit discharge process, and expressed in the following Kirchhoff's laws: dqc dqc qc L + ( R + Rp) + Eind + = (8) dt dt C 4

5 l dqc where I = ; Rp = h/ w σ pdx, while dt E is induced electromotive force among electrodes. ind The following simplified magneto-hydrodynamic equations are used to describe the one-dimensional plasma flow across boundary and boundary : ρ ρu + = (9) t B ρuu + p + ρu μ + = () t p u B p u B B ρ + + ρu up+ u ργ ( ) ρμ ργ ( ) ρμ μ + = j / σ () p t B ( ub) B + = () t μσ p where ρ u and p are respectively, the density, velocity and pressure of plasma μ is the permeability of vacuum B is the magnetic field intensity j is the current density x is the axial direction from wall surface to exit of the thruster Then we use two-step finite-difference MacCormack scheme to differentiate above plasma flow models by taking discharge starts among electrodes as initial conditions, that is, in discharge chamber: ρ = ρ u = T = T B= B. Initial density ρ is set based on in-chamber initial parameters; initial temperature is T = 3K; and initial magnetic induction intensity B For boundary conditions, we take thermodynamic state parameters of Position as flow inlet boundary parameters, namely, ρ in = mnv uin = V (3) Tin = T Considering that PPT flow outlet can meet supersonic flow conditions during discharge operation, that is to say, the flow outlet boundary conditions (boundary ) can be obtained by simple first-order extrapolation. III. Results and Discussion In this paper, we take the electrical and geometrical parameters of commonly used LES-6 PPT 7 as our simulation object, study on numeric simulation of PPT discharge process on the basis of the above models, and finally reveal the mechanism of PPT ablation and ionization. A. Ablation mechanism of Propellant Propellant ablation is closely related to its surface temperature changes. Figure 3 shows the trend of PTFE surface temperature during PPT discharge. It is apparent from Fig3 that the propellant temperature fluctuates in a way similar to that of discharge currents. This is because ohmic heating of plasma serves as the external energy source for propellant ablation, while this part of the heat energy to a large extent reflects the changes of discharge current energy. In the first positive peak section of discharge current, both Figure 3. PTFE surface temperature during PPT discharge 5

6 discharge current and released energy are at the maximum, at this time, the surface temperature of the propellant also reaches its first peak of about 9K. After the end of the main discharge, the surface temperature continues to decline, but remains at a high temperature above 7K, which is a necessary condition to incur late-time ablation phenomena. Further, we analytically compare modified K-B model with traditional Mikellides model and Langmuir model in terms of their application in PPT, and we obtain the variation laws of ablation layer parameters computed by different two-layer kinetic models. In modified K-B model, the boundary relations between wall-plasma interfaces are described by Equation ()(3); whereas inmikellides modelit is assumed that T = T ; n = n /; kt V = (4) m In Langmuir model, it is assumed that Figure 4 describes the transient variation of V. It is apparent from the Fig.4 that, V calculated by the modified K-B model is gradually increased from a lower speed and accelerates to the maximum on positive current peak sections, which has a waveform similar to that of the propellant ablation temperature or discharge process; after the main discharge is completed, V still stays at a higher value before declining, indicating that the propellant surface temperature is still greater than the decomposition temperature during late-time ablation period. As a result, gasification phenomenon is created continuously. Besides, local sound speed and V computed by Mikellide model or Langmuir boundary model are basically the same in waveform, this is because V computed by Mikellide model or Langmuir model and the local sound speed are kept at a certain value, i.e., their Mach number are ( ) / /γ and T = T ; n = n /; kt V = (5) π m Time, s ( /πγ ) / respectively. In fact, PTFE ablation produces vapor and flow when it is heated from room temperature to its decomposition temperature, therefore, V computed by Mikellide model or Langmuir model remains a large value at the beginning of the pulse, which is obviously not applicable. In the late pulse discharge, the value of V computed by modified K-B model stays broadly in line with that of V computed by Mikellide model, indicating the value of V is close to the local speed of sound with the ratio of about ( /γ ) /. Also after the main discharge comes to an V m/s Modified K-B model Sound speed, C Mikellide,V =C/ / Langmuir,V =C/(/) / Figure 4. Comparison of V modeling in PPT with different models T /T Modified K-B model Mikellide/Langmuir model Time(s) Figure 5. Comparison of T /T modeling in PPT with different models n /n Modified K-B model Mikellide/Langmuir model Time, s Figure 6. Comparison of n /n modeling in PPT with different models 6

7 end, the value of V computed by Mikellides model or Langmuir model shows no clear downward trend. By analytic comparison, this paper illustrates that the V calculated by the modified K-B model is consistent with PPT s actual operation process. Figures 5 and Figure 6 show the transience variation of temperature and density between the ablation boundary layer respectively. From Fig. 5, we can see that temperature transience relation calculated by the modified K-B model is very sensitive to changes in V. Compared with Fig. 4, two fluctuations in T /T curves during discharge (.5~3 s ) are caused by changes in V. Fig. 5 also shows the temperature transience relation assumed by Mikellide model and Langmuir model, that is, a simple single-valued correspondence relationship T /T =, which does not reflect conservation of energy within the ablation boundary layer and temperature gradient. While in Fig.6, density transience relation calculated by the modified K-B model is similar to temperature. In essence, the density transience relation reflects the momentum conservation within ablation boundary layer. The density tends to decrease conversely when flow velocity increases, which also means only part of the ablation mass (mainly plasma) is discharged during the discharge process. Figure 6 also shows the density transience relations assumed by Mikellide model and Langmuir model, that is, a simple single-value correspondence n /n =.5. In the actual discharge process, the value is greater than the ratio (about.3) calculated by modified K-B model during actual discharge process; this would inevitably create inaccurate flow inlet boundary conditions, may causing a considerable deviation between magnetic fluid dynamics simulation and a) actual situation. B. Temporal and Spatial Distribution Characteristics of Plasma species Based on modified K-B model, discharge ionization characters of LES-6 PPT are figured out. Figure 7 shows Carbon element plasma number density (including C ions of monovalence to trivalence, i.e. C +, C + and C 3+ ) changes over time in discharge chamber. In Fig. 7, longitudinal coordinate represents discharge time; horizontal coordinate represents the axial distance of the discharge chamber (from the propellant ablation surface to the discharge chamber outlet). From Fig. 7, we learn that C + and C 3+ peak number density is, two orders of magnitude smaller than C + peak number density ( 3 ), indicating that C ions generated by LES-6 PPT ablation mainly exist in the form of monovalence. In the early discharge, the upstream region of the discharge chamber is ablated and ionized a lot of C + ions; and these C + ions accelerated in the downstream and further ionized into high-valence ones, especially during the time span from to.5 s, higher concentrations of C + and C 3+ ions can be observed; as the discharge half-cycle ended, discharge energy starts to recede, and the possibility of ionizing trivalent ions is reduced. At this time, C + ion will exist in the downstream channel. In other words, the presence time of C + ion in the downstream is slightly later than that of C 3+ ion; Again, this is similar to C + ion. With further reduction of the discharge energy, the density of C + ions dropped sharply, then C + is the primary ions distributed in the discharge chamber downstream and the exit plane. 7 b) c) Figure 7. Temporal and spatial variation of the Carbon ion (C +, C + and C 3+ ) number density during discharge

8 Figure 8. Temporal and spatial variation of the Carbon atom number density during discharge Figure 8 shows the time-varying contour profile of C atoms in the discharge chamber. It can be seen from the Fig.8 that, C atoms are most populated in the upstream region of the discharge chamber during early pulse discharge and less populated in the downstream region, which is consistent with the change trend of C ions. The biggest difference between C atoms and ions distribution occurs at the end of pulse discharge and after discharge (>3s). At this time, there is still a considerable portion of C atoms in discharge chamber due to PPT s innate late-time ablation effect. Figure 9 shows Fluorine element plasma number density (including F ions of monovalence to trivalence, i.e. F +, F + and F 3+ ) changes over time in discharge chamber. Similar to C ions similar, F ions mainly exist in the form of monovalence. However, the peak number density of F ions is smaller than that of C ions by an order of magnitude. That is to say, the plasma components generated during PPT discharge and ionization are mainly C +. Unlike C ions that are mainly in the upstream region of the discharge chamber, F ions are ionized in the downstream region during early pulse discharge, which further demonstrates the F element is less ionized than the C element. The main reason for this is that the excitation energy of the outer electron transitions in F atoms is relatively larger than that in C atoms, particularly reflected in high-valence ions. Similar to C ions, F ions of higher valence would be ionized earlier than those of lower valence in the downstream channel, especially during the time span from to.5s; a large number of F 3+ ions are produced and discharged from discharge chamber via electromagnetic acceleration. With the decrease of discharge energy, F + and F + ions would appear respectively in the downstream channel. Figure shows the time-varying contour profile of F atoms in the discharge chamber. Compare with Fig. 8, the peak density of the neutral F atom is higher than C atoms by an order of magnitude, which is mainly determined by the PTFE propellant formula C F 4. It can be seen from Fig. 9 that, at the beginning of the pulse discharge, F atoms concentrated in the upstream region and gradually decreased with the downstream of the discharge chamber, which is consistent with the change trend of C atoms. While in the mid-to-late pulse discharge, F atom concentration diffuses continuously from the propellant to acceleration channel. At this time, discharge energy diminishes. As a 8 a) b) c) Figure 9. Temporal and spatial variation of the Fluorine ion (F +, F + and F 3+ ) number density during discharge

9 result, corresponding components are less ionized. Likewise, because of PPT s innate late-time ablation effect, the neutral gas in discharge chamber is primarily composed of F atoms (with its density greater than that of C atoms) at the end of pulse discharge and after discharge (>3s). Table. Formation times of the various plasma species at the exit plane Figure. Temporal and spatial variation of the Fluorine atom number density during discharge Species Peak time, s Experiment Simulation C.5.9 C +..8 C C F.3.9 F+.8. F F x x 7 5 x x 5 Number density, /m C + C + C 3+ C Number density, /m 3 5 F + F + F 3+ F 5 Figure Time, s Temporal variation of the Carbon atom and Carbon ion number density at the exit plane Time, s Figure. Temporal variation of the Fluorine atom and Fluorine ion number density at the exit plane In order to compare with the experimental results, this paper describes the numerical solution of C and F atoms and ions density changes in the discharge chamber outlet, as shown in Fig. and Fig.. It can be seen from the figures, in the early pulse discharge phase (.3~.8s) divalent and trivalent C and F ions are produced during ablation and ionization; the more fully ionized components show shorter presence duration, which is consistent with the plume test law developed by Vondra et al 5. Further, Table compares the numerical solution and experimental values between C atoms and F atoms and their valence ion number density at peak moments. It can be seen from Table, the numerical results are basically accord with the experimental values. IV. Conclusion The formulation of boundary conditions at the wall-plasma interface is very important for the modeling of ablation PPT. Therefore, a modified K-B model is derived and presented to numerically study of the ablation and ionization phenomenon in PPT. Taking the thermally chemical reaction of the solid propellant into account, the model integrates the resulted ablation multi-components and their mass distribution characteristics on the ablation boundary layer and plasma layer, so as to provide more accurate boundary conditions for PPT ablation and flow coupling. 9

10 Results of wall-plasma interactions in LES-6 PPT show that the numerical results based on the ablation boundary layer parameters of the modified K-B model accord with PPT s actual work process. On the contrary, Mikellide model and Langmuir model only reflects a simple single-valued ratio relation, it is the exceptions when modified K-B model is used at a high ablation speed on the outer boundary (Mach number is /πγ or /γ ), which does not reflect the dynamic parameter changes of plasma flow inlet in PPT s actual work process. Furthermore, the temporal and spatial variations of the different plasma species in the discharge channel are numerically studied. LES-6 PPT plasma exists mainly in the form of monovalent ionization. The ionization regions of C and F elements region are respectively in the upstream and downstream discharge channel, and C elements are far more ionized than F elements. Besides, the presence time of C and F atoms and their ions of different valences at peak concentration basically correspond to plume test data, indicating that a large number of short-lived highly ionized divalent and trivalent C and F ions appear in the channel outlet during early pulse discharge, and the more fully ionized components show shorter presence duration. Acknowledgments This work was supported by China Postdoctoral Science Foundation (No. 5M5798). References Popov, G.A. and Antropov, N.N., Ablative PPT. New quality, new perspectives, Acta Astronautica, Vol. 59 No.-5, 6, pp Ozaki, J., Ikeda, T., Fujiwara, T., Nishizawa, M., Araki, S., Tahara, H., and Watanabe, Y., Development of Osaka Institute of Technology Nano-Satellite PROITERES with Electrothermal Pulsed Plasma Thrusters, 3nd International Electric Propulsion Conference, Paper No. IEPC--35, Wiesbaden, Germany,. 3 Naka, M., Hosotani, R., Tahara, H., and Watanabe, Y., Development of Electrothermal Pulsed Plasma Thruster System Flight-Model for the PROITERES Satellite, 3nd International Electric Propulsion Conference, Paper No. IEPC--34, Wiesbaden, Germany,. 4 Zhang, Z., and Tang, H. B., Investigations on the Flowing Pulsed Plasma of a J Pulsed Plasma Thruster, 33rd International Electric Propulsion Conference, Paper No. IEPC-3-47, Washington, D.C., USA, 3. 5 Burton, R. L., and Turchi, P. J., Pulsed Plasma Thruster, Journal of Propulsion and Power, Vol.4, No.5, 998, pp Hiroyuki K., Ryosuke N., Kimiya K., and Yoshihiro A., Plasma acceleration processes in an ablative pulsed plasma thruster, 43 rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Paper No.AIAA-7-56, Cincinnati, OH, USA, 7. 7 Mikellides P. G., Theoretical Modeling and Optimization of Ablation-fed Pulsed Plasma Thruster, Ph.D. Dissertation, Ohio State Univ., USA, Langmuir, I., The Evaporation, Condensation and Reflection of Molecules and the Mechanism of Adsorption, Physical Review, Vol.VIII, No., Keider, M., Boyd, I.D., and Beilis, I.I., Model of an Electrothermal Pulsed Plasma Thruster, IEEE Transactions on Plasma Science, Vol.8, No.,, pp Keidar M., Boyd I. D., Ionization and Ablation Phenomena in an Ablative Plasma Accelerator, Journal of Applied Physics, Vol.96, No., 4, pp Zaghloul M. R., On the Vaporization of PTFE and Heated Compound-Materials in Ablation-Controlled Arcs, Journal of Applied Physics, Vol.95, No.7, 4, pp Mitchner M., Charles H., and Kruger J., Partially ionized gases, John Wiley, Goodman, F.O., and Wachman, H.Y., Formula for Thermal Accommodation Coefficients, Journal of Chemical Physics, Vol.46, No.6, 967, pp Wentink, T., High Temperature Behavior of Teflon, AVCO-Everett Research Lab., Rept. AF 4 (647)-78, Everett, MA, July Thomassen K. I., Vondra R. J., Exhaust Velocity Studies of a Solid PTFE Pulsed Plasma Thruster, Journal of Spacecraft, Vol.9, No., 97, pp