NASA Technical Reports Server (NTRS) 20030005460: Thermophysics Characterization of Multiply Ionized Air Plasma Absorption of Laser Radiation

12 Pages·0.72 MB·English

by  NASA Technical Reports Server (NTRS)

IIIIIII IIII II
AIAA 2002-2203
Thermophysics Characterization of Multiply
Ionized Air Plasma Absorption of Laser
Radiation
Ten-See Wang
NASA Marshall Space Flight Center
Huntsville, AL
Robert Rhodes
The University of Tennessee Space Institute
Tullahoma, TN
33rd AIAA Plasmadynamics and Lasers
Conference
20-23 Mav 2002 / Maui, Hawaii
For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
1801 Alexander Bell Drive, Suite 500, Reston, VA 20191
AIAA 2002-2203
Thermophysics Characterization of Multiply Ionized Air Plasma Absorption of Laser Radiation
Ten-See Wang"
NASA Marshall Space Flight Center, Huntsville, AL 35812
and
Robert Rhodes*
The University of Tennessee Space Institute, TN 37388
G Gaunt factor
h Plank Constant
The impact of multiple ionization of air plasma on the I laser intensity
inverse Bremsstrahlung absorption of laser radiation is H molar enthalpy at temperature for standard state
investigated for air breathing laser propulsion. Thermo- Ho molar enthalpy at 0 K for standard state
chemical properties of multiply ionized air plasma me electron mass
species are computed for temperatures up to 200,000 deg n nth state of excitation energy
K, using hydrogenic approximation of the electronic n_,ni number density of electron and ions
partition function; And those for neutral air molecules are na,nm number density of atoms and molecules
also updated for temperatures up to 50,000 deg K, using Q partition function
available literature data. Three formulas for absorption p pressure
are calculated and a general formula is recommended for R universal gas constant
multiple ionization absorption calculation. The plasma S entropy at temperature for standard state
composition required for absorption calculation is sc Sackur-Tetrode constant
obtained by increasing the degree of ionization si optical path length of the ith ray
sequentially, up to quadruple ionization, with a series of T temperature
thermal equilibrium computations. The calculated Z ion charge
second ionization absorption coefficient agrees
reasonably well with that of available data. The Greek Symbols
importance of multiple ionization modeling is o_ fine structure constant
demonstrated with the finding that area under the K absorption coefficient
quadruple ionization curve of absorption is found to be _a_ Boltzmann's constant
twice that of single ionization. The effort of this work is E0 permittivity of free space
beneficial to the computational plasma aerodynamics h Plank constant / 2n
modeling of laser lightcraft performance. I.t real refractive index
CO angular frequency
Ne.m.enJ_t_
ao first Bohr radius
al - a7 coefficients for thermodynamic functions e electron
bh b2 thermodynamic function integration constants i ith state
c light velocity in vacuum
Cp molar heat capacity at constant pressure
e proton charge Kantrowitz kl first suggested a new possibility for
E ionization potential dramatic cost reductions in mass launching to Earth orbit
El lowering of the ionization potential
Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. No copyright isasserted in the United States under Title 17,
U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Government purposes.
All other rights are reserved by the copyright owner.
Staff, Applied Fluid Dynamics Analysis Group, Senior Member AIAA
' Senior Scientist, Member AIAA
1
American Institute of Aeronautics and Astronautics
AIAA 2002-2203
withaground-basheigdh-powelarseirnthe70's.Sincecapable of absorbing more laser radiation), and most
thena, propulsiosnystemsupportebdyalaser-sustainimepdortantly of all, the thrust of the lightcraft propelled by
plasmhaasbeenthesubjecotfmanyresearchPel'Csl.'el"v2 the shock wave. Figure 1 shows a snapshot of the
The main advantage gained by laser propulsion over computed (heavy gas) temperature contours and laser
chemical propulsion is the low-weight system obtained beam traces at an elapsed time of 18 las.wt It can be seen
from decoupling the energy source from the vehicle, and that the laser beam reflects specularly on the optical
high specific impulse resulting in low fuel consumption. surface and focuses onto a focal "point" on the shroud
In addition, the flame temperature of a combustion where the breakdown of air starts. The temperature
process is limited, whereas the propellant temperature contours in Fig. 1also describes the growth of the plasma
reachable during laser propulsion can be several order- front. The "protrusion" of the plasma front indicates that
of-magnitude higher. the plasma front (and the shock wave) is propagating up
Several air-breathing laser propulsion concepts have the beam - a result of successive heating and ionizing of
been demonstrated in the past few years. For example, the medium (air) such that the medium becomes capable
recent publications show that a spin stabilized Myrabo of absorbing more laser energy and propagates further.
lightcraft reached 71 m in record height during vertical Figure 1 is an indication of the potential ability of the
free flights outdoors, Mt while a different parabolic flyer computational plasma aerodynamics in describing the
(design) was propelled from the ground of the laboratory optical breakdown phenomenon associated with laser
to its 8 m high ceiling. B2High energy CO2 lasers were propulsion. It also indicates the importance of a realistic
used in both tests. absorption model since the propulsion physics start with
Researches using computational plasma aerodynamics the absorption of laser energy. It goes without saying the
have also been making progress in the field of laser accuracy of the absorption model affects that of the
propulsion. For example, Molvik et al.M2considered the computed performance.
interaction between a continuous laser beam and a Other than the constant absorption coefficient used by
flowing hydrogen gas using a structured-grid formulation Molvik et al.,M2all the variable absorption formulas used
and constant absorptivity. Jeng and Keefer JI did similar by the afore-mentioned modeling efforts Jl" c|, Wl are of
analysis with an expression for the absorption coefficient the single ionization category. While applying single
at CO2 laser wavelength of 10.6 Ixm considering both ionization formula to a hydrogen plasma J1is reasonable,
electron-ion and electron-neutral inverse Bremsstrahlung. there is room for improvement when it is applied to
Conrad, et al.ct modeled a continuous optical discharge nitrogen and air plasmas, ci"wl since the atomic numbers
stabilized by nitrogen gas flows in weakly focused laser of nitrogen and oxygen atoms are eight and nine,
beam, using a absorption coefficient formula at 10.6 ktrn respectively. Given that the single ionization formula
ignoring second ionization of atoms, c_ Recently, Wang was formulated by Raizer and Tybulewicz al in the 70's,
et al. performed transient performance calculations wl on while a simplified procedure for calculating an averaged
a Myrabo lightcraft (energized by a pulsed laser beam) degree of multiple ionization was reported by Zel'dovich
using an unstructured-grid formulation and the same and Raizer zl in the 60's, and the same single ionization
single ionization absorption formula used by Conrad et formula was still used in the 90's, cl led the author to
al.cl speculate that the difficulty resides in the scarcity of
In a computational plasma aerodynamics study, using reliable high temperature thermodynamic properties for
the modeling of a Myrabo lightcraft as an example, the the multiply ionized air atoms. To understand the impact
focusing of the laser radiation is solved first, followed by of multiply ionized atoms on the absorption of laser
computing the initial air breakdown and the creation of radiation, reliable high temperature thermodynamic
seed free electrons. When enough seed electrons are properties for the multiply ionized air atoms have to be
produced, they absorb more photons and resulting in developed, and that is the motivation of this study.
more air breakdown and producing more free electrons.
An avalanche of free electrons soon follows and a strong Thermo_nhysic_ Characterization of Multinly
shock wave is generated. These are all solved with Ionized air nla_ma
transport equations of continuity, energy, momentum,
and species continuity, along with physical models such Thermo-Chemical gy_em
as finite-rate chemistry, high temperature In Ref. Wl, the initial free electrons for plasma
thermodynamics, beam attenuation through absorption, ignition and the subsequent avalanche of free electrons
beam refraction, and non-equilibrium radiation. The necessary for the optical breakdown were generated
computational model then computes the subsequent through the non-equilibrium, finite-rate air breakdown
traveling of the shock wave through air, the heating and chemistry sub-model, where Park's multitemperature air
ionizing of which (such that the air plasma becomes chemistry mechanism v3 was used. This mechanism
2
American Institute of Aeronautics and Astronautics
AIAA 2002-2203
composes of the dissociation, NO exchange, associative is chosen to be the energy of formation of the element
ionization, charge exchange, electron impact ionization, from its reference state as defined in Gordon and
and radiative recombination reactions. The eleven air McBride. Gz The result of the computation is a table of
plasma species used in this mechanism defines the thermodynamic properties for different atoms and
thermo-chemical system for single ionization multiply ionized ions as a function of temperature and
environment: Nz, 02, NO, NO +,N, N+, O, O+, N2+, 02 + pressures. Pressure is calculated from the ideal gas
and e'. N2, 02, and NO are neutral molecules; N and O equation of state plus the Coulomb pressure correction.
are neutral atoms; while NO+,N+,O+,N2+,02+are single
ions. In order to consider multiply ionized air plasma Thermodynamic Function C_eneration
atoms, up to quadruple ionization, six additional ions The next step is to construct the three thermodynamic
N+2,0 +2,N+3,0+3,N_, and 0 +4must be added and their functions of heat capacity, enthaipy and entropy as
thermodynamic properties must be characterized. functions of temperature in a form compatible to most
computational plasma aerodynamics codes. The standard
Hydro_enic Approximation of the Partitinn Fnnction form of Gordon and McBride _2is used:
The high temperature thermodynamic properties of the
si.x...additional tons N+2,O+2,N+3,O+3,N_, and O+4can be
C__p=.palT- 2+ a2T_ l +a3 +a4T +a5T2 + a6T3 + a7T4
expressed in terms of partition functions, following those T
formulated for monatomic gases. G2 For example, T2 T3
RHT =_alT- 2+ a2T-I lnT +a3 +a4T + a5--_- +a6--_-
Cp _T2 d 2In___.+_._2QTQd(lnQ) + 5 r4+ h
+_T Y
R dT 2 dT 2
S T-2 _-1 T2 T3
_- =-alT- a2- +a31nT+a4T+a5T+a6 T
H - H o=Td(lnO_)__._:.__5
+-- T4
RT dT 2
+_T+_
S = Td(lnQ) + lnQ + 31nM + 51nT + sc These coefficients are obtained through a least-square
R dT 2 2
curve-fit procedure for each temperature interval.
Following Gordon and McBride _2, three temperature
In this study, the partition functions of the multiply intervals are used in this study. Unlike Gordon and
ionized atoms are characterized with the method of McBride C2, the three temperature intervals are made
hydrogenic approximation, zt'J2 That is, the multiply different for different species in order to achieve best fit
ionized atoms are treated as hydrogen-like atoms, of the generated thermodynamic properties, since the
represented by a system consisting of a positive nucleus heat capacities of the multiply ionized atoms peak at
with a charge Z and a single electron. The transformed vastly different temperatures. To construct the enthalpy
electronic partition takes the expression curve, the heat of formation of multiply ionized ions at
reference state needs to be estimated. This is
accomplished by writing an ionization reaction, e.g., for
N+:
N_._N+ +e -
where the summation is truncated when [El(1 - l/nZ)] is
greater than [El - ZEd. The lowering of the ionization
The heat of reaction of this ionization reaction is the
potential is proportional to the square root of the sum of
ionization potential. The heat of formation of N+ takes
the electron density plus the ion densities times their
the form
charge squared divided by temperature. For consistency
purpose, the high temperature thermodynamic properties
of N, N+, O, O+are also characterized as the hydrogen- Hf ,N+ =H f, N + E- Hf, e-
like atoms.
The computational procedure is set up such that the For validation purpose, the calculated heat of
internal energy and density are used as input. The formations for singly ionized N+and O+are comparable
internal energy of a given species is a function of the to those published in Gurvich et al.o3 In addition, the
temperature, partition function, energy of ionization, and calculated entropy of formations using hydrogenic
reference point energy. This reference is arbitrary, but it
3
American Institute of Aeronautics and Astronautics
AIAA 2002-2203
approximatioofnthepartitionfunctiofnorN,O,N÷and curves can be extrapolated to much higher temperatures,
O÷are also comparable to those published in Gurvich, et say, 500,000 deg K. It is a moot point though since these
al. as well. species do not survive beyond 20,000 deg K.
Figure 2 shows the computed heat capacities and curve
fits for N, N+,N+z,N+3,and Na, while Fig. 3shows those l_aser Ah_orntian
for O, O+, 0.2, 0.3, and O_. The peak heat capacity In computational plasma aerodynamics modeling w_ of
increases with temperature as the number of electrons the laser lightcraft flowfield where geometric optics is
stripped increases. The sensible heat capacities of the used to simulate the local intensity of the laser beam, the
multiply ionized air plasma species cover a temperature laser beam can be split into a number of individual rays.
range from 10,000 deg K to approximately 200,000 deg. In the presence of absorption, the local intensity of each
K. The seven coefficients polynomials fit the computed ray follows the Beer's law:
heat capacities reasonably well.
The thermodynamic functions of the rest of the air d/i
- KIi
plasma species (N2, O2, NO, NO*, N2,+O2+and e-) can be dsi
found from Gordon and McBride °4 where the calculated
data from Gurvich et al.C3were curve-fitted. However,
Through inverse Bremsstrahlung absorption, or free-
the applicable temperature range for these species were
free absorption, the rays are attenuated by free-electrons
only calculated up to 20,000 deg K, as shown in Fig's 4-
in its path. The three types of inverse Bremsstrahlung
6. This temperature range appears to be too low, in light
absorption, depending upon what kind of particle the
of the computed heavy gas and electron temperatures can
electron is near when a photon is absorbed, are electron-
go as high as 500,000 deg K during optical breakdown of
1on, electron-atom, and electron molecular absorptions.
air inside the focused region of a laser lightcraft, wt In
According to Raizer and Tybulewicz, Rl the long-
addition, heat capacity data of many species do not level
wavelength infrared radiation of a CO2 laser at 10.6 ktm
off to a value at higher temperatures, indicating possible
is absorbed mainly by free electrons when it collide with
overprediction of the heat capacity when extrapolated
ions. Hughes m gives a theoretical derivation of the
beyond 20,000 deg K. Nevertheless, there is no problem
electron-ion inverse Bremsstrahlung absorption
with electron since its heat capacity is a constant at any
coefficient for radiation at frequency to:
temperature. For species NO+, N2÷, and O2+, the low
applicable temperature range does not present a problem
either, since only trace amount of these species are neniZ2e6 g[1-exp(-htO/KBT)]f me /1/2
produced at conditions of interest. For molecular species Kco -- IZ6E3CN_O3m2 _ 6IgK B-"""_)
N2, 02, and NO, Balakrishnan reported correlations for
specific heats up to 50,000 deg K.Bz However, the
formulas used by Balakrishnan were criticized as The advantage of Hughes' formula is its flexibility.
That is, itcan be used for radiation in any wavelength. In
inadequate." Jaffe's calculated heat capacities for N2, 02,
and NO were based on summations over all vibration- contrast, started with a different formulation from that of
Hughes, corrected for stimulated emission in the single
rotation energy levels for all known bound electronic
ionization range, assumed hto&aT << 1, omitted the
states, and a scheme for the partitioning of the internal
factor affecting only the photoionization, substituted hto
energy into vibrational, rotational and electronic
contributions was presented which consistently accounts for CO2 laser wavelength, a formula of electron-ion
for the nonseparable nature of the various energy modes. inverse Bremsstrahlung absorption coefficient is
expressed by Raizer and Tybulewicz: RI
Jaffe's work appears creditable and is used in this study.
Figures 4-6 show the heat capacities from all three
sources for N2, O2, and NO, respectively. It can be seen
that the heat capacities of Jaffe agree with those of 10.4pc 2g
Gordon and McBride reasonably well, while the heat _cth - (T/104) 7/2
capacities of Balakrishnan agree with those of the other
two sources only at lower temperatures. The heat
where
capacities of Jaffe are chosen for curve fitting for species
N2 and Oz. For species NO, Gordon and McBride's data , ]
were used for curve fitting up to 20,000 deg K, then
Jaffe's heat capacities were fitted for the higher
temperatures. Note that all three curves approach their
asymptote values near 50,000 deg K, meaning these Note the above absorption coefficient formula does not
4
American Institute of Aeronautics and Astronautics
AIAA 2002-2203
taketheseconidonizatio(norhigheri)ntoaccounAt.lso,
electronpressuries usedin lieuof electronnumberwhere D is a complicated power series represented as a
density.Bothformuladsescribeadboveconsideornlyfunction of h0_/_T and was given in a Appendix of
theelectron-ioinnversBeremsstrahluanbgsorptionO.nMertogul. M3For a CO2 laser wavelength of 10.6 grn, this
theotherhand,MertogMul3computetdheabsorption
expression of electron-molecule inverse Bremsstrahlung
coefficientusing all three types of inverseabsorption coefficient is only valid for temperatures less
BremsstrahluTnhge.formulausedforthecalculatioonf than 4321.5 deg K. In addition, Mertogul's formula was
electron-ioninverse Bremsstrahlungabsorption
derived for hydrogen plasma, a deviation from our
coefficienistthatgivenbyStallcospl:
interest in air breathing laser propulsion. Nevertheless,
Mertogul's formula is included in this study to compare
the relative importance of these three types of inverse
=n n.( 256Y_]"2- 2_(--_--E/3(---E--e]
Bremsstrahlung absorption.
!¢°J <'t 3 X3J VthcoJt_,r )
lll_ill;_i and l)i._l_ii_._hin
Thermodynamic functions generated in this study for
multiply ionized ions, atoms, and molecules are used as
data base for a series of constant pressure (1 atmosphere)
in which the flee-flee Gaunt factor was curve fitted form
and temperature thermal equilibrium computations, in
reported data of Karzas and Latter at wavelength of 10.6 order to obtain the necessary compositions of electron,
Ixm and T < 10,000 deg K: ions, atoms and molecules for laser absorption coefficient
calculations. In the temperatures of interest, equilibrium
g = 1.07 + 6.9643x10-5T - 2.6786x10-9T 2 state is probably a reasonable assumption. Minimization
of free energy of a thermo-chemical system, similar to that
described in Gordon and McBride, TM is used as the
and for T > I0,000 deg K:
algorithm for achieving the equilibrium state and is not
repeated in here. Figure 7 shows the air plasma species
g = 1.50 + 1.0xl0-ST
compositions considering single ionization only. As
temperature increases, the molecules disappear quickly and
The expression used for the electron-atom inverse atoms emerge. And then atoms disappear, while electron
Bremsstrahlung absorption coefficient in the infrared and ions (N+ and O+) rise, eventually, the species
limit is that given by Stallcop: s2 concentrations of electron and ions level off at about
32,000 deg K. The final electron mole fraction of 0.5 is
the result of single ionization. Note that the
K'(o concentrations of NO +, N2+, and 02+ are indeed
=nenaKBZ_.15xlO-29I-_l 2
negligible.
exp(-4.862kT(1 - 0.2096k T + 0.017kT2- 0.00968kT 3) Figure 8 shows the comparison of calculated
absorption coefficients of air for CO2 laser radiation
kT
using the information from Fig. 7. Also plotted in Fig. 8
are points read off from Fig. 6.18 of Raizer and
and
Tybulewicz gl while allowing for double ionization. At
low temperatures, the calculated absorption coefficients are
extremely low and rise sharply with increasing temperate
around 8000 deg K. The rise then slows down and the
absorption passes through a maximum. The calculated
absorption drops monotonically from the maximum as the
The expression used for the electron-molecule inverse
system completes the single ionization, eventually nearing
Bremsstrahlung absorption coefficient is that given by
zero absorption around 80,000 deg K.
Caledonia et al.c2from the work of Dalgarno and Lane: m
It can be seen that the curves using Raizer and
Tybulewicz formula and that of Hughes are reasonably
close, although the peak value of Hughes is higher. The
D
g_o = nenm (4.51xl O-44) peak value of Mertogul is the lowest among the three.
This is not surprising since Mertogul's formula was
meant for hydrogen plasma. Of interest is at lower
temperatures where the electron-atom, and electron-
5
American Institute of Aeronautics and Astronautics
AIAA 2002-2203
molecular inverse Bremsstrahlung absorptions should exceeding 50,000 deg K, those for triple ionization are
show some contribution, but none was observed, N.3 and O*3for temperatures exceeding around 95,000
indicating the free-free inverse Bremsstrahlung deg K, and those for quadruple ionization are N+4and
absorption is indeed the main absorption process among 0+4 for temperatures exceeding I00,000 deg K. The
the three as described by Raizer and Tybulewicz. peaks of those multiply ionized species concentration
On the other hand, the curve of Hughes Formula decrease as the degree of ionization increases. Most
agrees better with data points from Fig. 6.18 of Raizer importantly, the mole fractions of the free electron
and Tybulewicz than that calculated using Raizer and increase from 0.5 for single ionization, to 0.67, 0.75, and
Tybulewicz formula, until the second ionization takes 0.8 for double, triple, and quadruple ionizations,
place. This is somewhat perplexing and it is speculated respectively.
that difference in generating the electron pressures may Figure 12 shows the comparison of electron number
have been the problem. Raizer and Tybulewicz did not densities for double, triple, and quadruple ionizations. A
elaborate how the electron pressure was obtained, nor did second peak of the electron number density occurs at
they explain how the second ionization portion was around 30,000 deg K, due to the double ionization. Triple
arrived and only the single ionization formula was given. ionization increases the overall electron number density
Nevertheless, the mathematical reason for the monotonic from approximately 40,000 degree up. Quadruple
decrease of the calculated absorption coefficient after the ionization increases the electron number density from
passing of the maximum can be seen clearly from Fig. 7 around 65,000 degree up, but the amount of increase
that electron partial pressure is a constant as temperature becomes less as the degree of ionization increases. That
exceeds 30,000 deg K, that the Gaunt factor is essentially indicates for computational purpose, quadruple ionization
a constant since it ranges from 2.3 to 3.2 in the is probably enough.
temperature range of interest, and that the denominator of Figure 13 shows the comparison of calculated
Raizer and Tybulewicz formula eventually grows as absorption coefficient curves for double, triple, and
temperature increases. The downward trend of all three quadruple ionizations. A second maximum in the
curves after their peaks confirms the single ionization absorption coefficient at temperatures near 30,000 deg K
system does not produce a second rise in absorption occurs due to double ionization. As the system completes
coefficient. the second ionization, the absorption again passes a
Although only reported to 27,000 deg K,Rt the maximum, although it is much less obvious as the last
importance of second ionization is evident from Fig. 8 in peak, and so on. The earlier part of the second ionization
which the single ionization formulas under-predict the curve agrees well with the available points from Raizer
absorption coefficient at high temperatures where double and Tybulewicz. Note that the area under the quadruple
ionization occurs. This has strong implications for laser ionization curve is about twice that of the single
lightcraft performance computations using computational ionization. In summary, under a single ionization
plasma aerodynamics. The implication of double system, the absorption of photons drops sharply beyond
ionization also implies the potential importance of triple 25,000 deg K and appears to cease absorbing energy at
ionization ..... etc. That raises an issue of rising 80,000 deg K. When allowing for quadruple ionization,
computational cost if too high a degree of ionization is the absorption not only passes through multiple
considered however, for the computational cost is maximums, but also continues to absorb energy beyond
proportional to the square of the number of species 100,000 deg K.
considered.
Based on the result in Fig. 8, the general Hughes 12.nneht_inn._
formula is used to investigate the effect of multiple A thermophysics characterization of inverse
ionization, in conjunction with the Gaunt factor given by Bremsstrahlung absorption of laser radiation is performed.
Raizer and Tybulewicz. This is accomplished by Thermo-chemical properties of multiple ionized air plasma
performing a series of equilibrium computations using species are generated using hydrogenic approximation of
the characterized thermodynamic properties for multiply the electronic partition function and those for neutral air
.l.o..mzed air ionsN +2,O +2,N +3,O +3,N-+4, and O- +4. The molecules are also generated using updated literature data.
plasma composition required for absorption calculation is Three formulas for absorption are calculated and ageneral
obtained by increasing the degree of ionization formula is recommended for multiple ionization absorption
sequentially, up to quadruple ionization. calculation. A series of thermal equilibrium computations
Figures 9-11 show the equilibrium air plasma species are performed to show the effect of multiple ionization on
compositions for double, triple, and quadruple the free electron concentration and on the inverse
ionizations, respectively. As expected, the surviving ions Bremsstrahlung absorption coefficient. The calculated
for double ionization are N+2 and 0÷2for temperatures second ionization absorption coefficient agrees
6
American Institute of Aeronautics and Astronautics
AIAA 2002-2203
reasonabwlyellwithavailabledataof literature.In 8-11, Reno, NV, 2001.
additioni,t is foundthattheareaunderthequadruplaet Raizer, Y.P., and Tybulewicz, A., "Laser-Induced
ionizatiocnurveofabsorptioinsabouttwicethatoftheDischarge Phenomena", Studies in Soviet Science, Edited
singleionizationT.heresulotfthisstudycanbeappliedby Vlases, G.C., and Pietrzyk, Z.A., Consultants Bureau,
tothecomputationpalalsmaaerodynammicsodelinogf New York, 1977.
laseprropulsiopnhysics. zl Zel'dovich, Y.B., and Raizer, Y.P., "Physics of Shock
Waves and High Temperature Hydrodynamic
Phenomena", Vol. 1, Edited by Hayes, W.D., and
The leadauthorwishesto thankJohnColeof
Probstein, R.F., Academic Press, New York and London,
RevolutionaPryropulsioRnesearcfohrsupportintghis 1966.
study.HealsowishetsothankDrs.Yen-SeCnhenande3 Park, C., "Review of Chemical-Kinetic Problems of
JiwenLiu for discussionosn the laserabsorptioFnuture NASA Missions, I: Earth Entries," Journal of
coefficients.
Thermophysics and Heat Transfer, Vol. 7, No. 3, 1993,
gl_. 385-398.
References Gordon, S., and McBride, B.J., ''Thermodynamic Data
kl Kantrowitz, A., "Propulsion to Orbit by Ground-Based to 20,000 K for Monatomic Gases," NASA TP 1999-
Lasers," Astronautics and Aeronautics, Vol. 10, No. 5, 208523, Glen Research Center, Cleveland, Ohio, June
May 1972, pp. 74-76. 1999.
Pt Pirri, A.N., Monsler, M.J., and Nebolsine, P.E., n Richter, J., "Radiation of Hot Gases," Plasma
"Propulsion by Absorption of Laser Radiation," AIAA Diagnostics, edited by Lochte-Holtgreven, W., John
Journal, Vol. 12, No. 9, 1974, pp. 1254-1261. Wiley & Sons, New York, 1968, pp. 1-32.
GI Glumb, R.J., and Krier, H., "Concepts and Status of c3 Gurvich, L.V., Veyts, I.V., and Alcock, C.B.,
Laser-Supported Rocket Propulsion," Journal of "Thermodynamic Properties of Individual Substances,"
Spacecraft and Rockets, Vol. 21, No. 1,1984, pp. 70-79. Fourth Edition, Part Two, Hemisphere Publishing Co.,
B_ Brandstein, A., and Levy, Y., "Laser Propulsion New York, 1989.
System for Space Vehicles," Journal of Propulsion and c4 Gordon, S., and McBride, B.J., "Computer Program
Power, Vol. 14, No. 2, 1998, pp. 261-269. for Calculation of Complex Chemical Equilibrium
Phipps, C.R., Reilly, J.P., and Campbell, J.W., Compositions and Applications," NASA RP 1311, Lewis
"Optimum Parameters for Laser Launching Objects into Research Center, Cleveland, OH, 1996.
Low Earth Orbit," Laser and Particle Beams, Vol. 18, B2Balakrishnan, A., "Correlations for Specific Heats of
2000, pp. 661-695. Air Species to 50,000 K," AIAA Paper 86-1277, June
MtMyrabo, L.N., "World Record Flights of Beam_riding 1986.
Rocket Lightcraft: Demonstration of "Disruptive" J3Jaffe, Richard, '`The Calculation of High-Temperature
Propulsion Technology," AIAA Paper 2001-3798, July, Equilibrium and Nonequilibrium Specific Heat Data for
2001. N2, O2, and NO," AIAA Paper 87-1633, June 1987.
B2 Bohn, W.L., "Laser Lightcraft Performance," High m Hughes, T.P., "Plasma and Laser Light", John Wiley
Power Laser Ablation H, Proceedings of SPIE, Vol. and Sons, New York, 1975.
3885, 2000, pp. 48-53. M3 Mertogul, A.E., "Modeling and Experimental
ra2Molvik, G.A., Choi, D., and Merkle, C.L., "A Two- Measurements of Laser Sustained Hydrogen Plasmas,"
Dimensional Analysis of Laser Heat Addition in a Ph.D. Thesis, University of Illinois at Urbana-
Constant Absorptivity Gas," AIAA Journal, Vol. 23, No. Champaign, 1993
7, 1985, pp. 1053-1060. st Stallcop, J.R., "Absorption of Laser Radiation in a H-
Jt Jeng, San-Mou, and Keefer, Dennis, "Theoretical He Plasma. I. Theoretical Calculation of the Absorption
Evaluation of Laser-Sustained Plasma Thruster Coefficient," Physics of Fluids, Vol. 17, No. 4, pp. 751-
Performance," Journal of Propulsion, Vol. 5, No. 5, 758, April 1974.
Sept-Oct., 1989, pp. 577-581. k2 Karzas, W.J., and Latter, R., "Electron Radiative
ct Conrad, R., Raizer, Y.P., and Surzhikov, S.T., Transitions in a Coulomb Field," Astrophysical Journal,
"Continuous Optical Discharges Stabilized by Gas Flow Supplement Series, Supplement number 55, Vol. VI, pp.
in Weakly Focused Laser Beam," AIAA Journal, Vol. 34, 167-211, 1961.
No. 8, 1996, pp. 1584-1588. s2 Stallcop, J.R., "Absorption of Infrared Radiation by
wt Wang, T.-S., Chen, Y.-S., Liu, J., Myrabo, L.N., and Electrons in the Field of a Neutral Hydrogen Atom,'"
Mead, F.B. Jr., "Advanced Performance Modeling of Astrophysical Journal, Vol. 187, No. 1, pp. 178-183,
Jan. 1974.
Experimental Laser Lightcraft," AIAA Paper 2001-0648,
39 AIAA Aerospace Sciences Meeting & Exhibit, Jan. cz Caledonia, G.E., Wu. P.K.S., and Pirri, A.N.,
7
American Institute of Aeronautics and Astronautics
AIAA 2002-2203
90
"Radiation Energy Absorption Studies for Laser
Propulsion," NASA CR-134809, March 1975. 8O oN+
D_Dalgarno, A., and Lane, N.F., "Free-Free Transitions - oN+:'
70 ab/.3
of Electrons in Gases," Astrophysical Journal, Vol. 145,
-- _ ovNN+4 i
No. 2, pp. 623-633, July 1966. 6O -- curve fit
5O
o*
4O
3O
2O
I0
50000 100000 !50000 200000
T,deg K
Fig. 2 Computed heat capacities and curve fits for
multiply ionized nitrogen atoms N, N+, N+z, N+3,and N_.
90
_0
. f I :o:: I
7O
50
, -- curve fit I
50
4O
30
20
lO
o
Fig. 1 Computational plasma aerodynamics computed 50000 100000 150000 200000
temperature contours and laser ray traces for a Myrabo T,degK
lightcraft at 18 its. Contours scale: 0- 24180.
Fig. 3 Computed heat capacities and curve fits for
multiply ionized oxygen atoms O, O+,0 +2,0 ÷3,and O+4.
8
American Institute of Aeronautics and Astronautics
AIAA 2002-2203
18
.... Gordon & McBride .... Gordon & McBride |1:
.... Balakrishnan 16 --- - BelQkrishnon
0 Jaffe I 1J3affe
/"--_ [- curve fit
14
18 / _._-- :
20 I /A ,,,_ -- curve fit
16 ' '" ",\ . 12 /: ",,
o14 J
|2 10
I0 -\,. -
8
8
6
\, -
4 ":
2 iLl,l,,,,I J,_, I k,, t I I, ,, I,, * ,,, 4 ,,, ,I,,,, I , , , ,I, ,, , I .... t ....
0 10000 20000 30000 40000 50000 60000 0 10000 20000 30000 40000 50000 60000
T, deg K T.degK
Fig. 4 A comparison of the heat capacities and curve fitfor Fig. 6 A comparison of the heat capacities and curve fit for
neutral N2. neutral molecule NO.
18 ,,,,i,,,,i,,,, II
.... Gordon & McBride II""''"l'""'"'l"''''"'l"''""'l"'"''"l''"'''"l''"'"'q"'_
---- Bolakrishnon o.8 12 -- N. I
16 --IJ. I
0 Joffe
0.7 I_ ....... NO I
-- curve fit --- NO'I
14 --- N I
t "_. 0.6 I_ I N. I
/ -- [) I
e-
12 ....... f)" I
/ 0,5 ---- N-" I
u-0.4 IE ...... LL" I
10
o
_03
8
0.2 _
o
0÷
6 0.1 _
oo l_h.r.._,,, i......... i......... i...... ,..I ......... i......... h,,
o 20000 40000 60000 80000 tOOOOOt20000140000
4 , ,* Jl_t till, ,, I,, ,,I, , , , I , _,,,!
0 10000 20000 30000 40000 50000 60000 T.deg K
T, deg K
Fig. 7 A comparison of the equilibrium air plasma species
Fig. 5 A comparison of the heat capacities and curve fitfor compositions for single ionization.
neutral molecule Oz.
9
American Institute of Aeronautics and Astronautics