Spectroscopy of H2 - + N2-Mixture in Rarefied Flows
Hideo Mori∗ and Carl Dankert†
∗
Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
DLR Göttingen, Bunsenstraße 10, D-37073 Göttingen, Germany
†
Abstract. Spectroscopy methods for measurement of thermodynamic variables in gas flows have been applied to analyze
rotational and vibrational nonequilibrium in rarefied flows. Using the REMPI (Resonantly Enhanced Multiphoton Ionization)
method, molecules are ionized via a resonant state, leading to very high ionization probability and thus to very high detection
sensitivity, which is important for experimental studies in rarefied flows. The STG high vacuum facility, located at the DLR
Research Center in Göttingen, is routinely used to examine exhaust gas plumes from small chemical thrusters. Usually
hydrazine is the propellant for real thrusters, and in the supersonic gas plume H2 , N2 , and NH3 are the species resulting
from catalytic decomposition. Typical orders of number density are 1014 cm−3 in the jet core and 1011 cm−3 in the backflow
region. To detect the N2 and H2 molecules at these low densities, the REMPI method was selected. The theory of H2 - and
N2 -REMPI spectra was studied, and synthetic spectra of 2R+1 H2 - and N2 -REMPI are simulated to evaluate the possible use
of the Boltzmann plot for determining rotational temperature in a gas mixture of H2 and N2 .
INTRODUCTION
In space engineering, impingement of exhaust gas jets from satellite thrusters on the solar generator panels or antennas
is a serious problem including interaction of the gas molecules with these surfaces and contamination by the exhaust
gas molecules. Typical orders of number density of thruster jets are 10 14 cm−3 in the jet core and 10 11 cm−3 in
the backflow region. For measurement of backflow regions of thruster jets, a measurement technique with a high
sensitivity is needed. So far, mass spectrometers and Patterson probes have been used to measure the number density
of rarefied gas flows, but these methods cannot measure nonequilibrium among the internal (vibrational and rotational)
energy. This means that the molecular energy transport processes between gas molecules and solid surfaces cannot
be examined precisely. On the other hand, spectroscopic methods such as Laser Induced Fluorescence (LIF)[1] and
Coherent Anti-Stokes Raman Scattering (CARS)[2] have enabled to detect the nonequilibrium in rarefied gas flows,
because they are based on internal energy distributions of gas molecules. However, even LIF, which is the most
sensitive method among them, can hardly be applied to the rarefied gas flow below 10 12 molecules/cm3[3], because of
the sensitivity problem.
Resonantly Enhanced Multiphoton Ionization (REMPI) has very high sensitivity, and this method can be applied
to the measurement of highly rarefied gas flows below the number density of 10 12 molecules/cm3, which is too low to
detect by conventional methods such as LIF. Until now, several measurements of rotational temperature and number
density of highly rarefied flows by N 2 -REMPI method have been reported [4, 5, 6].
The actual exhaust gases of monopropellant satellite thrusters are mixtures of nitrogen, hydrogen, ammonia.
Hydrogen is a diatomic molecule that shows stronger nonequilibrium of temperature than any other diatomic molecules
such as nitrogen, because of its large rotational collision number and selection rule for transitions between symmetric
and antisymmetric states. For precise diagnoses of such gas mixtures, therefore, simultaneous measurements of
hydrogen and nitrogen in a gas mixture are demanded. The 2R+1 REMPI method will be applied to the measurement.
1 +
In this scheme, hydrogen molecules in the ground state (X 1 Σ+
g ) are excited to the resonance state of E, F Σg by two
1
+
photons around 200nm, and then ionized by one photon[7]. However, the a Σg state of a nitrogen molecule lies about
12eV above the ground state of X 1 Σ+
g , and nitrogen molecules are also excited and ionized by 202-203nm photons[8].
Therefore, the REMPI spectra of hydrogen and nitrogen REMPI may be overlapped, and it may cause problems for
the measurement of a mixture of hydrogen and nitrogen. However, if these spectra are separated from each other and
well resolved, the simultaneous measurement of hydrogen and nitrogen may be possible.
In this study, 2R+1 H 2 -REMPI and 2R+1 N 2 -REMPI spectra are simulated, and problems of applying the method
CP663, Rarefied Gas Dynamics: 23rd International Symposium, edited by A. D. Ketsdever and E. P. Muntz
© 2003 American Institute of Physics 0-7354-0124-1/03/$20.00
170
to measurement of a gas mixture of hydrogen and nitrogen are discussed based on the synthetic spectra of 2R+1 H 2 and N2 -REMPI. The plan of an experimental apparatus for simultaneous measurement of hydrogen and nitrogen in a
gas mixture is also sketched briefly.
THEORY OF REMPI SPECTRA
The theory of 2R+1 H 2 - and N2 -REMPI spectra is used to analyze the possibility of rotational temperature measurement of hydrogen. The possibility of measurement for mixtures of hydrogen and nitrogen gas is also examined. Theory
and analyses of 2R+2 N 2 -REMPI have already been described in other papers[4, 5, 6] and its theory is mentioned here
briefly.
If the rotational energy distribution follows the Maxwell-Boltzmann distribution, the rotational line intensity in
2R+1 H2 - and N2 -REMPI spectra is given by[9]
IJ ,J = Ag(J )S(J , J ) exp(−Erot /kTrot ),
(1)
where A is the constant independent of the rotational quantum number J of the ground state and J of the resonance
state, but including laser flux, number density, vibrational transition strength (Franck-Condon factor). g(J ) is the
nuclear spin degeneracy depending on the parity of J and the spin Is of the nuclei[10]. For N 2 (Is = 1), g(J ) takes 3
and 6 for odd and even J , respectively. For H 2 (Is = 1/2), it takes 3 and 1 for odd and even J .
S(J , J ) is the rotational transition strength (two-photon Hönl-London factor). The two-photon Hönl-London
1 +
factors for the 1 Σ+
g ← Σg transition[11] are shown in Table 1, assuming the ratio of the transition dipole factors
(µs /µI ) 1[9]. The transition probability via the P or R branch is zero, because the transition of J − J = ±1 is
1 +
forbidden for the 1 Σ+
g ← Σg transition by two-photon absorption.
The term exp(−E rot /kTrot ) indicates the Maxwell-Boltzmann distribution at the rotational temperature of T rot . k is
Boltzmann’s constant and E rot the rotational energy of the ground state. E rot is a function of J and is given by[10]
Erot = hcFv (J ),
Fv (J) = Bv J(J + 1) − DvJ 2 (J + 1)2 + · · · ,
(2)
(3)
where h is Planck’s constant and c is the speed of light. Fv (J ) is the rotational term of the ground state at the rotational
level J . Bv and Dv are the rotational constants in the vibrational level v. The values of B 0 (Bv at v = 0) and D0 of
hydrogen[12] are listed in Table 2, and those of nitrogen[8] are listed in Table 3, along with the electronic term T e and
vibrational term G(0) for v = 0 at the electronic level of ground and resonant states.
1 +
TABLE 1. Two-photon Hönl-London factors for the 1 Σ+
g ← Σg
transition using linearly polarized light
S(J , J )
Branch
J (J − 1)
30(2J − 1)
O (J − J = −2)
P (J − J = −1)
Q (J − J = 0)
0 (forbidden)
J (J + 1)
2J + 1
1+
9
5(2J − 1)(2J + 3)
R (J − J = 1)
0 (forbidden)
S (J − J = 2)
(J + 1)(J + 2)
30(2J + 3)
171
Constants[12] for deducing term values of hydrogen [cm−1 ]
TABLE 2.
states
Te
G(0)
B0
D0
E 1 Σ+
g
X 1 Σ+
g
100082
0
1262
2170.27
31.79
59.32
2.205 × 10−2
4.563 × 10−2
TABLE 3.
Constants[8] for deducing term values of nitrogen [cm−1 ]
states
a 1 Σ+
g
X 1 Σ+
g
Te
G(0)
B0
D0
98840.55
0
1088
1175.704
1.913748
1.98950
6.088 × 10−6
5.48 × 10−6
500
Temperature [K]
Tvib = 220K
100
Trot = 63K
50
10
5
1
0
Ttr = 4.9K
H2
P0 = 5bar
D = 0.6mm
T0 = 300K
10
Translational
Rotational(Z=300)
Vibrational(Z=10000)
20
30
Axial Distance ( x/D )
40
50
FIGURE 1. Temperature distributions of hydrogen along the center line of supersonic free jets (P0 = 5bar, D = 0.6mm)
500
Temperature [K]
Tvib = 200K
100
Trot = 7.0K
10
5
1
FIGURE 2.
Translational
Rotational(Z=4.2)
Vibrational(Z=10000)
50
N2
P0 = 5bar
D = 0.6mm
T0 = 300K
10
Ttr = 4.9K
20
30
Axial Distance ( x/D )
40
50
Temperature distributions of nitrogen along the center line of supersonic free jets (P0 = 5bar, D = 0.6mm)
172
RESULTS AND DISCUSSIONS
Simulated H2 -REMPI spectra
The rotational temperature distribution along the center line of a supersonic jet is estimated by solving the relaxation
equation derived by Gallagher and Fenn[13]. To solve the equation, the rotational collision number Z r was assumed as
300[13] for hydrogen molecules. Figure 1 shows the temperature distributions along the center line of free molecular
flows of hydrogen. The source pressure and temperature are 5bar and 300K, respectively, and the diameter D of the
nozzle is 0.6mm. This result indicates that the rotational temperature T rot freezes at 64K. The temperature distributions
of nitrogen are also calculated and are shown in Figure 2. The estimated T rot of nitrogen is 7.0K. Because the rotational
collision number of hydrogen is much larger than that of nitrogen, rotational temperature of a hydrogen flow freezes
at relatively high temperature.
Figures 3 and 4 are the simulated 2R+1 H 2 -REMPI spectra of the (0, 0) band for Trot = 64K and 300K, respectively.
In the simulations, the laser linewidth is assumed to be 2cm −1 . For Trot = 64K strong Q(0) and Q(1) lines and relatively
weak S(0) and S(1) lines exist, but there are no lines at J ≥ 2, On the other hand, for Trot = 300K the levels of J = 2
and 3 are populated, and the lines of Q(2) and Q(3) can also be observed. Lines of the O branch, which start from O(2),
cannot be observed because the transition probabilities of them are very low. It seems to be easy to analyze rotational
energy distributions of hydrogen by 2R+1 REMPI, because there is no overlap of spectral lines in the signal.
When studying any types of rotational transitions of homonuclear diatomic molecules such as H 2 , it is important
to take account of one selection rule: transitions between symmetric and antisymmetric states are forbidden not only
for absorption or emission of photons, but also for exchange of rotational energy by molecular collisions. For the
lowest electronic state X 1 Σ+
g of H2 , at which most of hydrogen molecules are populated, each state with odd J is
antisymmetric while each state with even J is symmetric. Therefore, transition between an odd- and an even-numbered
rotational level is forbidden, while transition among odd-numbered levels as well as that among even-numbered levels
is allowed. This selection rule holds for every type of Σ electronic state, one of which is the lowest electronic state of
many molecules such as N 2 and O2 . For analyses of most diatomic molecules except hydrogen the selection rule can
be ignored, but it becomes significant for analyses of hydrogen.
When gas expands into vacuum a supersonic free jet is formed, the ratio of molecules in odd levels to those in even
levels at the stagnation condition is preserved. Because the statistical weight g(J) of odd-numbered level and evennumbered level is 3 and 1, respectively, there exist about three times more hydrogen molecules with odd J (o-H 2 ) than
with even J (p-H 2 ). For example, at T0 = 300K the ratio of o-H 2 and p-H2 is 2.99. Figure 5 is the simulated H 2 -REMPI
spectrum for Trot = 64K, assuming the ratio of o-H 2 and p-H2 at the stagnation condition is preserved. The intensity
of Q(1) is about three times as high as that of Q(0), contrary to the result shown in Fig. 3, which is the spectrum of
the normal hydrogen in the static condition at 64K. As a result it is shown that the statistical weight of the rotational
levels has a very significant effect, and it cannot be ignored for analyses of precise rotational energy distribution of
hydrogen.
Analysis of a mixture of hydrogen and nitrogen
Nitrogen molecules, as well as hydrogen, are excited by two 202-203nm photons and then ionized by one photon[8].
In case of mixtures of hydrogen and nitrogen this property may enable the simultaneous measurement of nitrogen and
hydrogen, but if the spectral lines of hydrogen and nitrogen molecules are overlapped the Boltzmann plot using the
REMPI spectra of the mixture becomes difficult. Therefore, it is important to examine the possibility of temperature
measurement of nitrogen using 2R+1 N 2 -REMPI, and the overlap between H 2 - and N2 -REMPI spectra by simulating
the 2R+1 N2 -REMPI spectra and comparing with the H 2 -REMPI ones.
Figure 6 and 7 are the simulated 2R+1 N 2 -REMPI spectra for Trot = 7K and 300K. As mentioned by Lykke and
1 +
Kay[8], for 1 Σ+
g ← Σg transitions the Q-branch lines dominate in these spectra. From these figures it is obvious that
the Q branch of the spectra is very crowded and not each spectral line can be resolved. Moreover, lines of the Q branch
from J ≥ 12 overlap with that of the O branch and these lines cannot be used for the Boltzmann plot (Fig. 7). Therefore,
it is very difficult to use 2R+1 N 2 -REMPI method for analyses of the rotational energy distribution in gas flows by the
Boltzmann plot.
Figure 8 shows both the 2R+1 N 2 - and H2 -REMPI spectra for Trot = 300K. Although Q(3) line of hydrogen is
overlapped with lines of the S branch of nitrogen, other lines such as Q(0), Q(1), and Q(2) are separated from any lines
173
Q(0)
Signal Intensity [a.u.]
1
2R+1 H2-REMPI Spectrum
Trot = 64K
laser linewidth: 2cm-1
Q(1)
0.5
S(0)
S(1)
0
201.1
202
203
204
Wavelength [nm]
Simulated 2R+1 H2 -REMPI Spectra (Trot = 64K)
FIGURE 3.
Q(1)
2R+1 H2-REMPI Spectrum
Signal Intensity [a.u.]
1
Trot = 300K
laser linewidth: 2cm-1
0.5
Q(0)
S(1)
S(0)
0
201.1
Q(2)
Q(3)
202
203
204
Wavelength [nm]
FIGURE 4.
Q(1)
1
Signal Intensity [a.u.]
Simulated 2R+1 H2 -REMPI Spectra (Trot = 300K)
2R+1 H2-REMPI Spectrum
T0 = 300K
Trot = 64K
laser linewidth: 2cm-1
0.5
Q(0)
S(1)
S(0)
0
201.1
202
203
204
Wavelength [nm]
FIGURE 5.
Simulated 2R+1 H2 -REMPI Spectra (Trot = 64K, T0 = 300K)
174
Q branch
Signal Intensity [a.u.]
1
Trot = 7K
laser linewidth: 2cm-1
2R+1 N2-REMPI Spectrum
0.5
S(2)
S(0)
S(1)
O(2)
0
202.5
202.55
Wavelength [nm]
202.6
FIGURE 6. Simulated 2R+1 N2 -REMPI Spectra (Trot = 7K)
Signal Intensity [a.u.]
1
Q branch
Trot = 300K
laser linewidth: 2cm-1
Q(10)
2R+1 N2-REMPI Spectrum
Q(12)+O(2)
0.5
0
S(2)
Q(20)
S(0)
S(1)
202.5
FIGURE 7.
202.55
Wavelength [nm]
Simulated 2R+1 N2 -REMPI Spectra (Trot = 300K)
Q(1)
2R+1 H2-REMPI Spectrum
Trot = 300K
1
Signal Intensity [a.u.]
202.6
Q branch
2R+1 N2-REMPI Spectrum
Trot = 300K
S branch
0.5
Q(0)
S(1)
S(0)
0
201.1
laser linewidth: 2cm-1
Q(2)
Q(3)
Q and O branch
202
203
204
Wavelength [nm]
FIGURE 8. Simulated 2R+1 H2 - and N2 -REMPI Spectra (Trot = 300K)
175
Q(1)
Signal Intensity [a.u.]
1
Q branch
2R+1 H2-REMPI Spectrum
Trot = 64K
ortho / para = 2.99 at T0 = 300K
2R+1 N2-REMPI Spectrum
Trot = 7K
0.5
S(0)
Q(0)
S(1)
S(1)
S(0)
S(2)
0
201.1
laser linewidth: 2cm-1
202
203
204
Wavelength [nm]
FIGURE 9.
Simulated 2R+1 H2 - and N2 -REMPI Spectra (Trot = 64K for H2 and Trot = 7K for N2 . T0 = 300K for both species)
(Inside of STG)
The Same
Focal Point
Reference
Cell
Achromatic
Lens
Dichroic
Mirror
Mirror
Beam Splitter
280nm
for N 2
90 ° Prism
FIGURE 10.
Beam Splitter
200nm
for H 2
Optics to use two-color laser beam for REMPI measurement
of nitrogen. Therefore, this overlap problem is not critical for the Boltzmann plot.
Figure 9 shows the 2R+1 N 2 - and H2 -REMPI spectra for the source temperature T0 = 300K at x/D = 83 (the ratio of
the distance from the nozzle exit and the diameter of the nozzle). At the position, the rotational temperature of nitrogen
is measured as 7K[5]. On the other hand, the rotational temperature of hydrogen is estimated as 64K, but there seems
to be the effect of symmetric/antisymmetric states on the rotational energy distribution as shown in Fig. 5. In this case,
there is no overlap between the lines of nitrogen and hydrogen.
As a result, the feasibility of measurement by 2R+1 H 2 -REMPI in a gas mixture of hydrogen and nitrogen is proved,
because the spectrum of 2R+1 N 2 -REMPI does not interfere with that of 2R+1 H 2 -REMPI. However, measurement
of nitrogen itself with 2R+1 N 2 -REMPI with ∼200nm laser light is very difficult. Instead, the well-known 2R+2
N2 -REMPI around 280nm [14, 15, 5] is proposed for the measurement of the rotational temperature of N 2 .
Outline of experiment to measure a mixture of hydrogen and nitrogen
Figure 10 shows the proposed experimental setup for measurement of H 2 +N2 -mixtures in the space chamber STG.
As mentioned above, if the combination of 2R+1 H 2 -REMPI and 2R+2 N 2 -REMPI is used to take measurements,
two beams of around 200nm and 280nm are required. The two laser beams are coupled using a prism, before being
176
directed into the STG test chamber. As shown in the figure, an achromatic lens is needed to focus both beams at the
same focal point. If a number density measurement[5] is performed, the REMPI signal intensity in a reference cell
with known pressure has to be measured simultaneously and compared with the signal intensity in STG. In this case,
the laser beams must be separated by beam splitters with known reflectivity for the reference cell.
CONCLUSION
In this paper based on the theory of H 2 and N2 -REMPI, 2R+1 H2 - and N2 -REMPI spectra have been simulated to
examine the possibility of Boltzmann plots for measurement of rotational temperature in flows of a mixed gas of
hydrogen and nitrogen.
As a result, the feasibility of 2R+1 H 2 -REMPI for analysis of rotational energy distributions of hydrogen is shown.
However, we have to take account of statistical weight of odd- and even-numbered rotational energy levels for precise
analysis of hydrogen in supersonic free jets,
Measurements of hydrogen in gas mixtures are also possible using 2R+1 REMPI with ∼200nm laser light, because
the overlap of the spectral lines of hydrogen and nitrogen is not critical. However, it is difficult to apply the 2R+1 N 2 REMPI method with ∼200nm laser light to analysis of nitrogen, because the Q branch of the spectra is very crowded
and each spectral line cannot be separated. Therefore, the schemes of 2R+1 H 2 -REMPI and 2R+2 N 2 -REMPI are
appropriate for the measurement of mixed hydrogen and nitrogen.
ACKNOWLEDGMENTS
Hideo Mori wishes to thank the Japan Society for the Promotion of Science for a research fellowship.
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