**3. Resonantly Enhanced Multi‐Photon Ionization (REMPI)**

images are obtained at the same pressure condition: source pressure *Ps* = 16kPa and back‐ ground pressure *Pb* = 100Pa. It can be seen that the fluorescence intensity distributions are very different, depending on the absorption lines. If using two images among them, we can deduce

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

**Figure 4.** Supersonic free jets visualized by I2-LIF with different wavelengths. P and R means P- and R-branches, respec‐

tively, and the number the rotational energy level [4].

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**Figure 5.** Two-dimensional temperature distribution of a supersonic free jet [4].

the temperature distribution two‐dimensionally as shown in Figure 5.

To measure the rotational population in rarefied supersonic nitrogen free jets and finally to confirm the non‐Boltzmann distribution of the rotational levels experimentally, a REMPI (Resonantly Enhanced Multi‐Photon Ionization) method has been applied to detection of nitrogen ions directly as an ion current. REMPI is known to have high detection sensitivity, which allows obtaining the signal under the very low number density condition. Here the principle of REMPI is introduced and the (2+2) N2‐REMPI is applied to a supersonic nitrogen free jet to detect the non‐Boltzmann distribution of the rotational levels.

Figure 6 depicts the schematic energy level diagram for (2+2) N2‐REMPI, illustrating the relevant processes. In this process, nitrogen molecules at the ground state (*X*<sup>1</sup> *Σg* + ) are excited to the resonant state (*a*<sup>1</sup> Π*g*) by two‐photon absorption. Then the excited molecules are ionized by additionaltwo‐photon energy. Since four photons participate in this process,the ion current is proportional to the fourth power of laser flux in principle. However, when the laser flux is sufficiently high so that almost all the excited molecules are ionized, the ion current is proportional to square of laser flux, because the REMPI process reflects the two‐photon transition process from the ground to the resonant state. In other words, the REMPI spectrum reflects directly the rotational population in the ground state of neutral molecules, so the rotational temperature can be deduced from the REMPI spectra, provided that the flow is in equilibrium, that is, the rotational energy distribution follows the Boltzmann distribution.

The REMPI technique is applied to detection of the rotational non‐equilibrium in a nitrogen free‐molecular flow. All experiments are carried out in a vacuum chamber evacuated by a turbomolecular pump and a dry pump as a backing pump, allowing an oil‐free vacuum environment. Nitrogen gas is issued from a sonic nozzle with *D* = 0.50mm diameter, and expanded into the chamber. Stagnation temperature is kept at 293 K and source pressures P0 is set at 30 Torr (3.9 × 103 Pa) to 1 Torr (1.3 × 102 Pa). A Nd:YAG‐pumped dye laser operated

**Figure 6.** (2+2) N2-REMPI process.

with Rhodamine 6G dye is used as a laser source, and the output is frequency‐doubled by a BBO crystal. The wavelength of the laser beam is ranged from 283 to 284.1 nm. The beam is focused with a quartz lens on a centerline of a nitrogen free‐molecular flow. The ionized nitrogen molecules are detected by a secondary electron multiplier or a tungsten Langmuir probe. A wavelength is scanned by a step of 0.001 nm, and the signal intensity is integrated for 100 laser pulses per each step.

Figure 7 represents an experimental (2+2) N2‐REMPI spectrum of the (*vʹ*, *vʹʹ*) = (1,0) vibrational band, measured for *P0D* = 15 Torr‐mm and at a focal point of *x* = 2.5 mm downstream from the nozzle exit (*x*/*D* = 5) along the centerline of the jet. In this figure, the horizontal axis indicates the wavelength of the laser, and the vertical one the signal intensity normalized by a peak. Numbers on rulers in the figure correspond to spectral positions for O, P, Q, R and S branches. When the population number is designated by *N*(*Jʹʹ*), the rotational line intensity *IJʹ,Jʹʹ* in (2+2) N2‐REMPI spectra is given by

$$I\_{\{\mathbf{J}\_{\perp}\}\_{\perp}} = A \lg \begin{pmatrix} \mathbf{J} \ \mathbf{J} \end{pmatrix} \mathbf{S} \begin{pmatrix} \mathbf{J} \ \mathbf{J} \ \mathbf{J} \ \mathbf{J} \end{pmatrix} \mathbf{N} \begin{pmatrix} \mathbf{J} \ \mathbf{J} \ \end{pmatrix} / \begin{pmatrix} \mathbf{2J} \ \mathbf{J} \ \mathbf{J} \end{pmatrix} \tag{1}$$

where *Jʹ* and *Jʹʹ* are the rotational quantum number of the resonant and ground state, respec‐ tively, A is a proportional constant independent of the rotational quantum number, and g(*Jʹʹ*) is the nuclear spin statistical weight of nitrogen molecules formed by N14 atoms. S(*Jʹ*,*Jʹʹ*) is the two‐photon Hönl‐London factor [5] for the *a*<sup>1</sup> Π*<sup>g</sup>* ← *X*<sup>1</sup> *Σg* <sup>+</sup> transition. *N*(*Jʹʹ*) is proportional to (2*Jʹʹ*+1) exp (*‐E*rot/*kT*rot) (*E*rot: rotational energy, *T*rot: rotational temperature, *k*: Boltzmannʹs constant), provided that the rotational energy distribution follows the Boltzmann distribution. In this case, *IJ<sup>ʹ</sup>*,*Jʹʹ* is given by [6].

$$I\_{\{\",\"\}} = A \text{g} \{\text{J}^{\text{-}}\} \text{S} \{\text{J}^{\text{-}}, \text{ J}^{\text{-}}\} \exp\{-E\_{\text{rot}}/kT\_{\text{rot}}\} \tag{2}$$

**Figure 8.** Boltzmann plots [6].

**Figure 7.** N2-REMPI spectrum [6].

High Knudsen Number Flow — Optical Diagnostic Techniques 39

and the rotational temperature can be deduced from a slope of Boltzmann plot of ln(*IJ<sup>ʹ</sup>*,*Jʹʹ* / *gS(Jʹ*,*Jʹʹ*)) versus *E*rot/*k*. If there appears nonlinearity in the Boltzmann plot, therefore, the rotational energy distribution deviates from the Boltzmann distribution and the rotational temperature cannot be defined.

Figure 8 shows a result of Boltzmann plots at several *x* / *Dʹ*s for *P*0*D* = 15 Torr‐mm by using the measured REMPI spectra. In this figure, the horizontal axis indicates the *E*rot/*k* and the vertical one the ln(I*Jʹ*,*Jʹʹ* / *gS*(*Jʹ*,*Jʹʹ*)). Numbers attached to the data points are the rotational quantum numbers of the ground state. It is found from Figure 8 that all the Boltzmann plots demonstrate the nonlinearity even at *x* / *D* = 1.0 for *P*0*D* = 15 Torr‐mm and especially the data in higher rotational levels deviate from a line, confirming the non‐Boltzmann distribution of the rotational levels.

**Figure 7.** N2-REMPI spectrum [6].

with Rhodamine 6G dye is used as a laser source, and the output is frequency‐doubled by a BBO crystal. The wavelength of the laser beam is ranged from 283 to 284.1 nm. The beam is focused with a quartz lens on a centerline of a nitrogen free‐molecular flow. The ionized nitrogen molecules are detected by a secondary electron multiplier or a tungsten Langmuir probe. A wavelength is scanned by a step of 0.001 nm, and the signal intensity is integrated

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

Figure 7 represents an experimental (2+2) N2‐REMPI spectrum of the (*vʹ*, *vʹʹ*) = (1,0) vibrational band, measured for *P0D* = 15 Torr‐mm and at a focal point of *x* = 2.5 mm downstream from the nozzle exit (*x*/*D* = 5) along the centerline of the jet. In this figure, the horizontal axis indicates the wavelength of the laser, and the vertical one the signal intensity normalized by a peak. Numbers on rulers in the figure correspond to spectral positions for O, P, Q, R and S branches. When the population number is designated by *N*(*Jʹʹ*), the rotational line intensity *IJʹ,Jʹʹ* in (2+2)

where *Jʹ* and *Jʹʹ* are the rotational quantum number of the resonant and ground state, respec‐ tively, A is a proportional constant independent of the rotational quantum number, and g(*Jʹʹ*) is the nuclear spin statistical weight of nitrogen molecules formed by N14 atoms. S(*Jʹ*,*Jʹʹ*) is the

(2*Jʹʹ*+1) exp (*‐E*rot/*kT*rot) (*E*rot: rotational energy, *T*rot: rotational temperature, *k*: Boltzmannʹs constant), provided that the rotational energy distribution follows the Boltzmann distribution.

and the rotational temperature can be deduced from a slope of Boltzmann plot of ln(*IJ<sup>ʹ</sup>*,*Jʹʹ* / *gS(Jʹ*,*Jʹʹ*)) versus *E*rot/*k*. If there appears nonlinearity in the Boltzmann plot, therefore, the rotational energy distribution deviates from the Boltzmann distribution and the rotational

Figure 8 shows a result of Boltzmann plots at several *x* / *Dʹ*s for *P*0*D* = 15 Torr‐mm by using the measured REMPI spectra. In this figure, the horizontal axis indicates the *E*rot/*k* and the vertical one the ln(I*Jʹ*,*Jʹʹ* / *gS*(*Jʹ*,*Jʹʹ*)). Numbers attached to the data points are the rotational quantum numbers of the ground state. It is found from Figure 8 that all the Boltzmann plots demonstrate the nonlinearity even at *x* / *D* = 1.0 for *P*0*D* = 15 Torr‐mm and especially the data in higher rotational levels deviate from a line, confirming the non‐Boltzmann distribution of

Π*<sup>g</sup>* ← *X*<sup>1</sup>

*Σg*

, *J* ʹʹ)*N* (*J* ʹʹ)/(2*J* ʹʹ + 1) (1)

, *<sup>J</sup>* ʹʹ)exp(‐*E*rot / *kT* rot) (2)

<sup>+</sup> transition. *N*(*Jʹʹ*) is proportional to

for 100 laser pulses per each step.

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N2‐REMPI spectra is given by

In this case, *IJ<sup>ʹ</sup>*,*Jʹʹ* is given by [6].

temperature cannot be defined.

the rotational levels.

*IJ* ʹ

two‐photon Hönl‐London factor [5] for the *a*<sup>1</sup>

*IJ* ʹ

, *<sup>J</sup>* ʹʹ<sup>=</sup> *Ag*(*<sup>J</sup>* ʹʹ)*S*(*<sup>J</sup>* <sup>ʹ</sup>

, *<sup>J</sup>* ʹʹ<sup>=</sup> *Ag*(*<sup>J</sup>* ʹʹ)*S*(*<sup>J</sup>* <sup>ʹ</sup>

**Figure 8.** Boltzmann plots [6].

The rotational temperature is deduced from the Boltzmann plots of Figure 8 by using only the linear portion of the plots lying at smaller rotational quantum numbers. Figure 9 shows the rotational temperature distribution along the centerline of a supersonic free jet, where the horizontal axis indicates *x* / *D* and the vertical one the rotational temperature. Solid circles indicate the measured rotational temperatures, and the broken lines the translational temper‐ ature distribution calculated from isentropic relations using the Mach numbers [7]. The rotational temperature distribution measured by REMPI is compared with other data meas‐ uredbydifferent ways, i.e.the rotationaltemperatures measuredbyusing only some rotational lines constituting a linear portion ofthe Boltzmann plots obtained by the electron beam method [8] and calculated by using an equation of the rotational temperature distribution for the rotationalrelaxation [9]. As you can see, allresults agree with each other, if using only the data at smaller rotational quantum numbers for the REMPI and electron beam techniques.

population. Generally the higher rotational quantum number the molecules have, the lower the transition probability becomes, resulting in the deviation from the Boltzmann distribution particularly forthe higherrotational levels. This is the reason why the freezing of the rotational

High Knudsen Number Flow — Optical Diagnostic Techniques 41

**4. Pressure Sensitive Paints (PSP) and Pressure Sensitive Molecular Film**

There have been no appropriate techniques for the measurement of gas pressure on a solid surface inside micro‐systems. To measure pressure distributions in a low density gas‐flows with high Knudsen number, a pressure sensitive paint (PSP) technique [10, 11] have been

The pressure measurement technique using PSP is based on the oxygen quenching of lumi‐ nescent molecules. PSP is composed of luminescent molecules and a binder material to fix the luminescent molecules to a solid surface. Figure 11 depicts the schematic energy level diagram for PSP and oxygen molecules. When PSP layer applied to the surface is illuminated by UV light, the luminescent molecules are excited by absorption of photon energy, and then the molecules emit luminescence. On the other hand, oxygen molecule with triplet ground state acts as a quencher of the luminescence. As a result, the phosphorescence intensity decreases as an increase in partial pressure of oxygen. Pressure on the solid surface can be deduced from the relationship between pressure and the luminescence intensity (Stern‐Volmer plot [11]).

population starts partially at the higher rotational levels.

**Figure 10.** Rotational population obtained by REMPI [6].

**(PSMF)**

adopted.

**Figure 9.** Rotational temperature distribution along the centerline of a supersonic free jet [6].

To clearly reveal the non‐Boltzmann distribution, the rotational population obtained by REMPI for *P*0*D* = 15 Torr‐mm is presented in Figure 10, in which the horizontal axis indicates the rotational quantum number and the vertical one the population ratio of each rotational level to the total. Symbols such as solid circles correspond to the population ratio for each measurement point and each curve to a Boltzmann distribution at temperature deduced from a Boltzmann plot using only the data for smaller rotational quantum numbers as mentioned above. In the condition of *P*0*D* = 15 Torr‐mm, the rotational population at *x* / *D* = 1.0 follows almost the Boltzmann distribution, whereas at *x* / *D* = 7.0 the experimental data deviate from the Boltzmann distribution evidently. Comparing between the distributions of *x* / *D* = 7.0 and 20.0, for *Jʹʹ* ≥ 7 the both show the same tendency, suggesting partial freezing of the rotational

**Figure 10.** Rotational population obtained by REMPI [6].

The rotational temperature is deduced from the Boltzmann plots of Figure 8 by using only the linear portion of the plots lying at smaller rotational quantum numbers. Figure 9 shows the rotational temperature distribution along the centerline of a supersonic free jet, where the horizontal axis indicates *x* / *D* and the vertical one the rotational temperature. Solid circles indicate the measured rotational temperatures, and the broken lines the translational temper‐ ature distribution calculated from isentropic relations using the Mach numbers [7]. The rotational temperature distribution measured by REMPI is compared with other data meas‐ uredbydifferent ways, i.e.the rotationaltemperatures measuredbyusing only some rotational lines constituting a linear portion ofthe Boltzmann plots obtained by the electron beam method [8] and calculated by using an equation of the rotational temperature distribution for the rotationalrelaxation [9]. As you can see, allresults agree with each other, if using only the data

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

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at smaller rotational quantum numbers for the REMPI and electron beam techniques.

**Figure 9.** Rotational temperature distribution along the centerline of a supersonic free jet [6].

To clearly reveal the non‐Boltzmann distribution, the rotational population obtained by REMPI for *P*0*D* = 15 Torr‐mm is presented in Figure 10, in which the horizontal axis indicates the rotational quantum number and the vertical one the population ratio of each rotational level to the total. Symbols such as solid circles correspond to the population ratio for each measurement point and each curve to a Boltzmann distribution at temperature deduced from a Boltzmann plot using only the data for smaller rotational quantum numbers as mentioned above. In the condition of *P*0*D* = 15 Torr‐mm, the rotational population at *x* / *D* = 1.0 follows almost the Boltzmann distribution, whereas at *x* / *D* = 7.0 the experimental data deviate from the Boltzmann distribution evidently. Comparing between the distributions of *x* / *D* = 7.0 and 20.0, for *Jʹʹ* ≥ 7 the both show the same tendency, suggesting partial freezing of the rotational

population. Generally the higher rotational quantum number the molecules have, the lower the transition probability becomes, resulting in the deviation from the Boltzmann distribution particularly forthe higherrotational levels. This is the reason why the freezing of the rotational population starts partially at the higher rotational levels.
