Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas

Conventional material processes using plasmas generated in low pressure gaseous media are recently being transposed to high-pressure plasma processes, because of the potential of high-pressure plasmas to reduce costs for vacuum systems in industrial applications. In many kinds of high-pressure plasma sources, small-scale atmospheric-pressure plasmas (APPs) having a property of thermal non-equilibrium, have been especially attracting much interest of researchers over the last 20 years (Becker, 2005). In such a high pressure gaseous medium, generating the small-scale plasmas in mm or μm order is effective to keep its ignition voltage low and discharge behavior stable, following a famous rule on discharge ignition called a “Paschen’s law” (Paschen, 1889; von Engel, 1994). Using these small-scale high-pressure plasmas, localized maskless processes, for example etching (Ichiki et al., 2004) and deposition (Babayan et al., 1998), have been reported. Also, nanomaterial synthesis was realized by the APP utilizing their property of short residence time of source particles inside the plasma (Nozaki et al., 2007). In addition to the inorganic solid material processes, process objects of the APPs are spreading toward liquids (Bruggeman & Leys, 2009) and biocells (Kong et al., 2009) which cannot present in low-pressure conditions.


Introduction
Conventional material processes using plasmas generated in low pressure gaseous media are recently being transposed to high-pressure plasma processes, because of the potential of high-pressure plasmas to reduce costs for vacuum systems in industrial applications.In many kinds of high-pressure plasma sources, small-scale atmospheric-pressure plasmas (APPs) having a property of thermal non-equilibrium, have been especially attracting much interest of researchers over the last 20 years (Becker, 2005).In such a high pressure gaseous medium, generating the small-scale plasmas in mm or μm order is effective to keep its ignition voltage low and discharge behavior stable, following a famous rule on discharge ignition called a "Paschen's law" (Paschen, 1889;von Engel, 1994).Using these small-scale high-pressure plasmas, localized maskless processes, for example etching (Ichiki et al., 2004) and deposition (Babayan et al., 1998), have been reported.Also, nanomaterial synthesis was realized by the APP utilizing their property of short residence time of source particles inside the plasma (Nozaki et al., 2007).In addition to the inorganic solid material processes, process objects of the APPs are spreading toward liquids (Bruggeman & Leys, 2009) and biocells (Kong et al., 2009) which cannot present in low-pressure conditions.
In characterization and comparison of plasma properties, electron density is one of the most important parameters.This is because that electrons play a major role for carrying external energy to heavy particles inside the plasma, and all other excited species can be calculated theoretically from the plasma parameters of electron density, electron energy distribution, and gas composition.Diagnostics of electron density have in the APPs have been reported by many researchers using Langmuir probe methods (Chang, 1973;Chang & Laframboise, 1976), Stark broadening measurement (Laux et al., 2003), and laser Thomson scattering measurement (Kono & Iwamoto, 2004).However, these methods have limitations for the APP measurements due to their finite sensitivities, expected perturbations or interferences, spatiotemporal resolutions, etc.For instance, the Langmuir probe is difficult be applied to the small-scale APPs since its theory in a collision dominant condition is not well developed and there are discharge perturbations by the metallic probe.The Stark broadening spectroscopic method enables us to derive electron density only for over 5×10 13 cm -3 due to the large pressure broadening superposed over the Lorentzian shape (Laux et al., 2003).The laser Thomson scattering method is not applicable to molecular gases although its spatial resolution is high enough, because large Raman scattering components overlap with the Thomson scattering signal.
For the purpose of diagnostics in the small-scale high-pressure plasmas, refractive-index measurement using electromagnetic (EM) waves is appropriate since they can provide plasma property's information with negligible perturbation to the plasma.Also, in the refractive-index measurement, we can ignore excitation and scattering processes that are largely dependent on gas compositions and densities, which are indispensable for the above listed other measurement methods.For typical APPs whose electron densities range from 10 12 to 10 15 cm -3 , microwaves and millimeter-waves are suitable to detect absorption of the probing EM waves and derive the electron density from the absorption ratio (Tachibana et al., 2005(a), 2005(b); Sakai et al., 2005;Ito et al., 2010).However, diagnostics using those EM waves cannot have good spatial resolutions for the small-scale plasmas because of their diffraction limits.Meanwhile, a heterodyne interferometer of CO 2 laser beam, which is a theme in this chapter, can be in a category of the refractive-index measurement methods and have a good spatial resolution at the same time.This interferometer detects the laser beam's phase shift caused by the presence of tested plasma and provides line-integrated information of electron density with a spatial resolution in sub mm order (Leipold et al., 2000;Choi et al., 2009).This chapter is focused on descriptions of the CO 2 -laser heterodyne interferometer for the measurement in small-scale high-pressure plasma sources, because detailed descriptions of the interferometer for the low-pressure plasmas have been written in other chapters and textbooks (for example Hutchinson, 2002).In high-pressure plasmas, large contribution of gas-particle density (atoms and/or molecules in ground states) to the change of the refractive index is expected due to Joule heating in the discharge region, and this must be accurately separated from the signal in order to derive the absolute value of electron density.Therefore, we firstly explain how to divide the two components in the CO 2 -laser beam's phase shift, which are the phase shifts due to electron generation and gas heating.Then, the fundamental properties of our CO 2 -laser heterodyne interferometer, for example spatial resolution and lower limit of electron-density detection, are verified reviewing experimental measurements of the small-scale APPs driven by DC applied voltages (Choi et al., 2009).Finally, a combination measurement method composed of the CO 2 -laser heterodyne interferometer and a millimeter-wave transmission method is introduced as a solution of spatiotemporally resolved electron-density measurement in small-scale APPs with high-speed temporal evolution of electron density (Urabe et al., 2011).

Fundamentals of heterodyne interferometer
This section includes brief introduction of a Mach-Zehnder principle and a heterodyne technique used in our interferometer and theoretical descriptions of the phase shift in the CO 2 laser beam induced by electrons in a tested plasma source, and explanations how to derive electron density in small-scale high-pressure plasmas eliminating influence of gas heating from total phase shift signals.

Mach-Zehnder heterodyne interferometer
Measurements of refractive index in tested materials are often done by some forms of interferometer.Most of interferometers are in Michelson, Fabry-Perot, and Mach-Zehnder configurations.Mach-Zehnder interferometer is a two-beam interferometer having two paths in which the laser beams travel in only one direction.The original laser beam is www.intechopen.comHeterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas 211 separated by a beam splitter, and the beam's phase change is caused by variations of the refractive index of the tested material placed only in one path.Difference of the refractive indexes between the two paths is derived from the merged beam by a second beam splitter.
A heterodyne technique is a reducing method of observing frequency from light frequency to external oscillator frequency in a instrumentally manageable range.When this method is applied to the Mach-Zehnder interferometer, the light frequency in one of two paths is modulated, and in the other path the frequency is not modulated but its phase is shifted by the tested material.After merging the two laser beams, a beat signal at the modulation frequency in the merged beam can be isolated from the original output signal of a solid-state detecting device, I(t), which is expressed in a following equation.
where U 1 (t) = E 1 cos(ωt+Δωt) is the electric field of the laser beam passing through the frequency modulating device with a modulation frequency at Δω, U 2 (t) = E 2 cos(ωt+ΔΦ) is the electric field of the beam passing through the tested material, and ΔΦ is the phase shift of the beam by the tested material.Components in a light frequency range are automatically eliminated from the signal because of the response-speed limitation of detectors.From the output signal, I(t), we can derive the phase shift by the tested material ΔΦ using a phase detecting device and a reference signal which is separated from the frequency-modulation signal.
Fig. 1.Experimental setup of CO 2 -laser heterodyne interferometer in Mach-Zhender principle for measurement of electron density inside high-pressure plasma source.AOM is acousto optical modulator shifting CO 2 -laser frequency at frequency of RF driver's signal.DC is directional coupler taking small amplitude of RF signal driving AOM to input reference signal to lock-in amplifier.
A practical experimental setup of the CO 2 -laser heterodyne interferometer used in our studies is shown in Fig. 1.The original CO 2 laser beam was split by a ZnSe half mirror.The beam frequency in one path was shifted an acousto-optical modulator (AOM) whose modulation frequency Δω = 40 MHz.In the other path, the beam was focused on a tested plasma source by a pair of ZnSe lens, and the beam phase was shifted by the tested plasma.These two beams were superposed again at another ZnSe half mirror, and their beat signal was detected by a HgCdTe IR detector operated at room temperature.The output signal of the IR detector, I(t), was put into a lock-in amplifier with the reference signal, cos(Δωt), which was divided from a RF signal driving the AOM by a directional coupler (DC).The lock-in amplifier outputs a signal proportional to the phase shift, ΔΦ, and its temporal evolution was recorded in an oscilloscope.

Phase shift of CO 2 laser beam by electrons inside plasmas
In refractive-index measurement inside a tested plasma source having no gas temperature fluctuation, for example plasmas generated in gaseous media at very lower pressure than atmosphere, the phase shift by tested plasma, ΔΦ, measured using the Mach-Zehnder heterodyne interferometer becomes where k plasma and k 0 are the wavenumbers of the plasma and vacuum, N plasma is the refractive index of the plasma, and λ is the wavelength of the CO 2 laser beam.Absolute electron density inside the plasma, n e (m), can be derived using a following relationship.
where ω plasma and ω are the electron plasma frequency and the angular frequency of laser beam, m e is the mass of electron, ε 0 is the permittivity of vacuum, c is the velocity of light (Hutchinson, 2002).We used an approximate expansion in this calculation because electron density is sufficiently smaller than gas-particle density in weakly ionized plasmas generated in laboratories.When we assume that electron density inside the tested plasma is spacially homogeneous and its length along the laser path is d (m), the relationship between the phase shift and the electron density becomes ( ) in the CO 2 -laser heterodyne interferometer at λ = 10.6 μm.

Electron-density measurement in high-pressure plasmas
In this subsection, influence of dense gas particles in high-pressure plasmas on the calculation of electron density from the phase shift of the CO 2 laser beam, which can be ignored in the measurement of low-pressure plasmas, is introduced.It should be noted that increase of gas temperature corresponding to decrease of gas-particle density is promoted in the high-pressure plasmas because of high collision frequencies between electrons and gas particles.This change of gas-particle density results in the change of the refractive index in gaseous medium.The refractive index of the gaseous medium, N gas , is where A and B are the specific values for gas species, n g0 is the gas particle density under the standard temperature and pressure (STP) conditions, and n g is the gas-particle density inside the tested plasma source (Allen, 1973).Considering the influence of gas-particle density on the refractive index, the phase shift of the CO 2 laser beam in the high-pressure plasmas is described by two components of the electron density, ΔΦ e , and the gas-particle density, ΔΦ g , as a following equation.Whereas we used the gas-particle density n g for the calculation in Eq. ( 6), ΔΦ g can be also expressed using gas temperature in the plasma.Each component of the phase shift in the high-pressure plasma, ΔΦ e and ΔΦ g , changes to negative direction due to the electron production and the decrease of gas-particle density by the Joule heating.The separation of these two components becomes a crucial problem for accurate derivation of the electron density in practical measurements of the high-pressure plasmas, because these two components are only measured together in the heterodyne interferometer and start decreasing at the same timing.

Increase Decrease
Electron density Negative Positive

Gas-particle density Positive Negative
Gas temperature Negative Positive Table 1.Change directions of CO 2 -laser beam's phase shift by changes of electron density, gas-particle density, and gas temperature, when they increase or decrease.
For the separation of two components in the phase shift of the CO 2 laser beam, difference of time constants of the two phenomena is utilized, because the change of electron density is much faster than that of gas temperature in the high-pressure discharge (Leipold et al., 2000;Choi et al., 2009).Applicability of this technique can be confirmed by experimental evidence as explained below.Also, in general, the two terms of electron density, n e , and gas-particle density, n g , can be derived directly by solving a system of two equations using a twowavelength heterodyne interferometer, because the phase-shift components due to the electron and gas-particle densities depend differently on the laser wavelength.Some groups have tried to measure both electron and gas-particle densities inside the plasma by an additional heterodyne interferometer using a He-Ne laser beam at 633 nm (Adler & Kindel, 2003;Acedo et al., 2004).
Figure 2 shows an example waveform of the output phase-shift signal of the lock-in amplifier obtained in a small-scale high-pressure plasma source operated at 70 Torr driven by a pulsed DC voltage at 300 V with a 300-μs pulse duration.The phase-shift signal recorded in the oscilloscope is proportional to the phase shift in a specification ratio of the lock-in amplifier.Around 50 μs after the discharge ignition, the phase shift decreased rapidly in 150 μs, and then a slower change followed until the discharge termination.The 50-μs delay of the phase-shift signal is due to calculating delay time of the phase shift in the lock-in amplifier.The initial faster falling part is attributed to the increase of electron density, and the second slower part is to the decrease of gas-particle density by the Joule heating.Faster and slower slopes of the phase shift similar to the ignition timing were also observed in the termination timing.Subtracting the phase-shift component of gas-particle density, ΔΦ g , shown in a blue dashed-dotted curve in Fig. 2, the component of electron density, ΔΦ e , was obtained as shown in a red dashed curve.The absolute value of electron density can be derived from the amplitude of electron-density component.
Fig. 2. Temporal evolutions of phase-shift signal from lock-in amplifier and discharge current.Tested plasma source is small-scale discharge driven by 300-V pulsed DC high voltage at 70 Torr of He gas (Choi et al., 2009).As explained in the previous paragraph, because the temporal changes of electron and gasparticle density can be observed only in the discharge ignition or termination timings, there is a need to pulse modulation of continuous discharge for the separation of phase-shift components measured in the CO 2 -laser heterodyne interferometer.In order to understand appropriate range of duration times for the pulse modulation, especially minimum duration time, it is important to measure the phase-shift signal decreasing the modulating pulse duration.Figure 3 shows waveforms of the phase-shift signal measured in our heterodyne interferometer using five pulse duration times ranging from 60 to 700 µs.From the measured waveforms, it could be confirmed that the pulse modulation with the duration time shorter than 200 µs does not give us accurate information of electron density in our setup, and we used the modulation pulse with duration times larger than 500 µs in our studies.This temporal behavior of the output signal of the heterodyne interferometer is of course different in each IR detector and phase measuring system.Fig. 4. Calculated beam spot radii of CO 2 laser beam at 10.6 µm as a function of distance from lens (Yariv, 1997).Initial spot radius at 1.0 mm and focal lengths of lens at 5 and 20 cm correspond to practical conditions used in our experiments.
For measuring the spatial distributions of electron density, evaluation of the spot radius of the CO 2 laser beam inside the tested plasma source is required.In order to measure the spatial distribution of electron density inside the high-pressure plasmas whose scale are usually below cm order, the CO 2 -laser beam has to be focused in μm order using a pair of ZnSe lens as shown in Fig. 1.Assuming that the laser beam is a Gaussian beam, we can calculate a profile of the beam spot radius along the laser path from the beam parameter and focal length of the ZnSe lens using an ABCD matrix analysis (Yariv, 1997).Figrue 4 shows the beam-radius profiles after the two kinds of ZnSe lens used in our experimental study.
The location and length of the tested plasma source and a scanning pitch of the laser beam should be determined by reference to these kinds of beam-profile evaluations.

Spatial distribution of electron density in high-pressure plasmas
Some of the specific measurement results of our CO 2 -laser heterodyne interferometer are introduced in this section.Influence of gas heating on detected phase-shift signals, spatial resolutions of the heterodyne interferometer, and the combination measurement method for AC-voltage driven APPs, will be discussed in addition to the measured electron-density distributions in the tested plasma sources.

Small-scale DC discharge at high pressure
A short hollow cathode (HC) discharge tube shown in Fig. 5(a) was used for basic experiments of our CO 2 -laser heterodyne interferometer system with variable pressure in pure He gas.The results can be good references to measurement of other plasmas operated at atmospheric pressure introduced in following subsections.Two electrodes for anode and cathode had a 2-mm bore and a 4-mm hole length, and these electrodes were separated by a 1.5-mm thick ceramic disk also having the 2-mm bore.Two of ZnSe windows were equipped to seal the discharge region and transmit the CO 2 laser beam.Gas pressure inside the small chamber was controlled in a range from several tens to hundreds Torr.shows dependences of electron density in the short HC discharge on the discharge current measured at several He gas pressures.In the calculation of electron density from the phase shift signal, we used two assumptions that the plasma was uniform along the CO 2 laser path and its effective length was 9.5 mm.The electron density in the discharge increased monotonically with the increase of the discharge current and the gas pressure.This result indicates that the CO 2 -laser heterodyne interferometer is able to measure appropriate dependence of electron density on the gas pressure, because the electron density inside the high-pressure plasma must be increased at higher pressure by the slower drift velocity of electrons due to frequent collisions with gas particles when the discharge current is the same as that at lower pressure.
Here, the minimum sensitivity of electron density in our CO 2 -laser heterodyne interferometer is introduced.The minimum electron density which we recorded in the short HC discharge was corresponds to a line integrated electron density n e d of 7×10 12 cm −2 with a detected phase shift around 0.1 degree (Choi et al., 2009).However, the signal to noise ratio, for instance shown in Fig. 3, showed that the minimum sensitivity should be at least six times better than that.Therefore, it could be estimated that the minimum detectable phase shift in our system was about 0.02 degree, corresponding to n e d of 1×10 12 cm −2 , which is much smaller than the minimum sensitivity of Stark broadening measurement (Laux et al, 2003).

Atmospheric-pressure DC discharge in open space
Figure 6(a) shows a schematic diagram of DC discharge in open space operated in a He gas flow ejected from a tubular cathode to a pin anode.The cylindrical tubular cathode, whose outer and inner diameters were 3.1 and 2.1 mm, and the pin anode with a 0.5-mm diameter were faced to the cathode with a 3-mm gap.The measurement point between the cathode and the anode was scanned by putting the whole discharge device on a three-dimensional mechanical movement stage.The influence of temporal evolutions of the gas-particle density on the measured phase shift can be seen in Fig. 6(b) showing the phase-shift signals observed in the atmospheric-pressure DC discharge using two different flow rates of He gas (1 and 2 L/min).This measurement result clearly suggests that the contribution of the Joule heating on temporal evolution of the phase shift becomes much greater in the discharge operated at atmospheric pressure and the gas-particle component in the phase shift, ΔΦ g , has large dependence on the gas flow velocity.The fast time constant and large amplitude of ΔΦ g in both rising and falling periods of applied voltage in lower gas flow rate was due to less cooling effect by neutral gas particles.
In order to obtain radial distributions of electron density in the high-pressure plasmas, which cannot be evaluated by photographic observations, spatial distributions of lineintegrated electron density and inverse Abel transformation of the distributions are required.This diagnostic method of radial distribution is also applied for excited species measurements in the high-pressure plasmas by a laser absorption spectroscopy (LAS) and a laser induced fluorescence (LIF) methods (Urabe et al., 2010).its continuity.Considering that electron density near the central axis of the gas flow was not different at both measurement points, there were some losing mechanisms of the electrons outside of the He gas flow where ambient air contaminates into the flow.The electron loss was mainly due to an electron attachment process with O 2 molecules presenting in the ambient air in the DC discharge, because of μm-order short diffusion lengths of electrons in the atmospheric-pressure gas conditions which could be derived from calculations of electron diffusion coefficient (Hargelaar & Pitchford, 2005) and measurement results of electron lifetime (Moselhy et al., 2003).Whereas this negative-ion density, for example O 2 - ions, cannot be detected by the CO 2 -laser heterodyne interferometer, this selectivity of negatively charged particles in the interferometer enables us to distinguish kinds and fractions of the negatively charged particle inside the high-pressure plasmas with the estimation of total amount of the charged particles from the discharge current amplitude.

Pulsed AC discharge at atmospheric pressure
For the measurement of electron density inside the high-pressure plasmas driven by kHzorder AC applied voltage, the temporal resolution of CO 2 -laser heterodyne interferometer using the lock-in amplifier is often insufficient for direct measurement of temporal evolutions of electron density.In order to depict spatiotemporal structures of electron density inside such plasma sources, for example dielectric barrier discharges (DBDs) (Kogelschatz, 2003;Becker et al., 2005) and ns-order short pulsed discharges (Namihira et al., 2003;Walsh & Kong, 2007), it has been confirmed that an amplitude modulation of the kHz-order applied voltage at a frequency of a few hundreds Hz and additional measurement of a millimeter-wave (mm-wave) transmission method are effective.
Figure 8(a) shows a schematic diagram of atmospheric-pressure glow discharge (APGD) tested in our group.The APGD is a major kind of DBDs generating homogeneous plasmas with atmospheric-pressure He gas and kHz-order AC applied voltage (Kanazawa et al., 1988).Powered (upper side) and grounded (lower side) stainless-steel electrodes were round, and their diameters were 60 mm.Dielectric barriers of 1-mm thick alumina were placed on the electrodes' surface and a gap distance between the two barriers was set at 6.0 mm.Whole electrode setup was installed in a vacuum chamber with a pair of ZnSe windows to control the gas compositions and pressures.In the measurement of APGD, we used a pair of ZnSe lens with longer focal length (20 cm), in order to get constant beam shape in whole discharge region with 60-mm length along the CO 2 laser path.Therefore, the spatial resolution of the interferometer was worse than the measurement of small-scale DC plasmas explained in above subsections.
To divide the phase-shift signal into two components of the electron and gas-particle densities in a similar way to that used for the small-scale DC discharges, we used a squarepulse amplitude modulation at 125 Hz for the 30-kHz AC applied voltage, whose modulation-signal waveform is shown in Fig. 8(b).Using this amplitude modulation, the temporal evolution of phase shift has the fall and rise slopes in the both ends of modulation signal similar to that in the measurement of pulsed DC discharges.However, in the measurement of AC discharge, the phase-shift signal at the start-up timing of applied voltage (around −3.5 ms in the abscissa axis of Fig. 8(b)) is unsuitable for the derivation of the electron-density component in the phase shift.At this timing, the signal associated with the electron density was smoothed by the step-wise increase due to intermittent discharges in the APGD, and the influence of this smoothing effect on the phase-shift signal could not be resolved.Therefore, the measured phase-shift waveform should be divided into two components only at the cut-off timing of applied voltage (around 0 ms in Fig. 8(b)).
Calculation procedure of the temporally-averaged electron density after dividing the two components is the same as the calculation in DC discharges.The electron-density distribution inside the APGD was localized near the dielectric barriers, and this result had a good agreement with reported results of computational simulations in similar geometries (Massines et al., 1998(Massines et al., , 2003;;Martens et al., 2009).The electron density near the powered electrode was approximately two times larger than that near the grounded electrode in each gas composition.This asymmetric distribution was probably caused by diffusion of the discharge current flow into the chamber wall from the powered electrode not flowing into the grounded electrode.
To get temporally resolved information of the electron density inside the APGD, we inserted a mm-wave at 55 GHz through the vacuum chamber and measured temporal evolutions of the transmitted mm-wave intensity using a pair of horn antennas.In this mm-wave transmission method, spatial distributions of electron density cannot be measured because of the diffraction limit of the mm-wave.Details of the experimental setup and the calculation procedure of spatially-averaged electron density are introduced in our previous paper (Urabe et al., 2011).The temporal evolution of spatially-averaged electron density in the APGD derived from absorption ratio of the mm-wave in the plasma is shown in Fig. 10, Fig. 9. Spatial distribution of electron-density component in phase shift and calculated temporally-averaged electron density in APGD (Urabe et al., 2011).Fig. 10.Temporal evolution of spatially-averaged electron density in APGD measured by mm-wave transmission method under same conditions as interferometer measurement (Fig. 9), together with applied-voltage waveform (Urabe et al., 2011).together with the waveform of applied voltage.The electron density increased after the positive-and negative-main pulses around 2.6 and 19.0 µs in the abscissa time axis, and there were small increases in electron density after the main pulses caused by weak discharges in the ringing part of applied voltage.
From the measurement results of the CO 2 -laser heterodyne interferometer and the mmwave transmission method applied to the same plasma source, spatial distribution of temporal-peak electron density can be calculated dividing the temporally-averaged electron densities by a duty ratio of plasma.The duty ratio of plasma is the ratio of temporallyaveraged electron density to temporal-peak density in the result of the mm-wave transmission measurement, and it indicates the temporally averaging effects of the CO 2laser heterodyne interferometer.In an example case of the APGD measurement shown in Figs. 9 and 10, the calculated duty ratio of plasma was 0.33.Then, the temporal-peak electron densities near the dielectric barriers were derived approximately 5×10 12 cm −3 on the side of the powered electrode and 2×10 12 cm −3 on the grounded electrode.

Concluding remarks
In this chapter, we reviewed experimental studies for electron-density measurement in small-scale plasmas operated at high and atmospheric pressures using the CO 2 -laser heterodyne interferometer, from brief theoretical introduction of the interferometer to specific measurement results in the high-pressure plasma sources.It should be noted that separation of the CO 2 laser beam's phase shift into two components, which are due to changes of electron and gas-particle densities, is the most important procedure for the measurement in high-pressure plasmas, and pulse modulation of applied voltage is indispensable for the separation at the rise and fall timings of the modulation signal.
From the experimental results of the interferometer in high-pressure plasmas driven by pulsed DC voltage, fundamental properties of our interferometer including the minimum sensitivity of line-integrated electron density and the spatial resolution could be evaluated.Because these properties are changed due to specifications of the laser source and the phase detecting system, they must be confirmed in each setup of the interferometer before practical measurements.In addition to the interferometer, a mmwave transmission method with a good temporal resolution was used to AC-voltage driven plasmas having ns-order fast temporal behavior.This novel combination method has potentials to be applied to the refractive-index measurements requiring both spatial and temporal high resolutions.

Acknowledgments
Our studies on the CO 2 -laser heterodyne interferometer were partially supported by Grantin-Aid for Scientific Research from the MEXT of Japan and Global Center of Excellence program on Photonics and Electronics Science and Engineering at Kyoto University.The authors would like to thank Prof. Osamu Sakai, Dr. Nobuhiko Takano, Dr. Joon-Young Choi, and Dr. Yosuke Ito at Kyoto University for their substantial supports.The author U.K. would like to acknowledge support of Research Fellowship from Japan Society for the Promotion of Science.
Measurement of Electron Density in High-Pressure Plasmas 215 Fig. 5. (a) Cross-sectional diagram and photograph of short hollow cathode (HC) discharge.(b) Dependence of electron density on discharge current in the short HC discharge in He gas at three values of gas pressure.
Figure 5(b)  shows dependences of electron density in the short HC discharge on the discharge current measured at several He gas pressures.In the calculation of electron density from the phase shift signal, we used two assumptions that the plasma was uniform along the CO 2 laser path and its effective length was 9.5 mm.The electron density in the discharge increased monotonically with the increase of the discharge current and the gas pressure.This result indicates that the CO 2 -laser heterodyne interferometer is able to measure appropriate dependence of electron density on the gas pressure, because the electron density inside the high-pressure plasma must be increased at higher pressure by the slower drift velocity of electrons due to frequent collisions with gas particles when the discharge current is the same as that at lower pressure.

Figure
Fig. 6.(a) Schematic diagram and photograph of atmospheric-pressure DC discharge in open space.(b) Temporal evolutions of phase-shift signal in the DC discharge measured changing He gas flow rate.Calculation results of the inverse Abel transformation corresponding to the radial distribution of electron density, n e (r), at the measurement points in the DC discharge are shown in Fig.7(b).The calculated radial distributions showed two different structures which were a hollow shape near the cathode and a center-peaked shape near the anode, having a good agreement with the electrode structures.The inverse Abel transformation was performed using a following equation(Lochte-Holtgreven, 1968),

Fig. 7 .
Fig. 7. (a) Spatial distributions of line-integrated electron density measured in DC plasma jet near tubular cathode and pin anode.(b) Radial distributions of electron density derived from line-integrated electron density using inverse Abel transformation(Choi et al., 2009).The calculated results in Fig.7(b) indicate that total amounts of the electrons near the cathode and the anode are significantly different in this DC discharge and there must be another kind of negatively charged particles delivering the discharge current and keeping Fig. 8. (a) Cross-sectional diagram of parallel-plate dielectric barrier discharge (DBD).(b) Example temporal evolution of phase shift by the parallel-plate DBD together with amplitude modulation signal of 30-kHz AC applied voltage (Urabe et al., 2011).The spatial distribution of the electron-density component in the phase shift and the calculated temporally-averaged electron density from the four signal waveforms measured under the same condition are shown in Fig. 9.The points and both ends of error bars indicate the averaged value and the maximum and minimum values in each measurement.The electron-density distribution inside the APGD was localized near the dielectric barriers, and this result had a good agreement with reported results of computational simulations in similar geometries(Massines et al., 1998(Massines et al., , 2003;;Martens et al., 2009).The electron density near the powered electrode was approximately two times larger than that near the Table 1 lists change directions of the phase shift in the CO 2 -laser heterodyne interferometer.