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The effect of ambient pressure on laser-induced plasmas in air
ARTICLE IN PRESS
Optics and Lasers in Engineering 45 (2007) 27–35
The effect of ambient pressure on laser-induced plasmas in air Nick Glumac, Greg Elliott University of Illinois, Urbana-Champaign, Urbana, 1206, West Green Street, Urbana ILL 61801, USA Received 2 February 2006; received in revised form 14 April 2006; accepted 18 April 2006 Available online 27 June 2006
Abstract A detailed investigation of the effect of ambient pressure in the range of 0.1 to 1.0 atm on the size, temperature, electron number density, and fraction of laser energy absorbed in a laser-induced plasma in air has been conducted. As pressure is reduced the size of the plasma, its electron number density, its peak emission intensity, and the fraction of incident laser energy that is absorbed are all found to decrease significantly. The temporal temperature profile in the plasma and the fraction of the absorbed laser energy that is converted to thermal energy in the plasma remain constant, at least down to 0.2 atm. r 2006 Elsevier Ltd. All rights reserved. Keywords: Laser spark; Pressure; LIBS
1. Introduction Laser-induced plasmas have potential applications in high speed flow control due to their fast response times and ability to generate flow perturbations at a relatively long distance from the source. Most previous fundamental studies of laser sparks in air have investigated the characteristics of a laser-induced plasma at or near atmospheric pressure. However, for applications involving aircraft, the static pressures involved will undoubtedly be significantly sub-atmospheric. Indeed, for high-speed applications, where laser-based flow control offers significant advantages for a variety of flow control applications [1], flight trajectories often involve high altitudes where pressures can be less than 0.1 atm. Thus, there is a clear need to investigate the role of ambient pressure on laser spark characteristics. To our knowledge, few if any previous studies have quantified the effect of sub-atmospheric pressure on a laser spark in air. There have been similar studies, however. Bindhu et al. [2] investigated the effect of pressure on the absorption and scattering of energy in a laser spark in argon. They found that the absorbed fraction of light decreased strongly with pressure, especially for lower laser Corresponding author. Fax: +1 217 333 1942.
E-mail address: [email protected] (N. Glumac). 0143-8166/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2006.04.002
pulse energies. At 100 Torr, the plasma absorbed only 15% of the laser energy from a 230 mJ pulse and less than 5% from a 100 mJ pulse, even though both pulses were more than 90% absorbed at atmospheric pressure. The investigators reported that pressure altered the size and shape of the spark as well, but no quantitative numbers on these characteristics were provided. There have been no previous studies that have looked at the effect of reducing the ambient pressure on the temporal development of spark temperature and electron number density. These quantities are critical in the validation of laser spark models that are used to examine the effect of such discharges on high-speed flows. In this work, we investigate experimentally the effect of ambient air pressure on the laser spark shape, size, and growth rate, on the temperature and electron number density, and on the fraction of laser energy that is absorbed and scattered. 2. Experimental apparatus and data processing The experimental setup for the laser spark experiments is a slight variant on the setup used for atmospheric pressure experiments [3]. In general, a 10 Hz, Q-switched, frequencydoubled, Nd:YAG laser (532 nm) with 7 ns pulse width is focused with 100 mm focal length lens to create a laser spark. To allow for control of the ambient pressure, the spark is centered inside a small environmental chamber
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shown schematically in Fig. 1. The chamber is a T-junction with an inner diameter in each arm of 3 cm.The setup allows light to be collected perpendicular to the laser axis at f/1, though we typically use f/5 for these experiments where signal strength is high. In addition, light that passes through the focal region without being absorbed passes through the bottom window of the chamber and is collected by a laser power meter. The pressure in the chamber is continuously monitored and held constant to better than 0.01 atm during a measurement. For spectroscopic measurements, we image the laser spark onto the slit of an f/4 270 mm focal length imaging spectrometer using a 30 mm inlet slit and 1200 gr/mm grating to obtain 2.7 nm/mm dispersion and 0.15 nm resolution at the exit plane. The detector is an intensified CCD camera (Roper PI-MAX) with a fiber-coupled, 512 512 pixel array of effectively 23 mm pixels. The detector can be gated to 4 ns. For the measurements reported here, the spectrum is obtained by binning the signal from the central 2.3 mm of the laser spark into a single spectrum. Yalcin et al. [4] have shown previously that there are very small axial spatial gradients over the center few mm of laser sparks at atmospheric pressure. Spectra are wavelength calibrated using neon lines and intensity corrected using a tungsten calibration lamp. Direct images were taken of the laser spark emission using the ICCD camera described previously, by viewing the region of interest perpendicular to the laser propagation direction. Two hundred instantaneous images were taken at each delay time and averaged together. In order to reduce the scattered laser light reflected from the chamber, and to protect the ICCD camera, a red filter was placed in front of the camera lens in addition to neutral density filters. The light was collected with a 50 mm f1.2 Nikor lens with extension rings placed between the lens and ICCD camera to increase the size of image recorded. The gate
532 nm laser beam Focussing lens Air in
To spectrometer and ICCD
Pressure Tap
widths and delay times of the emission images were identical to those used for the emission spectra measurements. Photometry measurement were made of the laser spark using a Thorlabs DES210 photodiode which collected the light through a 25.4 mm lens and red filter to reduce the scattering of the 532 nm laser light from the chamber. The photodiode was placed far enough from the laser spark so that the signal was not saturated, and no spatial information of the spark was resolved. The signal from the photodiode was recorded on an Agilent 54845A Infiniium 1.5 Ghz Oscilloscope. Sixty four instantaneous traces (triggered from the laser pulse) were averaged together. Spectroscopic measurements are processed to yield a single temperature and electron number density for a given gated exposure. The methodology for this process is described in [3]. In brief, we monitor a spectral region where only N II lines are present and which has a spectrum that is very sensitive to temperature over the 10,000– 60,000 K region. A spectral model assumes an equilibrium distribution of population in electronic states corresponding to a single temperature. The linewidth is assumed to be a convolution of Doppler and Stark broadening due to a single electron number density. Experimental broadening factors are used for the N II lines, and a linear dependence of Stark width and shift with Ne are assumed [5]. A spectral model fits each spectrum to a single temperature, electron number density, and optical depth. A global scaling parameter and two parameters associated with the (assumed linear) background are also determined in the fit. Our measurements at 1 atm agree well with other investigators (see [4,6]), and uncertainties for temperature and electron number density are approximately 10% and 50%, where the error is primarily systematic. For temperature, the source of systematic error is primarily the single-temperature assumption. Yalcin et al. [4] found that peak temperature measurements for laser sparks in 1 atm air were approximately 5% high when using the single-temperature assumption, as compared to the temperature extracted from spatially resolved, Abel-inverted data. For electron number density, the primary sources of systematic uncertainty are the estimated Stark width vs. Ne dependence that is specific for each line, and the single Ne assumption. Values of Stark width at a given condition (T and Ne) can vary considerably from study to study. In our case, since the fit averages over all 46 lines in the spectrum, the effect of error in any single line is minimized. 3. Results 3.1. Photometry and geometry of the laser spark
Air out
BK7 windows
Power meter Fig. 1. A schematic of the experimental setup.
For a fixed laser power of 180 mJ, the fraction of the laser pulse that is scattered and absorbed is shown in Fig. 2 over the pressure range of 0.1 to 1 atm. In good agreement with the Bindhu et al. [2] results in argon, the peak absorbed/scattered fraction is around 90%, while it is less
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2.50
1.0
P= 0.75 atm
2.00
P= 0.5 atm
0.8
Intensity [a.u.]
Fraction of Laser Power Absorbed & Scattered
P= 1.0 atm
0.6
P= 0.3 atm
1.50
P= 0.2 atm P= 0.1 atm
1.00
0.50
0.4 0.00 0
50
100 Time [ns]
0.2
Fig. 3. A photodiode time trace of the emission from the laser-induced spark in air over a range of chamber pressures at fixed laser energy of 180 mJ/pulse. Each trace represents the average of 512 instantaneous traces triggered from the initiating laser pulse.
0.0 0.0
0.2
0.4
0.6 Pressure (atm)
0.8
1.0
Fig. 2. Absorbed and scattered laser light versus pressure for a laser spark in air using a 100 mm focal length lens and a 180 mJ incident laser pulse. Peak Intensity [a.u.]
3 2.5 2 1.5 1 0.5 0 0
where t1/e is the 1/e decay time in ns and pch is the chamber pressure in atm. It should also be noted that the spark reaches its peak intensity slightly more quickly as the pressure is decreased (approximately 4.5 ns earlier for the 0.1 atm case compared to the 1 atm case). Fig. 6 shows images of the laser spark emission measured over a range of delay times from the initiating laser spark for the chamber pressures studied. The images are based on the average of 200 instantaneous images taken using the ICCD camera arrangement described previously with the same delay times and gate widths used in the emission
0.4
0.6 0.8 Pressure [atm]
1
1.2
120 100 80 60 40 20 0 0
(1)
0.2
Fig. 4. Peak emission of the emission from the laser-induced spark in air over a range of chamber pressures.
1/e Decay Time [ns]
than 5% at 0.1 atm. The dependence of absorbed/scattered fraction is slightly weaker than linear with pressure near ambient conditions, and has a stronger than linear dependence from 0.3 to 0.8 atm. For pressures lower than 0.3 atm, the pressure dependence slightly weakens again. Photometry measurements collected by the photodiode (as described previously) were made by viewing the laser spark 901 to the laser propagation direction. These experiments were conducted to quantify relative changes in emission intensity and decay rate as recorded by the photodiode as the air pressure is varied from 1 to 0.1 atm. Fig. 3 gives traces of the initiation and decay of the laser spark emission from 0 to 176 ns as recorded by the oscilloscope. Based on these traces the peak intensity and time for the signal to reach 1/e of the peak are given in Figs. 4 and 5, respectively, over the range of pressures. The peak intensity is relatively constant as the pressure is decreased from 1 to 0.75 atm, after which it decreases rapidly as illustrated in Fig. 4. The decay rate of the emission trace (quantified by the time from the initiation of the spark for the trace to reach 1/e of the peak intensity) is observed to decrease for all of the pressures taken. This decrease can be fit to a second-order polynomial given by t1=e ¼ 59:28p2ch þ 31:01pch þ 16:95,
200
150
0.2
0.4
0.6 Pressure [atm]
0.8
1
1.2
Fig. 5. Time for the emission from the laser-induced spark in air to decay to a level of 1/e of the peak intensity for a range of chamber pressures. The line represents a second-order polynomial given by Eq. (1).
spectrum measurements. The imaging regions shown in Fig. 6 have a physical height and width of 6.9 mm and 3.8 mm, respectively. All images shown here have been normalized by the peak intensity so that the shape over the entire spark evolutions can be displayed. First, it is observed that for all chamber pressures the spark reaches a bimodal appearance by 100 ns. Also observed is the fact
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N. Glumac, G. Elliott / Optics and Lasers in Engineering 45 (2007) 27–35
Fig. 6. Images of the evolution of the emission from the laser-induced spark in air for a range of chamber pressures (given to the left) and delay times from the initiating laser pulse. The images are based on the average of 200 instantaneous images for each delay time and the laser propagation direction is from the top to the bottom of the image.
that at higher pressures (1 atm) the breakdown initiates at a location slightly before the focal point of the lens with the region of highest emission propagating toward the incoming laser beam. As the pressure decreases below 0.5 atm, the laser spark originates from a central point and propagates both toward and away from the focal point, resulting in a larger total area of the spark and a bimodal structure. This change in the propagation characteristics of the emission with pressure has also been observed for laser sparks created in argon by Bindhu et al. [2] who suggest that this observation is evidence that multi-photon ioniza-
tion is dominant at lower pressures. Although the size of the spark appears to be qualitatively constant for chamber pressures ranging from 0.5 to 1.0 atm, as the pressure is reduced further the size of the spark decreases significantly. In order to quantify this observation, the spark boundary has been defined by the region enclosing all locations with local intensities greater than 20% of the peak intensity. Figs. 7–9 give the maximum length, maximum width, and volume (assuming an axisymmetric profile) of the spark boundary using this definition over the range of delay times and chamber pressures studied. The uncertainties of the
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Length [mm] 6
Length [mm]
5 4
P = 1.0 atm
3
P = 0.75 atm P = 0.5 atm
2
P = 0.3 atm 1
P = 0.2 atm
0 0
200
400 600 Time Delay [ns]
P = 0.1 atm 800 1000
Fig. 7. Maximum length of the laser spark measured from the area defined by the region of the spark enclosed by 20% of the peak emission for each time delay. Each curve represents a different chamber pressure at a fixed incident laser energy of 180 mJ.
Width [mm]
3
Width [mm]
2.5 2 P = 1.0 atm 1.5
P = 0.75 atm
1
P = 0.5 atm P = 0.3 atm
0.5
P = 0.2 atm 0 0
200
400
600
P = 0.1 atm 800 1000
Time Delay [ns]
Fig. 8. Maximum width of the laser spark measured from the area defined by the region of the spark enclosed by 20% of the peak emission for each time delay. Each curve represents a different chamber pressure at a fixed incident laser energy of 180 mJ.
P = 1.0 atm
P = 0.75 atm
P = 0.5 atm
P = 0.3 atm
P = 0.2 atm
P = 0.1 atm
18 16
Volume [mm3]
14 12 10 8 6 4 2 0 0
200
400 600 Time Delay [ns]
800
1000
Fig. 9. Volume of the laser spark as defined by the portion of the spark enclosed by 20% of the peak emission and assuming an axisymmetric profile about the propagation direction for each time delay. Each curve represents a different chamber pressure at a fixed incident laser energy of 180 mJ.
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length and width measurements are estimated to be 70.05 mm (2 pixels). As observed in all of the spark dimension figures the length, width, and volume of the spark remain relatively constant for chamber pressures ranging from 0.5 to 1.0 atm (although the dimensions are slightly larger for 0.75 and 0.5 atm cases due to the change in shape of the spark from atmospheric conditions). However, as the pressure is lowered below 0.5 atm all size and volume parameters decrease rapidly. 3.2. Emission spectra-based measurements Though the spectra taken at different pressures showed the same set of spectral lines, the general appearance of the spectra and their time dependence varied significantly with pressure. At atmospheric pressure, the development of the emission spectra was reported in [3]. At roughly 50 ns after the laser pulse, N II peaks emerge from the continuum and can be fit to a temperature. Linewidths become smaller as time progresses and the Ne becomes smaller. As pressure is reduced, the linewidths are also clearly reduced at each respective time interval. Fig. 10 shows a series of plots for different pressures at identical times using the same incident laser power. It can be seen in the plots that for all pressures and times, the fits are generally good, indicating no extremely large departure from a Boltzmann distribution. Quantitative values of the temperature and electron number density are extracted from the spectra and presented in Figs. 11 and 12. Fig. 11 shows the temperature data for the first microsecond after the laser pulse. Considering the 10% uncertainty, the calculated temperatures for pressures of 0.2 to 1 atm agree very well from 150 ns to 1 ms. Between 50 and 150 ns there appears to be a slight increase in temperature with pressure though the 10% error bars at 0.2 and 1 atm just overlap. As was noted in [3] optical depth effects are strongest for times earlier than 150 ns, and optical depth effects tend to result in higher fit temperatures. Though our model fits the spectra to optical depth, the uncertainty in this particular fit parameter is fairly high. If the correction is not strong enough, then the fit temperature will be too high. As pressure is decreased, optical depth becomes smaller and the correction is not important. Therefore, it is quite possible that the small discrepancy in temperatures at very early times is an artifact of the optical depth correction in the spectral fit. At 0.1 atm, there appears to be a significant deviation from the temporal temperature profile of the higher pressure cases. For all times, the 0.1 atm temperatures were the lowest measured. By 400 ms, the temperature was 7000 K (25%) below the estimated temperatures from the other 5 pressures. Beyond 400 ns, the N II lines were no longer strong enough to obtain temperatures for the lowest pressure case. Electron number density versus time plots for the six pressures are shown in Fig. 12. The decline in Ne for all
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1.0 Atm 75 ns
1.0 Atm 400 ns
25640 K Fit Experiment
Intensity (arb. units)
41360 K Fit Experiment
495
500
505
510
0.2 Atm 75 ns
515
520
500
505
510
0.2 Atm 400 ns
515
520
26450 K Fit Experiment
Intensity (arb. units)
39490 K Fit Experiment
495
495
500
505 510 Wavelength (nm)
515
520
495
500
505 510 Wavelength (nm)
515
520
Fig. 10. Representative spectra and fits from two ambient pressures (1.0 atm—top, and 0.2 atm—bottom), at two delay times (75 ns—left and 400 ns— right).
50000
19.0
1.0 Atm 0.75 Atm 0.5 Atm 0.3 Atm 0.2 Atm 0.1 Atm
45000 40000
1.0 atm 0.75 atm 0.5 atm 0.3 atm 0.2 atm 0.1 atm
18.8 18.6
Log [Ne (cm-3)]
Temperature (K)
18.4 35000 30000 25000
18.2 18.0 17.8 17.6
20000
17.4 15000
17.2 17.0
10000 0
200
400
600 Time (ns)
800
1000
100
1000 Time (ns)
Fig. 11. Spectral fit temperature versus time after the laser pulse for six pressure cases at a fixed incident laser energy of 180 mJ/pulse.
Fig. 12. Electron number density versus time for six pressure cases at a fixed incident laser energy of 180 mJ/pulse.
times with pressure is quite apparent. Indeed the value of Ne at a 50 ns delay is more than an order of magnitude smaller at 0.1 atm than at 1 atm. A less obvious observation is the faster decay of the electron number density with time.
The decay curves can be fit to an expression of the form Ne ¼ Atn. Simple electron–ion recombination at constant temperature would suggest an exponent of n ¼ 1. At atmospheric pressure this exponent is slightly larger
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than 1 (0.9570.2 at 1 atm). As the pressure is reduced, the exponent decreases, suggesting relatively faster recombination of electrons. At 0.3 atm the exponent is 1.027.03, and at 0.2 atm it is 1.117.05. For all of the above comparisons, the incident laser power was kept constant while the pressure was varied. Some of the changes in electron number density can be attributed to the change in absorbed laser energy. To isolate this effect from other effects, we compared cases at 1 and 0.3 atm where the absorbed laser power was identical (40 mJ) in this case. We also compared these two cases with the case of 1 atm with full power incident and 160 mJ absorbed. Temperature and electron number density results are shown in Figs. 13 and 14. As expected, the observed temperature is not strongly dependent on either
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absorbed energy at a given pressure or on pressure for a given absorbed energy. All temperatures are well within the 10% uncertainty at each time for the three cases. However, the results for electron number density are more striking, as shown in Fig. 14. At 1 atm, as power is reduced fourfold, electron number density declines only slightly—in agreement with the results of Yalcin et al. [4]. However, when comparing the 1 atm case and 0.3 atm case, both with 40 mJ absorbed, the decrease in electron number density with pressure is strong. At 50 ns, the 1 atm, 40 mJ absorbed case shows a reduction of 20% in electron number density over the 1 atm, 160 mJ absorbed case, but the 0.3 atm, 40 mJ absorbed case shows a 66% reduction in Ne as compared to the full power 1 atm case. At 400 ns, the reductions are 28% and 80%, respectively. Clearly, the strong effect of pressure on electron number density is not simply due to a reduced absorbed energy fraction.
50000 1.0 atm, 160 mJ Absorbed 0.3 atm, 40 mJ Absorbed 1.0 atm, 40 mJ Absorbed
45000
Temperature (K)
40000 35000 30000 25000 20000 15000 10000 0
200
400
600 Time (ns)
800
1000
1200
Fig. 13. Temperature versus time for three cases: 1 atm, 160 mJ absorbed; 1 atm, 40 mJ absorbed; and 0.3 atm, 40 mJ absorbed.
1e+19
Ne (cm-3)
1.0 atm, 160 mJ Absorbed 0.3 atm, 40 mJ Absorbed 1.0 atm, 40 mJ Absorbed
1e+18
1e+17 100
1000 Time (ns)
Fig. 14. Electron number density versus time for three cases: 1 atm, 160 mJ absorbed; 1 atm, 40 mJ absorbed; and 0.3 atm, 40 mJ absorbed.
4. Discussion Of the results presented above, perhaps the least surprising is the reduction in absorbed/scattered energy fraction with pressure. Since the electromagnetic field at the laser focus is, to first order, independent of the number density of the gas, we can envision the laser focus as a constant volume region of space. More absorbers in that volume (i.e. higher density at higher pressures) will lead to larger absorbed fractions—as we observe. Though the dependence is not exactly linear, it does not deviate a great deal from the linear behavior, suggesting that the largest effect on the reduction in absorbed energy is initial number density. A secondary effect, which may be the reason for the deviation from linearity, is the transition in the mode of plasma generation from a cascade process to a multiphoton ionization, as suggested by Bindhu et al. [2]. However, further study would be required, with a focus on very early time behavior (i.e. during the laser pulse) in order to evaluate this assertion. Of possible importance is the fraction of light that is absorbed versus that which is scattered in these power measurements. The power meter only detects light along the axis of the incident laser beam, though the collection solid angle of the power meter covers a region larger than the expected beam diameter at that point. Certainly some fraction of light is scattered by the neutral molecules and ions, as well as by the electrons (i.e. Thompson scattering). In addition, there may be some steering of the beam off the incident axis. The fraction lost to scattering and steering is not expected to be large, in light of the relatively weak nature of scattering processes and the degree of steering that would be required for rays to miss the detector. However, we cannot quantify this fraction, and dramatic change in this fraction with pressure would lead to a slightly different interpretation of the results than we present below. The relative independence of spark temperature versus time, despite large differences in electron number density, is
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another important result of this work. With the possible exception of the lowest pressure (0.1 atm), there is no difference to within experimental uncertainty of any variation in temperature from 50 to 1000 ns over the pressure range investigated. In addition, there is no evidence of a strong variation of temperature with input laser power, in agreement with the results of Yalcin et al. [4]. Bergel’son et al. [7] presented a simple model of the laser breakdown process in which the strong temperature dependence of the plasma radiative power (T4) led to a relatively weak dependence of the plasma temperature on incident laser power of roughly TpI0.18 L . In addition, the Bergel’son model predicts that the effects of initial density cancel in the calculation of the plasma temperature, leading to a plasma temperature that is independent of initial density. Both of these predictions are consistent with our observations. The observation of lower temperatures at very low pressures (0.1 atm) may indicate the beginning of a region in which the Bergel’son model is no longer as applicable, but further study is required to verify this possibility. It is worth noting that there are other more recent works that predict and/or measure the peak plasma temperature in a laser spark (e.g. [8,9]) and suggest that there is an explicit temperature dependence on laser intensity. Ref. [8] suggests an exponent n in TpIn of 0.5, while Ref. [9] suggests that the exponent varies with optical depth from 2/3 to 1. In addition, the peak temperatures are predicted to be greater than 100,000 K. These relations cover the earliest times of the laser plasma, before significant cooling has occurred. Our temperature measurements span the temporal region later than 50 ns after the laser pulse, when line emission can be used as a diagnostic. Thus, our work cannot be used to validate the models used in [8,9]. However, our results do indicate that for times longer than 50 ns after the laser pulse, a strong laser energy dependence on temperature is not observed and that, if peak plasma temperatures are indeed above 100,000 K, then significant cooling must be occurring within the first 50 ns period after breakdown. The dependence of the electron number density on pressure is very strong, while the dependence on absorbed laser power is much weaker. In fact, if we normalize the electron number densities at each time interval by the Ne at 1 atm (see Fig. 15), the ratio varies approximately linearly with ambient pressure, suggesting that the plasma number density—at least for the period of 50 to1000 ns—scales roughly linearly with initial density for constant input laser energy. However, if we consider the weak but significant dependence of Ne on absorbed laser power, then we observe a slightly weaker dependence. Using the data from Fig. 14, we can compare two cases at 1 and 0.3 atm (a reduction in pressure of a factor of 3.33); one with constant input laser energy and the second with constant absorbed laser energy. In the former case, the reduction in Ne (averaged over the 10 time intervals) is a factor of 3.877.65—in good agreement with a linear dependence.
1.0
0.8 Ne/Ne(1 atm)
34
0.6
0.4 50 ns 100 ns 200 ns 400 ns
0.2
0.0 0.0
0.2
0.4 0.6 0.8 Ambient Pressure (atm)
1.0
Fig. 15. Electron number density for different times from the laser pulse, normalized by the electron number density for the 1 atm case. The line is a 1:1 reference.
In the latter case, however, the reduction in Ne is a factor of 2.737.39. Thus, for a fixed absorbed laser energy, the reduction in electron number density is slightly weaker than linear with ambient density. Though the absorbed laser energy for a fixed input laser energy clearly decreases with pressure as shown in Fig. 2, it is useful to estimate whether the distribution of that energy into various channels remains constant. The work of Phuoc [10] at atmospheric pressure suggested that the absorbed laser energy is primarily directed into the shock wave (51–70% of the absorbed energy), radiative emission to the surroundings (22–34%), and thermal energy in the plasma (7–8%). Since the plasma becomes more optically thin as ambient pressure is reduced, the resistance to radiative losses from the plasma is reduced, and thus we might expect the radiative loss term to increase with ambient pressure. The increase in radiative decay rate with a decrease in pressure (Fig. 5) would further suggest that radiative losses are enhanced at low pressure. However, the magnitude of change in these terms is difficult to estimate. We can, however, obtain a relative measure of the plasma thermal energy from our results. Assuming that the temperature at each time interval for each pressure is the same (e.g. Fig. 11), then at a given time the energy per unit mass of the plasma (uplasma) will be the same for every pressure. If this is true, then the total energy in the plasma is proportional to the gas density times the plasma volume. For times of few hundred nanoseconds, Phuoc has suggested that the pressure has returned to the ambient value in the plasma region. Thus we can estimate that the plasma energy at a given time interval is proportional to the plasma volume (V) times the ambient pressure (Po) as follows: (for fixed T) E plasma ¼ mplasma uplasma ðTÞ ¼ rVuplasma ðTÞ ¼
P Vuplasma ðTÞ / Po V , RT
(2)
ARTICLE IN PRESS N. Glumac, G. Elliott / Optics and Lasers in Engineering 45 (2007) 27–35 0.007 400 ns delay
Pambient Vplasma/Eabsorbed
0.006 0.005 0.004 0.003 0.002 0.001
100 ns delay
0.000 0.0
0.2
0.4 0.6 0.8 Ambient Pressure (atm)
1.0
1.2
Fig. 16. Thermal energy in the plasma divided by the absorbed laser energy, as a function of ambient pressure.
A relative measure of the fraction of absorbed energy that goes into the plasma can be obtained by dividing PoV by the absorbed energy Eabs. If the same fraction of energy is partitioned into thermal energy in the plasma, then the ratio PoV/Eabs should be independent of pressure at a given time delay. Utilizing the estimated plasma volume given in Fig. 9 we can plot the ratio PoV/Eabs, over the range of pressures studied (Fig. 16). The plot shows that, within the fairly large uncertainties for the measurements and assumptions given here, there does not appear to be significant evidence that the fraction of absorbed laser energy that goes into heating the plasma is dependent on pressure—except possibly at the very lowest pressure. 5. Conclusions A detailed investigation of the effect of ambient pressure over the range of 0.1 to 1.0 atm on a laser spark in air has been performed. The major conclusions of this study are as follows: (1) For a fixed input laser energy, the energy absorbed by the gas decreases with pressure. The decrease in absorption is slightly stronger than linear over the probed pressure range. At 0.1 atm, less than 5% of the incident laser energy is absorbed. (2) As pressure is reduced, the spark size and peak emission intensity decrease, but the temporal spark temperature profile remains fairly constant for pressures of 0.2–1.0 atm and times from 50 ns to 1 ms after the laser pulse. (3) At reduced pressures, the decay of intensity in the laser spark after breakdown is markedly faster than at atmospheric pressure, most likely due to a reduced optical depth in the plasma.
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(4) Electron number density in the plasma also decreases roughly linearly with ambient pressure for fixed input laser energy and slightly less than linearly for fixed absorbed laser energy. (5) From 0.2 to 1.0 atm the fraction of the laser power that is partitioned into the thermal energy of the plasma remains fairly constant, though an exact value for this fraction cannot be derived from this work. (6) There is evidence at the lowest pressure studied (0.1 atm) that the constant temperature profile trend and the constant energy fraction in the plasma both may be breaking down. Further studies in this regime are warranted.
Acknowledgements The authors would like to thank AFOSR with Dr. John Schmisseur for funding this work on energy deposition utilizing laser-induced optical breakdown (FA9550-040177). Any opinions, findings and conclusions or recommendations expressed in the material are those of the authors and do not necessarily reflect the views of AFOSR. Additionally we would like to thank our colleagues Prof. Doyle Knight, Prof. Graham Candler, Dr. Hong Yan, and Ramnath Kandala for their discussions and input regarding this work.
References [1] Knight D, Kuchinskiy V, Kuranov A, Sheikin E. Survey of aerodynamic flow control at high speed by energy deposition. AIAA Paper 2003–0525, 2003. [2] Bindhu CV, Harilal SS, Tillack MS, Najmabadi F, Gaeris AC. Laser propagation and energy absorption by an argon spark. J Appl Phys 2003;94:7402–7. [3] Glumac N, Elliott G, Boguszko M. Temporal and Spatial Evolution of the Thermal Structure of a Laser Spark in Air. AIAA J 2005;43:1984–94. [4] Yalcin S, Crosley DR, Smith GP, Faris GW. Influence of ambient conditions on the laser air spark. Appl Phys B 1999;68:121–30. [5] Hermann J, Boulmer-Leborgne C, Hong D. Diagnostics of the early phase of an ultraviolet laser induced plasma by spectral line analysis considering self absorption. J Appl Phys 1998;83:691–6. [6] Radziemski LJ, Loree TR, Cremers DA, Hoffman NM. Timeresolved Laser-Induced Breakdown Spectrometry of Aerosols. Anal Chem 1983;55:1246–52. [7] Bergel’son VI, Loseva TV, Nemichinov, Orlova TI. Propagation of plane supersonic radiation waves. Sov J Plasma Phys 1975;1: 498–503. [8] Chen YL, Lewis JWL, Parigger C. Spatial and temporal profiles of pulsed laser-induced air plasma emissions. JQSRT 2000;67:91–103. [9] Phuoc TX. Laser-induced spark ignition fundamental and applications. Opt Lasers Eng 2006;44:351–97. [10] Phuoc TX. An experimental and numerical study of laser-induced spark in air. Opt Lasers Eng 2005;43:113–29.
Optics and Lasers in Engineering 45 (2007) 27–35
The effect of ambient pressure on laser-induced plasmas in air Nick Glumac, Greg Elliott University of Illinois, Urbana-Champaign, Urbana, 1206, West Green Street, Urbana ILL 61801, USA Received 2 February 2006; received in revised form 14 April 2006; accepted 18 April 2006 Available online 27 June 2006
Abstract A detailed investigation of the effect of ambient pressure in the range of 0.1 to 1.0 atm on the size, temperature, electron number density, and fraction of laser energy absorbed in a laser-induced plasma in air has been conducted. As pressure is reduced the size of the plasma, its electron number density, its peak emission intensity, and the fraction of incident laser energy that is absorbed are all found to decrease significantly. The temporal temperature profile in the plasma and the fraction of the absorbed laser energy that is converted to thermal energy in the plasma remain constant, at least down to 0.2 atm. r 2006 Elsevier Ltd. All rights reserved. Keywords: Laser spark; Pressure; LIBS
1. Introduction Laser-induced plasmas have potential applications in high speed flow control due to their fast response times and ability to generate flow perturbations at a relatively long distance from the source. Most previous fundamental studies of laser sparks in air have investigated the characteristics of a laser-induced plasma at or near atmospheric pressure. However, for applications involving aircraft, the static pressures involved will undoubtedly be significantly sub-atmospheric. Indeed, for high-speed applications, where laser-based flow control offers significant advantages for a variety of flow control applications [1], flight trajectories often involve high altitudes where pressures can be less than 0.1 atm. Thus, there is a clear need to investigate the role of ambient pressure on laser spark characteristics. To our knowledge, few if any previous studies have quantified the effect of sub-atmospheric pressure on a laser spark in air. There have been similar studies, however. Bindhu et al. [2] investigated the effect of pressure on the absorption and scattering of energy in a laser spark in argon. They found that the absorbed fraction of light decreased strongly with pressure, especially for lower laser Corresponding author. Fax: +1 217 333 1942.
E-mail address: [email protected] (N. Glumac). 0143-8166/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2006.04.002
pulse energies. At 100 Torr, the plasma absorbed only 15% of the laser energy from a 230 mJ pulse and less than 5% from a 100 mJ pulse, even though both pulses were more than 90% absorbed at atmospheric pressure. The investigators reported that pressure altered the size and shape of the spark as well, but no quantitative numbers on these characteristics were provided. There have been no previous studies that have looked at the effect of reducing the ambient pressure on the temporal development of spark temperature and electron number density. These quantities are critical in the validation of laser spark models that are used to examine the effect of such discharges on high-speed flows. In this work, we investigate experimentally the effect of ambient air pressure on the laser spark shape, size, and growth rate, on the temperature and electron number density, and on the fraction of laser energy that is absorbed and scattered. 2. Experimental apparatus and data processing The experimental setup for the laser spark experiments is a slight variant on the setup used for atmospheric pressure experiments [3]. In general, a 10 Hz, Q-switched, frequencydoubled, Nd:YAG laser (532 nm) with 7 ns pulse width is focused with 100 mm focal length lens to create a laser spark. To allow for control of the ambient pressure, the spark is centered inside a small environmental chamber
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shown schematically in Fig. 1. The chamber is a T-junction with an inner diameter in each arm of 3 cm.The setup allows light to be collected perpendicular to the laser axis at f/1, though we typically use f/5 for these experiments where signal strength is high. In addition, light that passes through the focal region without being absorbed passes through the bottom window of the chamber and is collected by a laser power meter. The pressure in the chamber is continuously monitored and held constant to better than 0.01 atm during a measurement. For spectroscopic measurements, we image the laser spark onto the slit of an f/4 270 mm focal length imaging spectrometer using a 30 mm inlet slit and 1200 gr/mm grating to obtain 2.7 nm/mm dispersion and 0.15 nm resolution at the exit plane. The detector is an intensified CCD camera (Roper PI-MAX) with a fiber-coupled, 512 512 pixel array of effectively 23 mm pixels. The detector can be gated to 4 ns. For the measurements reported here, the spectrum is obtained by binning the signal from the central 2.3 mm of the laser spark into a single spectrum. Yalcin et al. [4] have shown previously that there are very small axial spatial gradients over the center few mm of laser sparks at atmospheric pressure. Spectra are wavelength calibrated using neon lines and intensity corrected using a tungsten calibration lamp. Direct images were taken of the laser spark emission using the ICCD camera described previously, by viewing the region of interest perpendicular to the laser propagation direction. Two hundred instantaneous images were taken at each delay time and averaged together. In order to reduce the scattered laser light reflected from the chamber, and to protect the ICCD camera, a red filter was placed in front of the camera lens in addition to neutral density filters. The light was collected with a 50 mm f1.2 Nikor lens with extension rings placed between the lens and ICCD camera to increase the size of image recorded. The gate
532 nm laser beam Focussing lens Air in
To spectrometer and ICCD
Pressure Tap
widths and delay times of the emission images were identical to those used for the emission spectra measurements. Photometry measurement were made of the laser spark using a Thorlabs DES210 photodiode which collected the light through a 25.4 mm lens and red filter to reduce the scattering of the 532 nm laser light from the chamber. The photodiode was placed far enough from the laser spark so that the signal was not saturated, and no spatial information of the spark was resolved. The signal from the photodiode was recorded on an Agilent 54845A Infiniium 1.5 Ghz Oscilloscope. Sixty four instantaneous traces (triggered from the laser pulse) were averaged together. Spectroscopic measurements are processed to yield a single temperature and electron number density for a given gated exposure. The methodology for this process is described in [3]. In brief, we monitor a spectral region where only N II lines are present and which has a spectrum that is very sensitive to temperature over the 10,000– 60,000 K region. A spectral model assumes an equilibrium distribution of population in electronic states corresponding to a single temperature. The linewidth is assumed to be a convolution of Doppler and Stark broadening due to a single electron number density. Experimental broadening factors are used for the N II lines, and a linear dependence of Stark width and shift with Ne are assumed [5]. A spectral model fits each spectrum to a single temperature, electron number density, and optical depth. A global scaling parameter and two parameters associated with the (assumed linear) background are also determined in the fit. Our measurements at 1 atm agree well with other investigators (see [4,6]), and uncertainties for temperature and electron number density are approximately 10% and 50%, where the error is primarily systematic. For temperature, the source of systematic error is primarily the single-temperature assumption. Yalcin et al. [4] found that peak temperature measurements for laser sparks in 1 atm air were approximately 5% high when using the single-temperature assumption, as compared to the temperature extracted from spatially resolved, Abel-inverted data. For electron number density, the primary sources of systematic uncertainty are the estimated Stark width vs. Ne dependence that is specific for each line, and the single Ne assumption. Values of Stark width at a given condition (T and Ne) can vary considerably from study to study. In our case, since the fit averages over all 46 lines in the spectrum, the effect of error in any single line is minimized. 3. Results 3.1. Photometry and geometry of the laser spark
Air out
BK7 windows
Power meter Fig. 1. A schematic of the experimental setup.
For a fixed laser power of 180 mJ, the fraction of the laser pulse that is scattered and absorbed is shown in Fig. 2 over the pressure range of 0.1 to 1 atm. In good agreement with the Bindhu et al. [2] results in argon, the peak absorbed/scattered fraction is around 90%, while it is less
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2.50
1.0
P= 0.75 atm
2.00
P= 0.5 atm
0.8
Intensity [a.u.]
Fraction of Laser Power Absorbed & Scattered
P= 1.0 atm
0.6
P= 0.3 atm
1.50
P= 0.2 atm P= 0.1 atm
1.00
0.50
0.4 0.00 0
50
100 Time [ns]
0.2
Fig. 3. A photodiode time trace of the emission from the laser-induced spark in air over a range of chamber pressures at fixed laser energy of 180 mJ/pulse. Each trace represents the average of 512 instantaneous traces triggered from the initiating laser pulse.
0.0 0.0
0.2
0.4
0.6 Pressure (atm)
0.8
1.0
Fig. 2. Absorbed and scattered laser light versus pressure for a laser spark in air using a 100 mm focal length lens and a 180 mJ incident laser pulse. Peak Intensity [a.u.]
3 2.5 2 1.5 1 0.5 0 0
where t1/e is the 1/e decay time in ns and pch is the chamber pressure in atm. It should also be noted that the spark reaches its peak intensity slightly more quickly as the pressure is decreased (approximately 4.5 ns earlier for the 0.1 atm case compared to the 1 atm case). Fig. 6 shows images of the laser spark emission measured over a range of delay times from the initiating laser spark for the chamber pressures studied. The images are based on the average of 200 instantaneous images taken using the ICCD camera arrangement described previously with the same delay times and gate widths used in the emission
0.4
0.6 0.8 Pressure [atm]
1
1.2
120 100 80 60 40 20 0 0
(1)
0.2
Fig. 4. Peak emission of the emission from the laser-induced spark in air over a range of chamber pressures.
1/e Decay Time [ns]
than 5% at 0.1 atm. The dependence of absorbed/scattered fraction is slightly weaker than linear with pressure near ambient conditions, and has a stronger than linear dependence from 0.3 to 0.8 atm. For pressures lower than 0.3 atm, the pressure dependence slightly weakens again. Photometry measurements collected by the photodiode (as described previously) were made by viewing the laser spark 901 to the laser propagation direction. These experiments were conducted to quantify relative changes in emission intensity and decay rate as recorded by the photodiode as the air pressure is varied from 1 to 0.1 atm. Fig. 3 gives traces of the initiation and decay of the laser spark emission from 0 to 176 ns as recorded by the oscilloscope. Based on these traces the peak intensity and time for the signal to reach 1/e of the peak are given in Figs. 4 and 5, respectively, over the range of pressures. The peak intensity is relatively constant as the pressure is decreased from 1 to 0.75 atm, after which it decreases rapidly as illustrated in Fig. 4. The decay rate of the emission trace (quantified by the time from the initiation of the spark for the trace to reach 1/e of the peak intensity) is observed to decrease for all of the pressures taken. This decrease can be fit to a second-order polynomial given by t1=e ¼ 59:28p2ch þ 31:01pch þ 16:95,
200
150
0.2
0.4
0.6 Pressure [atm]
0.8
1
1.2
Fig. 5. Time for the emission from the laser-induced spark in air to decay to a level of 1/e of the peak intensity for a range of chamber pressures. The line represents a second-order polynomial given by Eq. (1).
spectrum measurements. The imaging regions shown in Fig. 6 have a physical height and width of 6.9 mm and 3.8 mm, respectively. All images shown here have been normalized by the peak intensity so that the shape over the entire spark evolutions can be displayed. First, it is observed that for all chamber pressures the spark reaches a bimodal appearance by 100 ns. Also observed is the fact
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N. Glumac, G. Elliott / Optics and Lasers in Engineering 45 (2007) 27–35
Fig. 6. Images of the evolution of the emission from the laser-induced spark in air for a range of chamber pressures (given to the left) and delay times from the initiating laser pulse. The images are based on the average of 200 instantaneous images for each delay time and the laser propagation direction is from the top to the bottom of the image.
that at higher pressures (1 atm) the breakdown initiates at a location slightly before the focal point of the lens with the region of highest emission propagating toward the incoming laser beam. As the pressure decreases below 0.5 atm, the laser spark originates from a central point and propagates both toward and away from the focal point, resulting in a larger total area of the spark and a bimodal structure. This change in the propagation characteristics of the emission with pressure has also been observed for laser sparks created in argon by Bindhu et al. [2] who suggest that this observation is evidence that multi-photon ioniza-
tion is dominant at lower pressures. Although the size of the spark appears to be qualitatively constant for chamber pressures ranging from 0.5 to 1.0 atm, as the pressure is reduced further the size of the spark decreases significantly. In order to quantify this observation, the spark boundary has been defined by the region enclosing all locations with local intensities greater than 20% of the peak intensity. Figs. 7–9 give the maximum length, maximum width, and volume (assuming an axisymmetric profile) of the spark boundary using this definition over the range of delay times and chamber pressures studied. The uncertainties of the
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Length [mm] 6
Length [mm]
5 4
P = 1.0 atm
3
P = 0.75 atm P = 0.5 atm
2
P = 0.3 atm 1
P = 0.2 atm
0 0
200
400 600 Time Delay [ns]
P = 0.1 atm 800 1000
Fig. 7. Maximum length of the laser spark measured from the area defined by the region of the spark enclosed by 20% of the peak emission for each time delay. Each curve represents a different chamber pressure at a fixed incident laser energy of 180 mJ.
Width [mm]
3
Width [mm]
2.5 2 P = 1.0 atm 1.5
P = 0.75 atm
1
P = 0.5 atm P = 0.3 atm
0.5
P = 0.2 atm 0 0
200
400
600
P = 0.1 atm 800 1000
Time Delay [ns]
Fig. 8. Maximum width of the laser spark measured from the area defined by the region of the spark enclosed by 20% of the peak emission for each time delay. Each curve represents a different chamber pressure at a fixed incident laser energy of 180 mJ.
P = 1.0 atm
P = 0.75 atm
P = 0.5 atm
P = 0.3 atm
P = 0.2 atm
P = 0.1 atm
18 16
Volume [mm3]
14 12 10 8 6 4 2 0 0
200
400 600 Time Delay [ns]
800
1000
Fig. 9. Volume of the laser spark as defined by the portion of the spark enclosed by 20% of the peak emission and assuming an axisymmetric profile about the propagation direction for each time delay. Each curve represents a different chamber pressure at a fixed incident laser energy of 180 mJ.
31
length and width measurements are estimated to be 70.05 mm (2 pixels). As observed in all of the spark dimension figures the length, width, and volume of the spark remain relatively constant for chamber pressures ranging from 0.5 to 1.0 atm (although the dimensions are slightly larger for 0.75 and 0.5 atm cases due to the change in shape of the spark from atmospheric conditions). However, as the pressure is lowered below 0.5 atm all size and volume parameters decrease rapidly. 3.2. Emission spectra-based measurements Though the spectra taken at different pressures showed the same set of spectral lines, the general appearance of the spectra and their time dependence varied significantly with pressure. At atmospheric pressure, the development of the emission spectra was reported in [3]. At roughly 50 ns after the laser pulse, N II peaks emerge from the continuum and can be fit to a temperature. Linewidths become smaller as time progresses and the Ne becomes smaller. As pressure is reduced, the linewidths are also clearly reduced at each respective time interval. Fig. 10 shows a series of plots for different pressures at identical times using the same incident laser power. It can be seen in the plots that for all pressures and times, the fits are generally good, indicating no extremely large departure from a Boltzmann distribution. Quantitative values of the temperature and electron number density are extracted from the spectra and presented in Figs. 11 and 12. Fig. 11 shows the temperature data for the first microsecond after the laser pulse. Considering the 10% uncertainty, the calculated temperatures for pressures of 0.2 to 1 atm agree very well from 150 ns to 1 ms. Between 50 and 150 ns there appears to be a slight increase in temperature with pressure though the 10% error bars at 0.2 and 1 atm just overlap. As was noted in [3] optical depth effects are strongest for times earlier than 150 ns, and optical depth effects tend to result in higher fit temperatures. Though our model fits the spectra to optical depth, the uncertainty in this particular fit parameter is fairly high. If the correction is not strong enough, then the fit temperature will be too high. As pressure is decreased, optical depth becomes smaller and the correction is not important. Therefore, it is quite possible that the small discrepancy in temperatures at very early times is an artifact of the optical depth correction in the spectral fit. At 0.1 atm, there appears to be a significant deviation from the temporal temperature profile of the higher pressure cases. For all times, the 0.1 atm temperatures were the lowest measured. By 400 ms, the temperature was 7000 K (25%) below the estimated temperatures from the other 5 pressures. Beyond 400 ns, the N II lines were no longer strong enough to obtain temperatures for the lowest pressure case. Electron number density versus time plots for the six pressures are shown in Fig. 12. The decline in Ne for all
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1.0 Atm 75 ns
1.0 Atm 400 ns
25640 K Fit Experiment
Intensity (arb. units)
41360 K Fit Experiment
495
500
505
510
0.2 Atm 75 ns
515
520
500
505
510
0.2 Atm 400 ns
515
520
26450 K Fit Experiment
Intensity (arb. units)
39490 K Fit Experiment
495
495
500
505 510 Wavelength (nm)
515
520
495
500
505 510 Wavelength (nm)
515
520
Fig. 10. Representative spectra and fits from two ambient pressures (1.0 atm—top, and 0.2 atm—bottom), at two delay times (75 ns—left and 400 ns— right).
50000
19.0
1.0 Atm 0.75 Atm 0.5 Atm 0.3 Atm 0.2 Atm 0.1 Atm
45000 40000
1.0 atm 0.75 atm 0.5 atm 0.3 atm 0.2 atm 0.1 atm
18.8 18.6
Log [Ne (cm-3)]
Temperature (K)
18.4 35000 30000 25000
18.2 18.0 17.8 17.6
20000
17.4 15000
17.2 17.0
10000 0
200
400
600 Time (ns)
800
1000
100
1000 Time (ns)
Fig. 11. Spectral fit temperature versus time after the laser pulse for six pressure cases at a fixed incident laser energy of 180 mJ/pulse.
Fig. 12. Electron number density versus time for six pressure cases at a fixed incident laser energy of 180 mJ/pulse.
times with pressure is quite apparent. Indeed the value of Ne at a 50 ns delay is more than an order of magnitude smaller at 0.1 atm than at 1 atm. A less obvious observation is the faster decay of the electron number density with time.
The decay curves can be fit to an expression of the form Ne ¼ Atn. Simple electron–ion recombination at constant temperature would suggest an exponent of n ¼ 1. At atmospheric pressure this exponent is slightly larger
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than 1 (0.9570.2 at 1 atm). As the pressure is reduced, the exponent decreases, suggesting relatively faster recombination of electrons. At 0.3 atm the exponent is 1.027.03, and at 0.2 atm it is 1.117.05. For all of the above comparisons, the incident laser power was kept constant while the pressure was varied. Some of the changes in electron number density can be attributed to the change in absorbed laser energy. To isolate this effect from other effects, we compared cases at 1 and 0.3 atm where the absorbed laser power was identical (40 mJ) in this case. We also compared these two cases with the case of 1 atm with full power incident and 160 mJ absorbed. Temperature and electron number density results are shown in Figs. 13 and 14. As expected, the observed temperature is not strongly dependent on either
33
absorbed energy at a given pressure or on pressure for a given absorbed energy. All temperatures are well within the 10% uncertainty at each time for the three cases. However, the results for electron number density are more striking, as shown in Fig. 14. At 1 atm, as power is reduced fourfold, electron number density declines only slightly—in agreement with the results of Yalcin et al. [4]. However, when comparing the 1 atm case and 0.3 atm case, both with 40 mJ absorbed, the decrease in electron number density with pressure is strong. At 50 ns, the 1 atm, 40 mJ absorbed case shows a reduction of 20% in electron number density over the 1 atm, 160 mJ absorbed case, but the 0.3 atm, 40 mJ absorbed case shows a 66% reduction in Ne as compared to the full power 1 atm case. At 400 ns, the reductions are 28% and 80%, respectively. Clearly, the strong effect of pressure on electron number density is not simply due to a reduced absorbed energy fraction.
50000 1.0 atm, 160 mJ Absorbed 0.3 atm, 40 mJ Absorbed 1.0 atm, 40 mJ Absorbed
45000
Temperature (K)
40000 35000 30000 25000 20000 15000 10000 0
200
400
600 Time (ns)
800
1000
1200
Fig. 13. Temperature versus time for three cases: 1 atm, 160 mJ absorbed; 1 atm, 40 mJ absorbed; and 0.3 atm, 40 mJ absorbed.
1e+19
Ne (cm-3)
1.0 atm, 160 mJ Absorbed 0.3 atm, 40 mJ Absorbed 1.0 atm, 40 mJ Absorbed
1e+18
1e+17 100
1000 Time (ns)
Fig. 14. Electron number density versus time for three cases: 1 atm, 160 mJ absorbed; 1 atm, 40 mJ absorbed; and 0.3 atm, 40 mJ absorbed.
4. Discussion Of the results presented above, perhaps the least surprising is the reduction in absorbed/scattered energy fraction with pressure. Since the electromagnetic field at the laser focus is, to first order, independent of the number density of the gas, we can envision the laser focus as a constant volume region of space. More absorbers in that volume (i.e. higher density at higher pressures) will lead to larger absorbed fractions—as we observe. Though the dependence is not exactly linear, it does not deviate a great deal from the linear behavior, suggesting that the largest effect on the reduction in absorbed energy is initial number density. A secondary effect, which may be the reason for the deviation from linearity, is the transition in the mode of plasma generation from a cascade process to a multiphoton ionization, as suggested by Bindhu et al. [2]. However, further study would be required, with a focus on very early time behavior (i.e. during the laser pulse) in order to evaluate this assertion. Of possible importance is the fraction of light that is absorbed versus that which is scattered in these power measurements. The power meter only detects light along the axis of the incident laser beam, though the collection solid angle of the power meter covers a region larger than the expected beam diameter at that point. Certainly some fraction of light is scattered by the neutral molecules and ions, as well as by the electrons (i.e. Thompson scattering). In addition, there may be some steering of the beam off the incident axis. The fraction lost to scattering and steering is not expected to be large, in light of the relatively weak nature of scattering processes and the degree of steering that would be required for rays to miss the detector. However, we cannot quantify this fraction, and dramatic change in this fraction with pressure would lead to a slightly different interpretation of the results than we present below. The relative independence of spark temperature versus time, despite large differences in electron number density, is
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another important result of this work. With the possible exception of the lowest pressure (0.1 atm), there is no difference to within experimental uncertainty of any variation in temperature from 50 to 1000 ns over the pressure range investigated. In addition, there is no evidence of a strong variation of temperature with input laser power, in agreement with the results of Yalcin et al. [4]. Bergel’son et al. [7] presented a simple model of the laser breakdown process in which the strong temperature dependence of the plasma radiative power (T4) led to a relatively weak dependence of the plasma temperature on incident laser power of roughly TpI0.18 L . In addition, the Bergel’son model predicts that the effects of initial density cancel in the calculation of the plasma temperature, leading to a plasma temperature that is independent of initial density. Both of these predictions are consistent with our observations. The observation of lower temperatures at very low pressures (0.1 atm) may indicate the beginning of a region in which the Bergel’son model is no longer as applicable, but further study is required to verify this possibility. It is worth noting that there are other more recent works that predict and/or measure the peak plasma temperature in a laser spark (e.g. [8,9]) and suggest that there is an explicit temperature dependence on laser intensity. Ref. [8] suggests an exponent n in TpIn of 0.5, while Ref. [9] suggests that the exponent varies with optical depth from 2/3 to 1. In addition, the peak temperatures are predicted to be greater than 100,000 K. These relations cover the earliest times of the laser plasma, before significant cooling has occurred. Our temperature measurements span the temporal region later than 50 ns after the laser pulse, when line emission can be used as a diagnostic. Thus, our work cannot be used to validate the models used in [8,9]. However, our results do indicate that for times longer than 50 ns after the laser pulse, a strong laser energy dependence on temperature is not observed and that, if peak plasma temperatures are indeed above 100,000 K, then significant cooling must be occurring within the first 50 ns period after breakdown. The dependence of the electron number density on pressure is very strong, while the dependence on absorbed laser power is much weaker. In fact, if we normalize the electron number densities at each time interval by the Ne at 1 atm (see Fig. 15), the ratio varies approximately linearly with ambient pressure, suggesting that the plasma number density—at least for the period of 50 to1000 ns—scales roughly linearly with initial density for constant input laser energy. However, if we consider the weak but significant dependence of Ne on absorbed laser power, then we observe a slightly weaker dependence. Using the data from Fig. 14, we can compare two cases at 1 and 0.3 atm (a reduction in pressure of a factor of 3.33); one with constant input laser energy and the second with constant absorbed laser energy. In the former case, the reduction in Ne (averaged over the 10 time intervals) is a factor of 3.877.65—in good agreement with a linear dependence.
1.0
0.8 Ne/Ne(1 atm)
34
0.6
0.4 50 ns 100 ns 200 ns 400 ns
0.2
0.0 0.0
0.2
0.4 0.6 0.8 Ambient Pressure (atm)
1.0
Fig. 15. Electron number density for different times from the laser pulse, normalized by the electron number density for the 1 atm case. The line is a 1:1 reference.
In the latter case, however, the reduction in Ne is a factor of 2.737.39. Thus, for a fixed absorbed laser energy, the reduction in electron number density is slightly weaker than linear with ambient density. Though the absorbed laser energy for a fixed input laser energy clearly decreases with pressure as shown in Fig. 2, it is useful to estimate whether the distribution of that energy into various channels remains constant. The work of Phuoc [10] at atmospheric pressure suggested that the absorbed laser energy is primarily directed into the shock wave (51–70% of the absorbed energy), radiative emission to the surroundings (22–34%), and thermal energy in the plasma (7–8%). Since the plasma becomes more optically thin as ambient pressure is reduced, the resistance to radiative losses from the plasma is reduced, and thus we might expect the radiative loss term to increase with ambient pressure. The increase in radiative decay rate with a decrease in pressure (Fig. 5) would further suggest that radiative losses are enhanced at low pressure. However, the magnitude of change in these terms is difficult to estimate. We can, however, obtain a relative measure of the plasma thermal energy from our results. Assuming that the temperature at each time interval for each pressure is the same (e.g. Fig. 11), then at a given time the energy per unit mass of the plasma (uplasma) will be the same for every pressure. If this is true, then the total energy in the plasma is proportional to the gas density times the plasma volume. For times of few hundred nanoseconds, Phuoc has suggested that the pressure has returned to the ambient value in the plasma region. Thus we can estimate that the plasma energy at a given time interval is proportional to the plasma volume (V) times the ambient pressure (Po) as follows: (for fixed T) E plasma ¼ mplasma uplasma ðTÞ ¼ rVuplasma ðTÞ ¼
P Vuplasma ðTÞ / Po V , RT
(2)
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Pambient Vplasma/Eabsorbed
0.006 0.005 0.004 0.003 0.002 0.001
100 ns delay
0.000 0.0
0.2
0.4 0.6 0.8 Ambient Pressure (atm)
1.0
1.2
Fig. 16. Thermal energy in the plasma divided by the absorbed laser energy, as a function of ambient pressure.
A relative measure of the fraction of absorbed energy that goes into the plasma can be obtained by dividing PoV by the absorbed energy Eabs. If the same fraction of energy is partitioned into thermal energy in the plasma, then the ratio PoV/Eabs should be independent of pressure at a given time delay. Utilizing the estimated plasma volume given in Fig. 9 we can plot the ratio PoV/Eabs, over the range of pressures studied (Fig. 16). The plot shows that, within the fairly large uncertainties for the measurements and assumptions given here, there does not appear to be significant evidence that the fraction of absorbed laser energy that goes into heating the plasma is dependent on pressure—except possibly at the very lowest pressure. 5. Conclusions A detailed investigation of the effect of ambient pressure over the range of 0.1 to 1.0 atm on a laser spark in air has been performed. The major conclusions of this study are as follows: (1) For a fixed input laser energy, the energy absorbed by the gas decreases with pressure. The decrease in absorption is slightly stronger than linear over the probed pressure range. At 0.1 atm, less than 5% of the incident laser energy is absorbed. (2) As pressure is reduced, the spark size and peak emission intensity decrease, but the temporal spark temperature profile remains fairly constant for pressures of 0.2–1.0 atm and times from 50 ns to 1 ms after the laser pulse. (3) At reduced pressures, the decay of intensity in the laser spark after breakdown is markedly faster than at atmospheric pressure, most likely due to a reduced optical depth in the plasma.
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(4) Electron number density in the plasma also decreases roughly linearly with ambient pressure for fixed input laser energy and slightly less than linearly for fixed absorbed laser energy. (5) From 0.2 to 1.0 atm the fraction of the laser power that is partitioned into the thermal energy of the plasma remains fairly constant, though an exact value for this fraction cannot be derived from this work. (6) There is evidence at the lowest pressure studied (0.1 atm) that the constant temperature profile trend and the constant energy fraction in the plasma both may be breaking down. Further studies in this regime are warranted.
Acknowledgements The authors would like to thank AFOSR with Dr. John Schmisseur for funding this work on energy deposition utilizing laser-induced optical breakdown (FA9550-040177). Any opinions, findings and conclusions or recommendations expressed in the material are those of the authors and do not necessarily reflect the views of AFOSR. Additionally we would like to thank our colleagues Prof. Doyle Knight, Prof. Graham Candler, Dr. Hong Yan, and Ramnath Kandala for their discussions and input regarding this work.
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