Laser Absorption Measurements of Electron Density in Nanosecond-ScaleAtmospheric Pressure Pulsed Plasmas
LLaser Absorption Measurements of Electron Density in Nanosecond-ScaleAtmospheric Pressure Pulsed Plasmas
T.Yong, A.I.Abdalla, and M.A. Cappelli a) Stanford Plasma Physics Laboratory, Department of Mechanical Engineering, Stanford CA,94305-3032
We report on time-resolved measurements of electron number density by continuous-wave laser absorption in a low-energy nanosecond-scale laser-produced spark in atmospheric pressure air. Laser absorption is a result of free-freeand bound-free electron excitation, with the absorption coefficient modeled and evaluated using estimates of the time-variation in electron temperature and probe laser absorption path length. Plasma electron number densities are deter-mined to be as high as n e = × cm − , and decay to 1 / e of their peak values over a period of about 50 ns followingplasma formation using a 20 mJ, 10 ns pulse width frequency-doubled Nd:YAG laser. The measured plasma densi-ties at later times are shown to be in reasonable agreement with Stark broadening measurements of the 3s[ S o ]-3p[ P ]electronic transition in atomic oxygen at 777 nm. This study provides support for the use of such continuous wavelaser absorption for time resolved electron density measurements in low energy spark discharges in air, provided thatan estimate of the electron temperature and laser path length can be made by accompanying diagnostics. I. INTRODUCTION
Current-driven and laser-driven discharges of short dura-tion and relatively low energy ( <
100 mJ) in reactive gasesor liquids, i.e., of tens of nanoseconds or less, have attractedconsiderable attention because they afford the ability to se-lectively heat electrons leading to desirable chemical kineticswhile reducing the degree of background gas heating . Suchlow-energy nanosecond-scale plasmas generated in gases athigh pressure conditions have been studied for several appli-cations, such as gas reforming , flow actuation , plasma-assisted combustion , and biomedical treatment . The ap-propriate plasma for a particular application is determined bya number of parameters, most important of which are the elec-tron density and temperature ( n e and T e ). The peak electrondensities in these plasmas can reach extremely high valuesas the gas is significantly ionized prior to which significantexpansion of the plasma can occur. A convenient means ofmeasuring these parameters at these high pressures is indis-pensable to the understanding of the kinetics but presents achallenge especially for n e above 10 cm − .More common methods to measure n e in plasmas in-clude the use of Langmuir probes , interferometry , Thom-son scattering (TS) , and Stark broadening of spectral lineemission . Langmuir probes are relatively straightforwardin their implementation but can be perturbing of the plasma forplasma scales comparable to the probe size and the collectedcurrent is difficult to interpret in collisional conditions. Thom-son scattering, particularly collective TS (CTS) , is a power-ful diagnostic tool that can provide good spatial resolution,but its implementation requires an expertise and equipmentthat is often not available to researchers outside of plasma dis-ciplinary areas. Interferometry, while less demanding thanTS in its implementation by comparison, is also a diagnos-tic that is not often used outside of traditional plasma re-search laboratories. Optical emission spectroscopy (OES), on a) Author to whom correspondence should be addressed: [email protected] the other hand, is widely accessible to non-experts in plas-mas. OES is often used to identify species present throughtheir spectral signatures and the broadening of atomic con-stituent spectral lines due to interactions with free electronsand ions (Stark broadening ) constitutes a relatively straight-forward way to measure the electron density. However, at veryhigh plasma densities, spectral lines may experience interfer-ences with neighboring lines, blend into the continuum , orsome are lost altogether due to the lowering of the ioniza-tion potential . In nanosecond-scale discharges at high pres-sures, this precludes the measurements at early times whenthe plasma densities are quite high but has provided infor-mation on the later recombination kinetics of the plasmas .Furthermore, self-absorption may become important at highpressures, greatly distorting the spectral profiles .This paper reports on time-resolved measurements of n e ina low-energy nanosecond-scale high pressure (1 atm) plasmaby continuous-wave (cw) laser absorption. The cw laser isattenuated as a result of free-free and bound-free excitationof the free and bound electrons, respectively. This methodhas been used successfully in the past as an electron densitydiagnostic . Its development in our laboratory is intendedfor measurements of the time-dependent evolution and decayof n e in a nanosecond pulse discharge plasma which we, andothers, have used for studying chemistry and electron-drivenkinetics in reactive gases, and nanosecond scale laser dis-charge plasmas used in plasma-assisted combustion . Dur-ing the initial tens of nanoseconds, high pressure plasmas aresufficiently optically thick to absorb visible light . Using afast (sub-nanosecond resolution) and sensitive photodetector,Beer’s law allows the extraction of the plasma absorption co-efficient, κ , provided an estimate of the path length throughthe plasma can be made. As described below, n e can be de-termined through a comparison to the absorption coefficientpredicted theoretically. The drawback of this measurement,like most absorption-based diagnostics, is that it is a line-of-sight average. Also, an accurate determination of n e requiresan estimate of the electron temperature, T e . The great advan-tage of the measurement is that it is relatively simple in itsimplementation and particularly applicable to these high den- a r X i v : . [ phy s i c s . p l a s m - ph ] F e b FIG. 1. (a) Schematic diagram of the experiment. (b) Representative streak image of the plasma emission. The pulsed Nd:YAG laser entersfrom the right. The slit to the streak camera is parallel to the direction of the incoming pulsed laser. sity and relatively small plasmas. At lower plasma densities(e.g., below 10 cm − ), the absorption is tenuous, requiringa relatively large-scale plasma for good signal-to-noise ratios.Below, we describe the bread-boarding of this laser absorp-tion measurement on a pulsed laser-produced plasma in air atatmospheric pressure. Such laser-sparks are rich in the spatial-temporal structure, as shown in the study of Harilal et al. ,and even more recently, in the computational and experimen-tal studies by a team at the University of Illinois . Forlaser absorption measurements we use a simple helium-neon(HeNe) laser of low (1 mW) power. For later times in theplasma evolution we compare the measured n e to that deter-mined from time-resolved Stark broadening of the 3s[ S o ]-3p[ P ] transition in atomic oxygen (OI) centered at a wave-length of approximately 777 nm. The absorption measure-ments of n e make use of previous measurements of T e in sim-ilar laser produced plasma sparks . These previous measure-ments are consistent with an estimate for our plasma basedon the absolute intensity and spectral variation in the back-ground continuum over a broad region in the visible range ofthe spectrum. The electron density measurement also makesuse the computed transverse plasma kernel dimensions pre-sented recently by Alberti et al. As shown below, the plas-mas formed by focusing the frequency-doubled output from aNd:YAG laser of modest power into air reach a peak electrondensity in excess of 5 × cm − and temperatures of ≈ ≈
100 nsduration of the luminous plasma. These electron temperaturesare also found to be consistent with measured shift-to-widthratios of the OI 777 nm spectral line emission from the centralregion of the plasma. Imaging of the evolution of the plasmaalong a direction coincident with the ionizing laser using astreak camera provides insight into its shape, and translatingthe image of the camera slit along a direction transverse to thelaser path provides an experimental estimate of the size of theplasma along the direction of the HeNe probe beam at a time ≈
20 ns, when the plasma is most luminous.
II. EXPERIMENT
The experimental set up is illustrated schematically in Fig1(a). The 15 Hz pulsed output of a frequency-doubled (532nm) Nd:YAG laser (Gemini PIV 15, New wave research) witha 10 ns pulse duration (FWHM) and 20 mJ pulse energy isused to produce a laser-breakdown plasma kernel in air. The5 mm diameter laser beam is focused using a 50 mm focallength plano convex lens to an image distance of 54 mm. Thefiring of the laser is triggered by the 15 Hz TTL output from apulse delay generator (SRS model DG535), which also sup-plies a second TTL pulse to trigger the various plasma di-agnostics hardware. The laser absorption is carried out witha continuous wave (cw) 632.8 nm HeNe probe laser (5mW,Melles Griot), 1 mm in diameter, focused through the laser-breakdown plasma at an image distance of 120 mm using a100 mm focal length plano convex lens to a beam waist ofapproximately 40 µ m. The precise location of the focus ofthe probe beam within the plasma is varied to maximize itsabsorption using a 3-axis micrometer stage on which the fo-cusing lens is mounted. The transmitted probe beam is thenre-focused using a second 150 mm focal length lens onto afast photodiode detector (DET025AL, Thorlabs) which hasa 400-1100 nm spectral range sensitivity and a 150 ps tem-poral resolution. The detector has a built-in lens which fo-cuses the beam onto its active region, 250 µ m in size. Us-ing a micrometer stage on the focusing lens the transmittedbeam is centered onto the active area of the photodiode. Thetime-varying voltage output of the photodiode is recorded onan oscilloscope, the trace of which is triggered by a secondoutput from the delay generator and averaged (typically overfour Nd:YAG laser shots). A narrow pass band filter (centeredat 632 nm) is placed between the plasma and the photodiodedetector to minimize interference from the bright, broadbandplasma emission. Residual plasma emission still detected bythe photodiode is corrected for by recording its small contri-bution with the HeNe laser blocked. As described below, fora typical laser breakdown plasma the HeNe probe laser is at-tenuated by as much as 65%.Time-resolved evolution of the spatial distribution ofwavelength-integrated plasma emission along the dimensioncoincident with the Nd:YAG laser propagation is recorded us-ing a streak camera (Hamamatsu Streakscope Model C4334).The camera is capable of streaking over as small a temporalwindow of 1 ns with a 2 ps resolution. The streak camera isalso triggered by the same delay generator that is used to trig-ger the photodiode and Nd:YAG laser. The plasma emissionis imaged onto the horizontal entrance slit (parallel to the di-rection of the pulsed laser-forming plasma) using a 100 mmfocal length and 26 mm diameter plano-convex lens to a mag-nification of 0.6 resulting in an estimated spatial resolution of4.3 µ m. In a typical experiment, the emission is streaked overa period 50 ns with 100 ps resolution. A neutral density filter(0.5 stopping power) is used at the entrance of the streak cam-era to prevent saturation. A representative streak is shown inFig. 1(b). Here, the laser arrives from the right hand side. Thestreak shows an initial rapid expansion of the plasma, whichis brightest on both the incoming and trailing side of the laser,qualitatively similar to the results of Nishihara et al . In someexperiments, the streak camera is coupled to the output of anoptical monochromator (Hamamatsu Model C5094 1/4-m fo-cal length, f/d = 4). The monochromater collects the emis-sion using fibre-coupled optics to image the plasma onto its50 µ m vertical entrance slit. A fibre lens assembly serves toimage the plasma emission onto the horizontal entrance slit ofthe streak camera which is mounted to the exit plane of themonochromator. The lens assembly is adjusted to optimizethe signal, imaging the brightest (and hence hottest) region ofthe plasma. The streak camera sweeps the spectral emissionover a spectral window of 20 nm. This allows the recording ofthe Stark-broadened OI line at 777 nm. For results describedhere, the spectra are streaked over a period of 100 ns time du-ration with 200 ps time resolution. In both cases, the collec-tion optics is aligned such that the image of the streak cameraentrance slit is coincident with the centerline of the incidentNd:YAG laser. Finally, for an estimate of the electron temper-ature, we image the the brightest region of the plasma usingoptical fiber coupling onto the entrance of a compact opticalspectrometer (Ocean Optics), calibrated for absolute and rela-tive spectral response. However, the compact monochromatoraverages the signal over a 1 ms time window. The resultingspectra are therefore more representative of an average overthe period of strongest (and presumably highest temperature)emission typically, 50-100 ns in duration. To estimate the ab-solute intensity of the continuum, we correct the spectrometersignal for the ratio of the plasma duration to spectrometer in-tegration time. III. RESULTS
A representative temporal photodiode signal from the cwHeNe probe laser is shown as a dashed black line in Fig. 2(a).In a separate shot, with the probe laser blocked, we recordthe broadband plasma emission on the same photodiode (solidred line, expanded by 8 × ) to correct the probe laser tracefor background interference, which causes the inflection seennear the onset of the drop in the transmitted probe laser signal.It is noteworthy that the peak in the plasma emission occursapproximately 8 ns before the maximum attenuation in theprobe laser signal suggesting that for early times, the plasma isbrightest before reaching its most strongly ionized state. Theemission-corrected probe laser signal, I , is the solid blue linein Fig. 2(a). In the corrected signal, we see that the onset ofthe attenuation is monotonic, as expected. It is apparent thatthe plasma becomes quite opaque with a maximum attenua-tion in the probe laser of about 65%. The temporal variationin the transmission in probe laser intensity, T = I / I o , allowsus to determine the plasma absorption coefficient, κ , throughBeer’s law, κ = − L ln (cid:18) II o (cid:19) . (1)Here, I o is the probe laser intensity (proportional to therecorded photodiode signal) in the absence of the absorbingplasma and L is the path length traversed by the probe throughthe plasma, which varies in time as the plasma forms andexpands. A representative plasma absorption coefficient (at632.8 nm) is shown as the red line in Fig. 2(b). Qualitatively,we see that the plasma is most opaque between approximately10 and 20 ns, representing the period in time when the plasmais most dense as the attenuation is a consequence of electronfree-free and bound-free absorption. An analyses of absorp-tion data based on experimental and computational measure-ments of electron temperature and probe laser path length pro-vides determination of the electron number density. In ourstudies, the path length is estimated at a time when the plasmaemission is most luminous, i.e., at ≈ L ≈ , theshape of the plasma varies considerably. In the first ≈
30 nsthe plasma kernel increases quickly in size as a result of laserheating and expansion, and less so at later times due to theincreasing importance of plasma recombination. We also in-clude in Fig. 2(b) the transverse plasma size, L ( t ) , at its widestlocation, using a fit to the computational data of Alberti et al .In general, absorption by the free electrons in the plasmaincludes contributions to the absorption coefficient frombound-bound transitions ( κ bb ), bound-free (electron-ion)interactions ( κ eib f ), as well as free-free electron-ion ( κ eif f )and electron-neutral ( κ enf f ) interactions. The total spectralabsorption coefficient for these interactions can be expressedas: Time (ns) P ho t od i ode s i gna l ( V ) -3 Measured He-Ne laserMeasured plasma emission(x8)Corrected HeNe laser
Time (ns) A b s o r p t i on C oe ff i c i en t ( m - ) -5 T r an sv e r s e p l a s m a s i z e ( m ) FIG. 2. (left) Representative photodiode signal recording transmission through the plasma (dashed black curve), corrected for plasma emission(red curve) recorded with the HeNe laser blocked (solid blue curve). (right) Resulting absorption coefficient (red curve) and a fit to the largesttransverse dimension of the plasma kernel as computed in the study of Alberti et al (blue curve). κ = κ bb + κ eib f + κ eif f + κ enf f . (2)The spectral absorption coefficients can be obtained fromavailable theoretical expressions for the corresponding spec-tral emission coefficients, ε ( λ ) , using Kirchoff’s Law, ε ( λ ) κ ( λ ) = B λ ( λ , T ) = hc λ (cid:16) hc λ kT e (cid:17) − B λ is the spectral energy radiance of a black-body. Ex-pressed in this way, h , c , λ , and k , represent Planck’s constant,the speed of light in vacuum, wavelength, and the Boltzmannconstant, respectively. We assume that free and bound statesare redistributed by collisions with free electrons at a temper-ature, T e , as over this short period of time, we expect the elec-trons to be hotter than the heavy particle temperature as littleelectron-ion energy transfer will take place. Since we expectthe ionization fraction to be high and that free electron-ion in-teractions are much stronger than free electron-neutral atominteractions , we take as a consequence, κ eif f >> κ enf f This assumption will be revisited and examined in thediscussion in Sec. IV. The laser probe wavelength (632.8 nm)is relatively free of nearby bound-bound transitions in laserplasma sparks in air so we take κ bb ≈
0. The correspondingremaining contributions to the spectral emission coefficientare obtained from Venugopalan , ε eif f ( λ ) = ∑ s C n e n s λ T e z s (cid:20) G s exp (cid:18) − hc λ kT e (cid:19)(cid:21) ε eif b ( λ ) = ∑ s C n e n s λ T e z s · g s , U s ( T e ) (cid:20) ξ s (cid:18) − exp (cid:18) − hc λ kT e (cid:19)(cid:19)(cid:21) (4)where C = . × − Wm K sr − . Here, z s , g s , and U s ( T e ) represent the charge, ground-state degeneracy andpartition function of the of s − ionic species, and the summa-tion extends over the ionized species in the air mixture. Theparameters, G s and ξ s are the Gaunt and Bieberman factorsthat account for non-hydrogenic effects which are speciesdependent. The Gaunt factors, G s , are taken to be approxi-mately unity regardless of species, which is seen to be a goodapproximation for a broad range of electron energy ( kT e ) andincident photon wavelength expected in our studies . Onthe other hand, ξ s can vary substantially with the ion speciesand while there are estimates of its value for atomic ions,there are very few studies on its determination for molecularions. In the studies of Bibermann et al., ξ s ranges from about0.5 to 1.5 for a number of atomic ions . We use this rangeof values for estimating the bound-free contribution to thetotal absorption, assuming that the most abundant ionizedspecies is singly-ionized atomic nitrogen ( N + ), consistentwith the studies of Orriere et al . This assumption reducesthe summation in Eq.(4) to a single contribution from N + ,and the absorption coefficient becomes: Temperature (eV) F a c t o r s -3 -2 -1 f ff f fb with =0.5f fb with =1.0f fb with =1.5 FIG. 3. Contributing factors of free-bound and free-free transitionsto the total absorption coefficient for N + taken to be the dominantion in the plasma. Bound-free factors are evaluated for a range ofBiberman factors. κ ( λ ) = C n e λ hc T e × (cid:20) − exp (cid:18) − hc λ kT e (cid:19) + ξ N + g N + , U N + (cid:18) cosh (cid:18) − hc λ kT e (cid:19) − (cid:19)(cid:21) (5)Studies of similar pulsed laser-produced air sparks havereported n e ≈ × cm − and T e ≈ f f f ) andits dependence on T e is shown in blue in Fig. 3, whereas themulti-colored lines are that for the bound-free factor (secondterm in parenthesis, f b f ), for a range of Biberman factors. Forthese calculations, we use the N + partition function tabulatedby Capitelli et al. We see that for temperatures below ≈ N + at the higherend of the temperature range.Since the absorption coefficient is sensitive to T e , an esti-mate of the electron temperature is beneficial, including its Time (ns) E l e c t r on T e m pe r a t u r e ( e V ) T e =2 eVT e =4 eV FIG. 4. Temporal variation in electron temperature of a laser-produced spark. The blue line represents a fit to the experimentaldata of Borghese . Also shown as the horizontal red lines representthe lower and upper values for our electron temperature estimatedfrom continuum measurements averaged over the duration of strongplasma emission. temporal variation. For similar laser-produced plasmas in air,the temporal variations in T e have been reported . It tendsto peak at values of T e ≈ T e ≈
1- 2 eV over a range of about 100 ns. As we have not mea-sured the temporal variations in T e for our plasmas we usethe measurements reported by to reduce our measured time-resolved absorption coefficients to electron number density. Areproduction of this temperature variation with time is shownin Fig. 4. As a check on this data, we have carried out mea-surements of time-averaged relative and absolute continuumemission for comparison. Although spectra recorded with thecompact spectrometer are time-averaged over the duration ofthe emission, as mentioned earlier, the temporal variation inthe emission recorded by the fast photodiode suggests that thisemission lasts for approximately 100 ns. This value, togetherwith an absolute intensity calibration of the spectrometer af-fords a confirmation on the temperature (averaged over 100ns), for self consistency. We plot the measured spectral radi-ance of the plasma over a broad wavelength range in Fig. 5.Also plotted is the computed total continuum blackbody emis-sion for electron temperatures ranging from 2-4 eV. Our mea-sured time-averaged temperatures are biased somewhat lowerthan the temperatures expected at early times, somewhere nearthe peak in plasma emission (10-20 ns). We see that a temper-ature of T e ≈ in Fig. 4. It is expectedthat our measured average temperature is somewhere abovethe lowest and below the peak in the time-resolved data. Wavelength (nm)
450 500 550 600 S pe c t r a l r ad i an c e ( W / ( m " s r " n m )) FIG. 5. Comparison in the measured and computed absolute contin-uum intensity, assuming a black-body radiation spectrum.
Using the T e ( t ) shown in Fig 4, and, for the free-bound con-tribution to absorption, a Biberman factor of 1, we now evalu-ate the absorption coefficient and hence the temporal variationin the electron number density, n e . The result is displayed asthe blue line in Fig. 6. The error bars represent our estimatedrange of uncertainty in these values.We see that n e peaks at a density of approximately 7 × cm − . The peak exceeds, by more than a factor of two, theLoschmidt number. We attribute some of this to the disso-ciation of the diatomic species as the temperature rises sub-stantially in the first approximately 10 ns. A further elevationabove the Loschmidt number can also be a result of multi-ple ionization. We also see that at 100 ns, the plasma densityfalls to about 2 × cm − approaching our estimated noisefloor of about 10 cm − , limited mainly by Nyquist (John-son) noise associated with thermally-induced fluctuations inthe photodiode current. Finally, we note in the electron den-sity the presence of temporal fluctuations that are quite pro-nounced at later times. The frequency of these fluctuationsis approximately 0.3 GHz. These fluctuations are also seen inthe detected plasma emission trace, as evident in Fig. 2. Therehave been reports of propagating striations of 0.1 mm scale insimilar laser-induced sparks through schlieren imaging . Asreported in that study, the origin of such features is still notclear, however, it is noteworthy that the spatial and temporalscales associated with these fluctuations suggest disturbancesthat propagate close to the ion sound speed.As a second measurement of electron density we performtime-resolved emission measurements of the Stark broaden-ing of the 777 nm atomic oxygen line, which is somewhatintense relative to the background continuum radiation so that n e , particularly at early times, can be determined with reason-able accuracy. The recorded spectra are fit to Voigt profilesto distinguish the Lorentzian width of the Stark broadened lines from the Gaussian contribution ( w G ) from both instru-ment ( w I ) and Doppler broadening ( w D ), given by: w G = (cid:113) w D + w I w D = . × − × λ o (cid:114) TM Here λ o is the center wavelength of the line, T is the transla-tional temperature of atomic oxygen in K, and M is its atomicmass in atomic mass units. As an estimate to evaluate theimportance of Doppler broadening, we use T =10,000 K, re-sulting in w D (cid:39) w I is approximately 0.36 nm. The resul-tant w G combined with the measured spectral width ( w meas )is used to deconvolve and determine w L , which is mainly dueto the electron-impact collisional Stark broadening width, w S ,corrected for quasi-static ion microfields : w S ( n e , T e ) = w e ( T e ) × [ + . α e ( T e )( − . R e )] n e n eo with R e = . × − n / e T / e . Here, w e is the electron Stark half-width (in Angstroms), α e is a dimensionless parameter that accounts for the effect ofion microfields, R e , also dimensionless accounts for the De-bye shielding of the ion perturbers by the free electrons, and n eo = cm − is the reference electron density for the tab-ulated values of w e . The estimated range of T e from the con-tinuum radiation spectrum of Fig. 4 is used to evaluate w e and FIG. 6. A comparison of the temporal variation in n e measured byabsorption (blue line) to that measured using optical emission andthe Stark broadening of the oxygen 777 nm electronic transition. α e . At these high densities, temperatures, and correspond-ing pressure, we should consider the impact of van der Waalsbroadening on the OI 777 nm transition lineshape. Using thebroadening theory described by Griem , and the specific re-duction for the 777 nm line as presented by Laux , the vander Waals broadening rate (in Angstroms) is approximately ∆ λ vdW = (cid:0) . − . × − T (cid:1) T − . p . Here, T is the gastemperature (in Kelvin) and p is the gas pressure (in atm). Wetake, as a conservative estimate, T =3 eV and a number den-sity of 7 × cm − , and find ∆ λ vdW =0.08 nm, confirmingthat van der Walls broadening of this OI transition is relativelysmall in comparison to other broadening mechanisms for ourplasma conditions.Fig. 7(a) shows a representative 777 nm emission spec-trum (white-filled circles) observed early in the evolution ofthe plasma kernel (30 ns). Also shown is an underlying redcurve, the slope of which represents the continuum radiationcalculated based on values of T e = 3 eV, scaled to blend withthe lowest wavelength limit of the spectral scan. This cor-rected spectrum using the T e = 3 eV background continuum isshown In Fig. 7(b) (also white-filled circles). The black lineshown is a double-Voigt profile fit to account for the possibil-ity of a higher density (and hotter) plasma core (center), sur-rounded by a lower density (and cooler) plasma corona (edge),as it is apparent that a single-Voigt profile would not be suit-able due to the distorted high wavelength side attributed toa non-uniform plasma density distribution. The best fit, ob-tained by a regression analysis, consists of a wider and moreshifted Voigt profile (green curve) together with a more nar-row and less shifted profile (red curve). The values of n e ob-tained from the Lorentzian contributions to the two-Voigt fitgives a center and edge value of n e,center = . × cm − and n e,edge = . × cm − , respectively.For comparison, Fig. 6 also includes in addition to the mea-sured electron number density from the laser absorption, theelectron number density inferred from the Stark-broadened OIline. The red and magenta circles represent the plasma valuesinferred from the double-Voigt fits, with n e , center and n e , edge ,respectively. We also show the results of a single-Voigt fit(green circles), which tends to lie between the other two, asexpected. The data shows a good agreement with those ob-tained from the HeNe laser absorption, and seem to agree bestwith the data extracted from the single Voigt fit analysis al-though all three analyses are likely to be within the range ofthe uncertainty in the laser absorption measurements at theselater times. For earlier times, i.e., before 30 ns, the Starkbroadening is extremely wide and the spectral line blends intothe continuum, precluding its use as a definitive measurementof n e . It is noteworthy that for nearly the entire range ofmeasurements extracted from the Stark-broadened OI line, theStark shift-to-width ratios for this transition estimated fromthe contribution to the profiles from the plasma core result invalues of T e ≈ . Thisestimate, as well as that of the electron density, is somewhatsensitive to the determination of the continuum backgroundplacement in Fig. 7(a), although its slope is constrained bythe temperature of T e = 3eV. IV. DISCUSSION AND SUMMARY
The results described here indicate that laser absorption,primarily through free-free (inverse Bremsstrahlung) andbound-free electron-ion interactions affords a convenient andaccurate way to study the early electron number density dy-namics of a low-energy laser spark plasma. We believe thatthis measurement can also be applied to the measurement ofelectron density in plasmas formed by pulsed nanosecond-scale electric discharges. In its implementation it requires ahigh speed photodiode detector and a low power cw probelaser, preferably one that has high wave front quality and lowdivergence, such as a HeNe gas discharge laser. The temporalvariation of n e is extracted directly from the laser attenuationgiven a determination of the absorption coefficient using anestimate of the electron temperature and probe laser absorp-tion path length. This measurement has advantages in rela-tively high density laser or discharge spark plasmas at earlytimes during the plasma formation where the analysis of theemission spectra is made difficult as a result of overlappingand/or blending of emission lines into the continuum. Fur-thermore, while both methods may be line-of-sight based, theuse of Stark broadened emission lines from neutral species forextracting n e is further complicated by the fact that highly-ionized regions of the plasma, i.e., central regions of highplasma density, are less emitting as this region of high tem-perature experiences neutral species burnout.In our theoretical determination of the absorption coeffi-cient, κ , we have assumed that the contribution of free-freeelectron-ion interactions dominate over electron-neutral inter-actions. To determine this contribution to the absorption weuse the volume emission coefficient given by Venugopalan , ε enf f ( λ ) = C n e n a T / e λ × (cid:34)(cid:18) + hc λ kT e (cid:19) + (cid:35) Q en ( T e ) exp (cid:18) − hc λ kT e (cid:19) (6)with C =1.026 × − Wm K − sr − . Here, Q en is the av-erage electron-neutral momentum scattering cross-section,which is dependent on T e . At early times (10-30 ns), we as-sume based on the high electron number densities estimated,that the plasma is fully ionized, decreasing in number den-sity to ≈ cm − largely because of the initial expansion .For later times, the density falls from 10 cm − to about2 × cm − through further expansion and electron-ion re-combination. As a worst case, assuming that the drop in elec-tron density beyond 30 ns is solely due to recombination, thenat these later times we might have a more weakly ionizedplasma with n n / n e ≈
5. To estimate the potential impact that κ enf f may have on the inferred electron number density we in-clude its contribution using Eqn. 6, assuming a total electron-neutral momentum scattering cross section, Q en ≈ − m . In doing so, we consider values of n n / n e = 0, 1, and10. n n / n e = 0 represents neglecting the electron-neutral free-free interactions, whereas n n / n e = 1 and n n / n e = 10 repre-sent a moderate degree of ionization, and a very low degree
765 770 775 780 785 790
Wavelength (nm) I n t e n s i t y ObservedContinuum
765 770 775 780 785 790
Wavelength (nm) I n t e n s i t y CorrectedEdgeCenterBest fit
FIG. 7. (a) The observed emission spectrum (white-filled circles) and scaled 3eV continuum background (red line). (b) Corrected spectrum(white-filled circles) and fitted Voigt profiles for the center (green) and edge (orange) of the plasma, and the resultant fit of summing the twoVoigt profiles. of ionization respectively. We find that with Biberman fac-tors near unity, the electron-neutral contributions have littleeffect on the measurements at later times (because of the rela-tively low electron temperature). At early times, the peak elec-tron number density falls to n e = 6 × cm − and 5 × cm − with n n / n e = 1 and 10, respectively. As a result, webelieve that for our conditions, neglecting the electron-neutralcontributions to the free-free absorption coefficients is justi-fied. However, more accurate values that these contributionsmake to the overall free-free absorption would require accu-rate data for the momentum scattering cross sections for theserelatively low temperatures, and a determination of the neu-tral atom density, which is strongly affected by the complexgas dynamics.Our measurements of n e are also predicated on measure-ments of T e , which we have made only indirectly throughstudies of the continuum emission averaged over a period oftime in which the emission is strongest. Our measured Starkbroadening shift-to-width ratios do confirm the relatively lowvalues of T e in the range of t = 30-80 ns, consistent with pastmeasurements of laser plasmas in air . To analyze our exper-imental measurements at times during the plasma formationand subsequent early expansion phase, we used the results ofBorghese et al. , which, although similar in its experimentto ours, was at slightly higher laser pulse energy and at theNd:YAG fundamental wavelength (1064 nm). A strongly-varying temperature during these early times seems to havea significant impact on the inferred temporal variation of n e .A temporally-resolved measurement of T e for our experimen-tal conditions is desirable, and future experiments will explorethe possibility of using a second, lower energy and shorter du-ration (picosecond) pulsed laser to evaluate and confirm boththe time-dependent T e and n e by Thomson scattering.Finally, we note that while the measurement of the absorp-tion coefficient does provide a quantitative measure of the av- erage of the the electron number density-path length product,a measure of the electron density provides a more meaning-ful determination of the plasma state. An accompanying andaccurate measurement of L ( t ) is necessary for such a determi-nation. In the current study, we used the computations, con-firmed by experiments, from Alberti et al. Our future exper-iments will involve a re-arrangement of our experimental plat-form to use our streak camera to obtain a more complete char-acterization of the plasma kernel shape variation with time.
ACKNOWLEDGMENTS
We wish to acknowledge the support provided through theNSF/DOE Partnership in Basic Plasma Science and Engineer-ing, grant number DE-SC0020068, with Dr. Nirmol Podder asthe Program Manager.The data that support the findings of this study are availablefrom the corresponding author upon reasonable request. P. K. Chu and X. Lu,
Low temperature plasma technology: methods andapplications (CRC Press, 2013). U. Kogelschatz, “Dielectric-barrier discharges: their history, dischargephysics, and industrial applications,” Plasma chemistry and plasma process-ing , 1–46 (2003). M. S. Bak, S.-K. Im, and M. Cappelli, “Nanosecond-pulsed dischargeplasma splitting of carbon dioxide,” IEEE Transactions on Plasma Science , 1002–1007 (2015). J. Little, K. Takashima, M. Nishihara, I. Adamovich, and M. Samimy,“Separation control with nanosecond-pulse-driven dielectric barrier dis-charge plasma actuators,” AIAA journal , 350–365 (2012). A. Vincent-Randonnier, S. Larigaldie, P. Magre, and V. Sabel’nikov,“Plasma assisted combustion: effect of a coaxial dbd on a methane dif-fusion flame,” Plasma sources science and technology , 149 (2006). S. Shcherbanev, S. Stepanyan, N. Popov, and S. Starikovskaia, “Dielectricbarrier discharge for multi-point plasma-assisted ignition at high pressures,”Philosophical Transactions of the Royal Society A: Mathematical, Physicaland Engineering Sciences , 20140342 (2015). H. Ayan, D. Staack, G. Fridman, A. Gutsol, Y. Mukhin, A. Starikovskii,A. Fridman, and G. Friedman, “Application of nanosecond-pulsed di-electric barrier discharge for biomedical treatment of topographically non-uniform surfaces,” Journal of Physics D: Applied Physics , 125202(2009). M. Hopkins and W. Graham, “Langmuir probe technique for plasma pa-rameter measurement in a medium density discharge,” Review of scientificinstruments , 2210–2217 (1986). D. E. T. Ashby and D. Jephcott, “Measurement of plasma density using agas laser as an infrared interferometer,” Applied Physics Letters , 13–16(1963). H. Kempkens and J. Uhlenbusch, “Scattering diagnostics of low-temperature plasmas (rayleigh scattering, thomson scattering, cars),”Plasma Sources Science and Technology , 492 (2000). X.-M. Zhu, Y.-K. Pu, N. Balcon, and R. Boswell, “Measurement of theelectron density in atmospheric-pressure low-temperature argon dischargesby line-ratio method of optical emission spectroscopy,” Journal of PhysicsD: Applied Physics , 142003 (2009). T. Orrière, E. Moreau, and D. Z. Pai, “Ionization and recombination innanosecond repetitively pulsed microplasmas in air at atmospheric pres-sure,” Journal of Physics D: Applied Physics , 494002 (2018). J. F. Kielkopf and N. F. Allard, “Shift and width of the balmer series h α lineat high electron density in a laser-produced plasma,” Journal of Physics B:Atomic, Molecular and Optical Physics , 155701 (2014). S. Cameron, M. Tracy, and J. Camacho, “Electron density and tempera-ture contour plots from a laser-produced plasma using collective ultravi-olet thomson scattering,” IEEE transactions on plasma science , 45–46(1996). H. Griem,
Spectral line broadening by plasmas (Elsevier, 2012). A. Bataller, J. Koulakis, S. Pree, and S. Putterman, “Nanosecond high-power dense microplasma switch for visible light,” Applied Physics Letters , 223501 (2014). D. Hoarty, P. Allan, S. James, C. Brown, L. Hobbs, M. Hill, J. Harris,J. Morton, M. Brookes, R. Shepherd, et al. , “Observations of the effect ofionization-potential depression in hot dense plasma,” Physical review letters , 265003 (2013). A. Offenberger and R. Kerr, “Transient plasma diagnostics using simulta-neous co2 laser interferometry and absorption,” Journal of Applied Physics , 354–356 (1972). M. S. Bak, S.-k. Im, M. G. Mungal, and M. A. Cappelli, “Studies on thestability limit extension of premixed and jet diffusion flames of methane,ethane, and propane using nanosecond repetitive pulsed discharge plas-mas,” Combustion and flame , 2396–2403 (2013). H. Zhang, J. Lu, Z. Shen, and X. Ni, “Investigation of 1.06 µ m laser in-duced plasma in air using optical interferometry,” Optics communications , 1720–1723 (2009). S. S. Harilal, B. E. Brumfield, and M. C. Phillips, “Lifecycle of laser-produced air sparks,” Physics of Plasmas , 063301 (2015). A. Alberti, A. Munafò, M. Koll, M. Nishihara, C. Pantano, J. B. Freund,G. S. Elliott, and M. Panesi, “Laser-induced non-equilibrium plasma kerneldynamics,” Journal of Physics D: Applied Physics , 025201 (2019). A. Alberti, A. Munafò, C. Pantano, J. Freund, and M. Panesi, “Modelingof air breakdown by single-mode and multi-mode lasers,” in
AIAA Scitech2019 Forum (2019) p. 1250. A. Munafò, A. Alberti, C. Pantano, J. B. Freund, and M. Panesi, “A com-putational model for nanosecond pulse laser-plasma interactions,” Journalof Computational Physics , 109190 (2020). M. Nishihara, J. Freund, N. Glumac, and G. Elliott, “Influence of mode-beating pulse on laser-induced plasma,” Journal of Physics D: AppliedPhysics , 135601 (2018). A. Borghese and S. S. Merola, “Time-resolved spectral and spatial descrip-tion of laser-induced breakdown in air as a pulsed, bright, and broadbandultraviolet–visible light source,” Applied optics , 3977–3983 (1998). T. P. Hughes, “Plasmas and laser light,” nyhp (1975). M. Venugopalan, “Reactions under plasma conditions,” rupc (1971). R. S. Sutherland, “Accurate free—free gaunt factors for astrophysical plas-mas,” Monthly Notices of the Royal Astronomical Society , 321–330(1998). L. Biberman and G. É. Norman, “Continuous spectra of atomic gases andplasma,” Soviet Physics Uspekhi , 52 (1967). V. Hohreiter, J. Carranza, and D. Hahn, “Temporal analysis of laser-induced plasma properties as related to laser-induced breakdown spec-troscopy,” Spectrochimica Acta Part B: Atomic Spectroscopy , 327–333(2004). A. El Sherbini, H. Hegazy, and T. M. El Sherbini, “Measurement of elec-tron density utilizing the h α -line from laser produced plasma in air,” Spec-trochimica Acta Part B: Atomic Spectroscopy , 532–539 (2006). S. Yalçin, D. Crosley, G. Smith, and G. W. Faris, “Influence of ambientconditions on the laser air spark,” Applied Physics B Lasers and Optics ,121–130 (1999). M. Capitelli, G. Colonna, L. Marraffa, and D. Giordano,
Tables of inter-nal partition functions and thermodynamic properties of high-temperatureMars-atmosphere species from 50K to 50000K (European Space Agency,2005). H. Griem, “Plasma spectroscopy, mc graw-hill, new york (1964),” . C. Laux, “Optical diagnostics and radiative emission of air plasmas [ph. d.dissertation], htgl report t288,” (1993). R. Neynaber, L. L. Marino, E. W. Rothe, and S. Trujillo, “Low-energy elec-tron scattering from atomic nitrogen,” Physical Review , 2069 (1963). L. Thomas and R. Nesbet, “Low-energy electron scattering by atomic ni-trogen,” Physical Review A12