RD-RIBS 739 DOPPLER SHIFT METHODS FOR PLASMA DIAGNOSTICS(U) 1/1CALIFORNIA UNIV BERKELEY DEPT OF MECHANICAL ENGINEERINGM SASS I ET RL. 92 JUL 87 AFOSR-TR-97-li82 N

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M. Sassi and J.W. Daily

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17. COSATI C00E8 IS. SUsikoJE RMS 1Con tine. on reverse if' noeseary a"d Jentify by block mn inerDFILD cfouP Sue. OR. Laser Diagnostics, Plasmas, Laser Induced Fluorescence,20 13 Doppler Shift Spectroscopy.20 08

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Work to develop novel advanced laser spectroscopy plasma diagnostic methods isdescribed. The methods are based on observing the doppler shift in the absorption linesof ionic species. Two methods under study are Velocity Modulated Laser Spectroscopy andTwo-Beam Doppler Shift Laser Spectroscopy. The theoretical basis of the methods isdescribed and preliminary experimental results presented.

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AFOSR-T 87-1182

RIR-87-1528Doppler Shift Methodsfor Plasma Diagnostics

M. Sassi and J. 14. DailyUniversity of California,Berkeley

AIAA 22nd Thermophysics ConferenceJune 8-10, 1987/Honolulu, Hawaii

For permission to copy or republish, contact the America Institute of Aeronautics and Atonautics1633 Broadway, New York, NY 10019

ill~lim "'I'lilil I

Abstract

Work to develop novel advanced laser spectroscopy plasmadiagnostic methods is described. The methods are based onobserving the doppler shift in the absorption lines of ionicspecies. Two methods under study are Velocity Modulated LaserSpectroscopy and Two-Beam Doppler Shift Laser Spectroscopy. Thetheoretical basis of the methods is described and preliminaryexperimental results presented.

I) Introduction

The purpose of our work has been to develop advanced laserspectroscopy methods to diagnose partially ionized plasmas. Wehave focused on methods that are based on observing the Dopplershift in ionic spectra due to the presence of an ion driftvelocity. Two particular methods we are working with areVelocity Modulated Laser Spectroscopy (VMLS) and Two Beam DopplerShift Laser Spectroscopy (TBDSLS).

The scientific goal of our work is to increase understandingof the role of flow non-unlformities and plasma/wall interactionsin plasma devices by making in-situ measurements of electricfield strength, ion mobilities, concentrations and temperaturesin a non-intrusive fashion that allows point, one, and twodimensional imaging.

The scientific approach is to use conventional laserspectroscopic methods such as Rayleigh scattering, Ramanscattering, or fluorescence, to probe ion absorption lineprofiles. If there is an electric field present, the ions willexperience a net force and undergo drift, resulting in a shiftin the position of the line profile. If the ion mobility isknown, then the electric field component along the probedirection can be calculated. If the electric field driving theplasma is modulated, one will observe an oscillating shift in theline profile that arises because of the oscillating force imposed 0%6on the ions. The shift may be related to the ion mobility, thusconductivity.

Temperature and concentration may be recovered byconventional laser spectroscopic means. The methods are speciesand state selective, allowing one to make measurements on morethan one species and to study the effect of internal modenonequilibrium.

The merit of the methods lies in their ability to provide U

simultaneous measurements of important parameters in plasmas. ...

The methods are well suited to multi-dimensional imaging. Onemay use an array detector to image lines and planes in additionto the more conventional point configuration.

CodesThere has been a far amount of work done by the physical

chemistry community on VMLS. VMLS applied to plasmas was

Cepyfitht C Anrica Imutale Of ArWO°N0 Nd/AstreomsIlc. Inc.. 17. AN 6l0t re md. 1

initially exploited by Woods et al who observed Doppler shifts in

microwave transitions of HCO + [1,2] and then used the shifts to

infer ion mobility [33. Microwave measurement of HCO+, NO + , CO +

and HNN + were performed by DeLucia et al [4-7].

VMLS was extended to the infrared region by two groups, that

of Professor Richard Saykally of the Chemistry Department at UC

Berkeley [8-14) and that of Professor T. Oka of the Chemistry

Department at the University of Chicago [15-19]. Saykally'sgroup has focused on the spectroscopy of ions in plasmas whileOka has focused on measurements of ion mobility.

The Chicago group has observed ArH + , NH4, HCNH+ and HCOP + .

The Berkeley group has made observations of H 30, NH+, H 2 F ,HCO

+, HNN+, and H+.

The Berkeley group has extended the method to the visible

region [20-21]. They have observed both CO + and N+ in CO or N2seeded He plasmas.

The probe method in all the studies so far is absorption

spectoscopy. The infrared work was done with a diode laser

(Chicago group) and a Krypton pumped color center laser (Berkeley

group.) The visible work was done with a single mode dye laser.

One of the unique aspects of our work is that we are exploring a

number of different probe methods so as to be able to extend the

method into the ultraviolet and to molecules that do not absorbat appropriate frequencies.

In the following we describe the theoretical basis of

doppler shift methods, outline the nature of the two methods we

are pursuing, and describe experimental results to date. The

work is then summarized and appropriate conclusions drawn.

II) Theoretical Basis

a) Ion Response to a Modulated Electric Field

S'-The basis of Doppler shift methods is Coulomb's Law which

. states that the force felt by a charged particle is directly

propotional to the imposed electric field

F-qE(1)

where E Is the electric field, q the charge of the particle and F

the force. In a collisional plasma, one may write a momentum

equation for the ions that is of the form (in the absence of a

magnetic field)

dv/dt - (q/m)E - VcV(2)

2

-Ill

where m is the ion mass, and vc the collision frequency. Ifthere is a DC electric field present, then the ion drift velocitywill be (after an initial transient)

" I E V P i E( 3 )

where

1.11 q/mvc

is the ion mobility. Likewise, if the electric field isoscillating in form

E - Eo exp(iwt)(4)

where w is the angular frequency, , then the velocity will be

modulated (after an Initial transient) in the form

V - (1i/(+i(w/vc))) E o exp(iwt)~(5)

Because of the Doppler effect, the observed resonantabsorption or emission frequency of a molecule with a non-zerodrift velocity Is shifted according to the relation

dv - (vo/C) v(6)

.5. where v 0 is the line center frequency, c the speed of light, andv the component of velocity along the line of sight. Thus, for aDC field, the shift will be

dv/v o - IEI/c

and the depth of modulation in resonant frequency due to anoscillating field will be

dv/v o - ((Pj/c)/(l+i(w/vc)) Eo exp(iwt)

where E and E o are the component of the electric field along theline of sight in the DC and AC cases respectively. The magnitudeof the AC shift will be

3

dv/v 0 _ (Pi/C) (l+(w/vc)2 ) - 1 / 2 Eo (9)

and the phase of the shift will be

* = tan-l(-w/vc)(10)

Note that in the limit of small w/vc, the modulated resultbecomes the same as the DC result. When w>>Vc, however, themodulation depth goes to zero and is independent of the collisionfrequency. Since the experimentalist controls w, however, thisis not a serious problem. If the collision frequency wereextremely small the plasma would be in a collisionless domain.

In practice, ions in a hot plasma will have a thermalvelocity distribution that will result in a fairly broadabsorption line profile. The modulated shift will be easier tosee if it is large with respect to the profile. If we take theline width to be given approximately by the Doppler profile wecan estimate the ease with which a shift can be seen. Theequilibrium Doppler width is

dvD/vo - (/1n2/c) vt (11)

where vt is the mean thermal velocity. Since the ion collisionfrequency may be written

Vc = nTQv t (12)

where nT is the total number density and Q the collision crosssection, one may write (if w << vc or for the DC case)

d /dvD - q/((v/ln2)nTmQv) E (13)

Invoking the perfect gas law and noting that

vt - (8kT/wm) 1 / 2

where k is Boltzmann's constant and T the ion temperature, weobtain

dv/dvD - (q/8Q ln2) (E/P)(15)

where P is the gas pressure.

The coefficient (vq/8QVin2) is of order unity in typicalplasmas for E in volts per meter and pressure in Pascals. Thusone can obtain significant modulation depths or DC shifts atmoderate values of E.

b) The Effect of a Magnetic Field

The effect of a steady magnetic field is to cause theconductivity to become a tensor quantity. In the direction ofthe magnetic field, however, the conductivity is the same as thatgiven above. Thus by a suitable experimental arrangement one maystill utilize the above equations. Furthermore, if the collisionfrequency is large compared to the plasma gyro frequency, thenthe tensor conductivity reduces to its zero magnetic field scalarlimit.

The plasma gyro frequency is

WB - qB/m (16)

For singly ionized argon, the value of q/m is about 5.32E6 C/kg,so that for a magnetic field of one Tesla, the gyro frequencywould be of the order of a megahertz. Under collisionalconditions in most plasmas, the collision frequency will behigher than this. If not, the full equations must be used.

c) Spectroscopic Methods

The choice of a spectroscopic method depends on thespectroscopic properties of the ionic species to be probed and onthe thermodynamic state of the plasma.

The candidate methods include single and multi-photon laserinduced fluorescence, Rayleigh scattering and electronic Ramanscattering (both coherent and incoherent.) If molecular Ions areof interest, then rotational and vibrational Raman scattering arepossible candidates.

At the present time we must divide ionic species into twospectroscopic classes according to whether their lowest lying

*electronic states can or cannot be directly excited by availablelaser systems. Hydrogen and argon are two common propelantswhose ionic ground states are extremely difficult to accessdirectly. Barium is an element commonly added as easilyIonizable seed with an easily accessed ionic ground state.

The therodynamic state of the plasma is important indetermining the possible modes of operation. For a plasma that

5

is fully ionized, one may utilize non-resonant methods such asRayleigh scattering because the plasma is almost pure ions andelectrons. If the degree of ionization is much less than unityor there is more than one ionic specie present, one must be ableto distinguish between species, requiring a resonant method suchas laser induced flourescence.

d) Signal Behavior for VMLS

Consider the case in which we chose a spectroscopic method(laser induced flourescence or Rayleigh scattering, for examplesee Figure 1) that probes the Doppler profile. That is for whichthe signal is proportional to the Doppler line shape function.If the laser source has a line width much narrower than theDoppler width then the signal will be directly proportional tothe Doppler line shape function

Sig a (2/ln2/ vD '/i ) exp-((2 ln2/lvD)(v-vo)) 2 (17)

The effect of velocity modulation on the Doppler profile isfelt as a modulation of Vo. By differentiating the signal twice,one obtains the result that the signal is most sensitive tochanges in vo when vL - vo ± 0.425 AVD and the fractionalsensitivity is

dSig/Sig = 2.35 dvo/,vD(18)

Using the expression for the modulation depth previously derived,we may recast this expression into a detectabilty limit for thedetection of a given modulation voltage

EoDet = 1.08 (Q/q) P (dSig/Sig)Det (19)

If one assumes a moderate one percent for the signaldetectability limit, and a typical ten square Angstroms for the

collision cross section, then one obtains

EoDet(V/m) - 0.00675 P(Pa) (20)

At one atmosphere, the detectable electric field is only 6.75V/cm, a field readily achievable in the laboratory. By utilizingphase sensitive detection, one can achieve significantly lowerdetectability limits.

d) Signal Behavior for TBDSLS

6

In principle, any method which probes the Doppler profilewith sufficient resolution can be used to determine a DC lineshift. If only one probe is used, however, there may be aproblem of absolute frequency calibration. By using two beams inopposite directions, an in-situ calibration is achieved.

Consider the arrangement illustrated in Figure 2. Assumethat there is a drift velocity in the positive x direction. Ifthe laser frequency is scanned through the line, then therightward running beam will probe the profile labeled R in figure2, while the leftward running wave will probe the profile labeledL.

As the laser frequency is scanned through the line (or linesas it were,) from v < v o to v > v o , signal will first appear fromthe right running beam. As the frequency is increased, theleftward running beam will begin to contribute. If the twosignals are independently observed, they will look like that ofFigure 2. (By chopping the beams at a rate fast compared to thefrequency scan rate, one may use the same imaging optics todetect both signals.) The peak separation is just twice theDoppler shift and the crossing point of the two signals is theunshifted line center.

For the method to be useful one must also simultaneouslydetermine the Ion collision frequency. If one assumes to firstorder that the collision cross section is constant, then

Vc - P/IT) (21)

Thus, one may obtain relative profiles without knowing the crosssection, or absolute profiles if calibration is possible or thecross section Is known. The temperature can be obtained byfitting the line shape of one of the lines to the appropriateVoigt or Doppler profile, or by other means when the line profileis insensitive to temperature. The pressure can be measured byconventional means.

The detectability limit for the method is determined by theresolution with which the distance between the two peaks can beresolved. If the precision with which the line shape signal canbe measured is As, then for Doppler broadening the precision withwhich the separation in peaks, and thus electric field, can beresolved is

AE/E - (1/121n2) (AvD/AvE) (As/s)1/2

(22)

If we define the detectability limit as that value of E forwhich a precision of 10% is achieved when the spectroscopicsignal is detected with a precision of 1%, then we can write

approximately

Edet(V/cm) - 0.04 P(Bar)/T(K) I / 2

(23)

(Assuming that Q - 1OA 2 , m is the mass of a proton, and the linecenter is at 5000A.) Thus at a pressure of 0.01 Bar and 5000K,the detectability limit is about 1 V/cm.

It should be noted that least squares fitting the line shapeto the appropriate profile as suggested above, wouldsignificantly increase the precision with which the line centeris detected and thus reduce the detectability limit for theelectric field. Also, if a suitable transition is found,saturation spectroscopy [22] could be used to locate the linepeak with high precision, although the in situ calibration forthe zero shift position would be lost.

e) Effect of Plasma Conditions

Plasmas of interest in propulsion applications span a widerange of state conditions. At the inlet of a MPD thruster, forexample, the pressure is quite high and the gas, as yet un-ionized, is collision dominated. As the gas becomes ionized andthe resulting plasma is accelerated and expands through theexhaust nozzle, the pressure drops dramatically until collisionsbecome unimportant. The temperature may start out very low, roomtemperature in the laboratory, but can rise to values as high asfifty or one-hundred thousand degrees Kelvin.

Pressure and temperature changes affect the diagnosticmainly through changes in the collision frequency and in theratio of modulation depth to the Doppler width. As long as theformer is large compared to the gyro frequency and the latterlarge enough to detect, the diagnostic will operate.

Figure 3 is a parametric plot of the collision frequency,the ratio of modulation to Doppler width, and the mean free pathas a function of pressure and temperature. A collision crosssection of ten square Angstroms and an electric field of onehundred volts per centimeter were used to calculate theparameters. As can be seen, as the pressure drops, themodulation depth increases at a much faster rate than thecollsion frequency decreases. Thus the flow becomescollisionless long before the measurement fails.

Another consideration is pressure or Stark broadening athigh electric field strengths . The methods will still work evenif pressure or Stark broadening [23) make an importantcontribution to the line width, although they are best suited tothe Doppler dominated and low ion and electron concentrationlimits. The detectability limit will merely be increased becauseit is determined by the peak detection resolution. The broader

8

peak of a pressure or Stark broadend line is harder to resolve.

The Stark effect will cause shifts in the line position dueto both the imposed electric field and the field of electrons andother ions. The DC Stark effect can be accounted for in astraightforward fashion, and at some plasma conditions willdominate the shift.

The presence of a Stark shift due to electrons and ions willbe more of a limiting factor. Unless one can calibrate out theshift, it will appear as a systematic error. Of course if theline width is dominated by Stark broadening, then the Stark widthcan be measured and the contribution of the Stark effect to themeasured shift calculated.

III) Experimental Apparatus

Our system is illustrated in Figure 4. We have an argon ionlaser (Spectra Physics 171-19) pumped ring dye laser (Coherent699-21). The ring laser is fully stabilized and has a line widthof legs that one megahertz. The output of the laser is directedthrough a Fabry-Perot interferometer (Coherent Model 251 SpectrumAnalyzer) as a means of measuring the relative wavelengthprecisely. A small portion of the beam is also split off andsent to a wavemeter (Burleigh Model WA 10) for absolutewavelength calibration.

The beam is then directed into the test section (Figure 5)in either the VMLS or TBDSLS configuration. In either case, thebeam (or beams) pass through small holes in the electrodes.

The signal is detected by observing the fluorescence atninety degrees (Figure 4). The signal is collected with F/9optics and passed through a 1/4 meter Jarrell-Ash monochromator.A RCA 1P28 photomultiplier is used as the detector.

The burner is a cappilary, diffusion flame burner designedby Krupa, et. al. [24]. It allows a wide range of operatingconditions without the normal difficulty of using acetelyne andoxygen as reactants. The burner is mounted in a low pressurevessel and can be operated down to about 20 Torr.

IV) Experimental Results

We are conducting preliminary experiments in a flameenvironment using barium as a seed material. This method isattractive because we can create a partially ionized plasmawithout a discharge. Electrodes are easily inserted into theflame, which is located in a vacuum vessel and can be operatedover a pressure range from 2 Bar to about 20 Torr. Barium ion isattractive because it has a strong ground state absorption lineat about 45O nanometers.

9

We have obtained data on the linewidth of the barium ion at

atmospheric pressure. Figure 5 shows a typical line shapeprofile. The series of sharp peaks is the Fabry-Perot signalsuperimposed to provide a measure of the frequency. The peaksare 1.5 GHz apart, thus the line is about 4.5 GHz wide.

V) Summary and Conclusions

We have presented the theoretical basis of two laserspectroscopy methods for plasma diagnosis based on observing thedoppler shift in the absorption lines of ions subject to a driftvelocity. The methods are Velocity Modulated Laser Spectroscopyand Two-Beam Doppler Shift Laser Spectroscopy.

Calculations indicate that the methods will lead toexcellent detectability for measurement of electric field (or ion

mobility), species concentration, and temperature. By usingfluorescence detection, the methods are adaptable to line and

planar imaging.

Preliminary data on the linewidth of the barium ion are

reported.

Acknowledgements

This work was supported by the Air Force Office ofScientific Research Grant AFOSR-86-0067. The authors gratefullyacknowledge many fruitful conversations with Professor R. J.Saykally and his graduate students.

References

1. Woods, R.C., Dixon, T.A., Saykally, R.J., Szanto, P.G. 1975.Phys. Rev. Lett. 35: 1269

2. Guderman, C.S. 1982. PhD thesis. University Wisc., Madison.Unpublished

3. Woods, R.C., Saykally, R.J., Anderson, T.G., Dixon, T.A.,Szanto, P.G. 1981. J. Chem. Phys. 75. 4256

4. Sastry, K.V.L.N., Herbst, E., DeLucia, F.C. 1981. J. Chem.Phys. 75:4169

5. Bowman, W.C., Herbst, E., DeLucia, F.C. 1982. J. Chem. Phys.77:4261

6. Sastry, K.V.L.N., Helminger, P., Herbst, E., DeLucia, F.C.1981. Astro-phys. J. Lett. 250:L91

7. Sastry, K.V.L.N., Helminger, P., Herbst, E., Delucia, F.C.1981. Chem. Phys. Lett. 84:286

10

A.-L .1 W-P6% M- - - - - - - - - -

8. Gudeman, C.S., Bergemann, N.H., Pfaff, J., Saykally, R.J.1983. Phys. Rev. Lett. 50:727

9. Guldeman, C.S., Begemann, N.H., Pf af f, J., Saykally, R.J. 1983J. Chem. Phys. 78:5837

'a10. Begemann, N.H., Gudeman, C.S., Pfaff, J., Saykally, R.J.

1983. Phys. Rev. Lett. 51:554

1 1. Schafer, E., Begemann, N.H., Gudeman, C.S., Saykally, R.J.1983. J. Chem. Phys. 79:3159

12. Schafer, E., Saykally, R.J. 1 984. J. Chem. Phys. 80:2973

13. Gudemann, C.S., Saykally, R.J. 1 984. In preparation

1 4. P e t ek, H., Nesbitt, D.J., Begemann, N.H., Gudeman, C.S.,Moore, C.B., Saykally, R.J. 1984. In preparation

1 5. Haese, N.N., Pan, F.-S., Oka, T. 1983. Phys. Rev. Lett.5 0:157 5

16. Crofton, N.W., Oka, T. 1983. J. Chem. Phys. 79:3157

17. Oka, T. 1983. See Ref.1 J-pp.73-90

18. Altman, R.S., Crofton, N.W., Oka, T. 1984. Preprint

19. Haese, N.N., Oka, T. 1984. J. Chem. Phys. 80:572

20. Gudeman, C.S., Nartner, C.C., Saykally, R.J. 1984. Chem.Phys. Lett. 122:108

21. Nartner, C.C., Gudeman, C.S., Saykally, R.J. 1984. Inpreparati on

22. N. D. Levenson, Introduction to Nonlinear Laser Spectroscopy,(Academic Press, New York 1982)

23. H. R. Griem, Spectral Line Broa deni ng by Plasmas, (AcademicPress, New York 174 )

24. Krupa, R. J., G. Zizak and J. D. Winefordner, "A SheildedDiffusion Flame Flaskback-Resistant Burner for CombustionDiagnostics," Department of Chemistry, University of Florida,Gainsville, FL 32611.

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