Contains report on one research project.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

Garosi, G. A.

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XI. GASEOUS ELECTRONICS'Academic and Research StaffProf. G. Bekefi Prof. J. C. Ingraham J. J. McCarthyProf. S. C. Brown Prof. B. L. Wright W. J. MulliganDr. W. M. ManheimerGraduate StudentsW. B. DavisG. A. GarosiA. CONTINUUM PROBE STUDIES OF A POSITIVE COLUMNIN FLOWING ARGON GASThis report presents additional experimental results obtained on the apparatusreported upon previously. 1This apparatus produced a weakly ionized plasma (the positive column of a glow dis-charge) in a region of neutral-gas pipe turbulence. A movable probe assembly, describedby R. L. Kronquist, was added to permit data to be taken as a function of radius. Theprobe assembly was demountable to permit the probe to be changed quickly and conve-niently. Furthermore, the tube diameter was increased to 2. 2 cm in order to obtainthe maximum flow permitted by the pumping capacity while maintaining the pressure inthe discharge region at approximately 20 Torr.It has been stated previously I that the electron temperature changed negligibly withincreasing flow when compared with changes in the gas temperature. Electron tempera-ture measurements for this tube were made with a double probe. The results substan-tiated the previous claiml and also showed that the electron temperature was essentiallyindependent of radius (see Fig. XI-1).The experimental data reported here were obtained from one or two electrostaticprobes immersed in the plasma. Since the plasma is in a flowing medium, the timedependence of the probe signals will, in general, result from both an explicit time vari-ation of the plasma parameters and from the passage of spatial variations past theprobe. Under certain conditions, the explicit time variation can be neglected with theresult that the spatial variations can be related to a frequency throughfUwhere U is the mean flow velocity, and f is the length, in the axial direction, of thespatial inhomogeneity. In the absence of shear flow the condition for Eq. 1 to hold isgiven 3 byThis work was supported by the Joint Services Electronics Programs (U. S. Army,U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E).QPR No. 89(XI. GASEOUS ELECTRONICS)2U'5 << 1 ,-2Uwhere U'1 is the rms value of the axial component of the fluctuating velocity. Since thecriteria for the validity of Eq. 1 in the presence of shear flow is unknown, it must bechecked experimentally.1.2-1.00.8j0.60.40.4Id  1.8 Amp p = 25 Torr3o FLOW OF 40.5 cm3 sec at STPx FLOW OF 1320 cm3 sec at STPI I I I I I I I I I I I I I0 0.1 0.2 0.3 0.4 0.5r//'RFig. XI-1.0.6 0.7 0.8 0.9 1.0Electron temperature from double-probe curves.One method, described by V. L. Granatstein, is to compare the plasma densityspectrum for different flow velocities while keeping the Reynolds number, Re, constant.If the frequency scale of the spectrum analyzer is varied so that f/U remains unchanged,then, according to Eq. 1, the resulting spectra should be similar. Another methodinvolves the use of the frequency spectra of the fluctuating floating potential and electricfield in the plasma. The electric field was measured by taking the output of two floatingprobes oriented in the axial direction and separated by 0. 5 mm and feeding them into aTektronix 1A6 differential preamplifier. This procedure was superior to that describedpreviously.The spectrum of the potential is related to that of the electric field byFE(kl) cc kF (k'where k I is the axial wave number of the eddy, and FE(k l ) and F (kl) are the electricQPR No. 89I100(XI. GASEOUS ELECTRONICS)field and potential spectra, respectively. In terms of wave number Eq. 1 becomesk-UCombining Eqs. 3 and 4 yieldsE(f) F(f)20 lo0 f = 0 log 0  10 log 1 00 FE(fo) 0 F(fo)where f is a convenient normalizing frequency necessary to remove the unknown pro-portionality constant in Eq. 3. If it is assumed that instead of Eq. 4 the following rela-tionship holdsS2Trfa (6)U b 'Uwhere a and b are any real numbers, then Eq. 5 may be replaced byf FE (f) F (f)20a log 10 f ( = 10 og10 10 log 10Oo0 0 FE (fo) F (fo)Thus a plot of the right-hand side of Eq. 7 against log f should yield a straight line witha slope of 20 if Eq. 4 is valid. The results of this analysis are shown in Fig. XI-2.Thus, to a good approximation, the use of Eq. 1 is justified for Reynolds numbersSLOPE = 20 x 20 1og10 (k/ko) vs log fo Re = 2400x Re = 6300Id = 1.8 Ampp = 25 TorrQPR No. 89SOC0Ooe2 3 4 5 6 8 10 20 30 40 50 60 80 100f - kHzFig. XI-2. Check of frozen-flow assumption (Eq. 4).101(XI. GASEOUS ELECTRONICS)between 2400 and 6000 and the resulting flow is referred to as frozen flow.The behavior of the plasma density and axial electric field with flow was very similarto that reported previously., l' 4 The floating potential was also measured, and its behav-ior was similar to that of the plasma density and electric field. An explanation of thepotential (or electric field) behavior is still being sought.The development with flow of plasma density inhomogeneities of various sizes can beobserved by using a bandpass filter as previously shown.l The bandpass filter that wasRe 2000 4000 60002 3 4 6 8 10 2 3 4 6 8 10 2 3 4 6 8 10Q cm /sec at STPFig. XI-3. Development of plasma density eddies.used was a Spencer-Kennedy Laboratory Model 302 which has an 18 dB/octave frequencyrolloff. The data, plotted in Fig. XI-3, shows that, although the large-scale fluctuationsbegin at very low flows, the inhomogeneities with axial scale lengths k, such that I << D,do not appear until the flow attains a Reynolds number of -~1500, where D is the tubediameter. The results also show that the larger eddies grow in intensity more rapidlythan the smaller eddies do and that they all show a tendency to saturate. (Note that theabscissa scale is logarithmic.)Measurements made by Granatstein 4 showed that the intensity of the large-scaleQPR No. 89 102(XI. GASEOUS ELECTRONICS)plasma density fluctuations, J > D, had a radial profile similar to that of the meanplasma density gradient. This effect was observed in this experiment for medium flows,but for the larger flows it was not seen (see Fig. XI-4). This discrepancy is beingId = 1.8 Ampp = 25 Torr Q = 1700 Re = 6200Q 690 Re 2400 0-80 kHz16-32 kHzo20-40 kHz8-16 kHz 000Z R<i<D0 0-10 kHzS 0-k00.20.2 0 0rro oooo0LI I I I I  1 I I I0.2 0 0.2 0.4 0.6 0.8 1.0 0.2 0 0.2 0.4 0.6 0.8 1.0r/RFig. XI-4. Density fluctuation and density gradient profiles.investigated. There are some indications that the answer may be in the behaviorof the very large inhomogeneities.The tendency of turbulence to smooth out gradients in any of the properties ofthe medium is shown by the effect of increased flow on the mean plasma densityprofile (see Fig. XI-5). The zero-order Bessel function is plotted for reference; thisis the predicted profile for a diffusion-dominated discharge. Argon shows a bell-shaped profile for the low flows as a result of the rapid increase with energy ofthe electron-neutral scattering cross section. 5 Note that for the larger flows thedensity profile becomes flatter than that associated with a diffusion-dominated dis-charge. The initial contraction in going from a flow of 82. 5 cm3/sec at STP to242 cm 3/sec is still unexplained.QPR No. 89 103(XI. GASEOUS ELECTRONICS)SNvn /sec at STPo0TUBE0.1 WALL0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Fig. XI-5. Density profile normalized to unity on axis.Radial profiles for the floating potential and for the axial electric field are plottedin Fig. XI-6. Comparing this with Fig. XI-5, we see that there is a strong simi-larity between the potential, axial electric field and the plasma density. Furtheranalysis is necessary to explain fully the origin of the potential fluctuations.As stated above, it is the floating potential, 4f, which is measured; however,it is the plasma potential, 4p, which is related to the electric field in the plasmabyE = -V , (8)where the vector potential has been neglected, because of the very low frequenciesinvolved. It is thus necessary to compute the error involved in using the floatingpotential.QPR No. 89 104(XI. GASEOUS ELECTRONICS)).2 0 0.2 0.4 0.6 0.8 1.0 0.2 0 0.2 0.4 0.6 0.8 1.0rR r/RFig. XI-6. Radial profiles for the floating potential and the axial electric field.It can readily be shown by using the expression= +Vthat the fluctuating components of the potential satisfy() = (f)2 + (Vo) + 2Vo, (10)where the bar represents time average, and the prime denotes the fluctuating com-ponent so thatp = , + ppPpPf = f + cjV = V + V',pY=V V OQPR No. 89(11)105(XI. GASEOUS ELECTRONICS)An expression for the potential difference, V , between a cylindrical probe at floatingpotential and the plasma has been given by Zakharova et al.6urSpTV /T T + 1 20 X Ve = .02 / + -- _ (12)e 0r p + T TAT n 1 +.015r p(1-+u) cpwhere T and T are the electron and ion temperatures in electron volts, respec-tively, I is the probe length, r is the probe radius, ur is the sheath thick-P P pness, k+ and k_ are the ion and electron mean-free paths, respectively, A isthe atomic weight of the ions, and V is the potential difference between thecundisturbed plasma and the sheath edge. Note that both V and V are negativefor a floating probe.For the parameters of this experiment Eq. 12 reduces toVo/T- Be : , (13)a - kn(l+u)where a = in = 1. 9, and B = 0. 02p pIn order to obtain Vo, it was assumed that fluctuations in the sheath thickness wereETD = e (14)D neand n is the plasma density. Although this assumption is reasonable, it has notyet been possible to verify that it is consistent with the expression for u givenby Zakharova et al. 61/5u = 0. 23 1 + , (15)r 22where J+ is the ionic current density in ma/cm . It is also assumed, for rea-By using the assumption above and Eqs. 13 and 14, and dividing by (c )2Eq. 9 becomesQPR No. 89 106(XI. GASEOUS ELECTRONICS)( )2 -2 2p T (n') 1()2 2[a-n(1+u) 1+ ] n (2[]2T (n') 1+ 2p(4 , V) - (16)K (1+)[a-n(l+u) 2where2 Vis the correlation coefficient. To evaluate Eq. 16, p is set equal to one, since this givesthe worst case. For the worst condition present in this experiment we obtain__) 2 1/21. 14.Thus using the floating potential results in an error of approximately 14% at worst andis generally much better.It is possible to obtain the scale size of the smallest eddies by means of the two-pointcorrelation. For homogeneous turbulence the two-point plasma density correlationcoefficient reduces, for sufficiently small separation,7 to2rR (r) = 1 r (17)Xwhere X is the microscale for the density fluctuations, and r is the separation of thetwo observation points. For the condition of frozen flow it is possible to obtain the axialscale length for density fluctuations by means of the temporal correlation at one point(autocorrelation). Then the autocorrelation, for sufficiently short delay time, is given 8by2RE (t) = 1 2 (18)E, ywhere TE = /U.,YQPR No. 89 107(XI. GASEOUS ELECTRONICS)The autocorrelation was taken with a Honeywell 9410 correlation, and the expectedparabolic section was observed. A plot of 1 - RE(t) against t2 yielded a straight line0.05 -0.04 -0.03 - I-RE(t) vs t2SId = 1.8 Ampp = 25 Torr0.02 - rE,y = 6 .0 7 pseco X = 0 .117cmX0.01f 0.051 cm0.010000 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0t 2-10- 12sec 2Fig. XI-7. Microscale length.over the first two microseconds and gives a value of TE,y of 6. 07 psec (see Fig. XI-7)or a microscale length of 0. 117 cm. This scale length for the plasma density fluctua-tions can be related to longitudinal neutral-gas velocity scale length byXDf D (19)where Xf is the microscale length for velocity fluctuations in the axial direction, D isthe diffusion coefficient for the plasma, and v is the kinematic viscosity. For theparameters of the discharge used in getting Fig. XI-7, Eq. 19 yields Xy /f 2. 3.Thus the smallest inhomogeneities in the plasma density are approximately one-tenththe tube radius, and approximately twice as large as the smallest eddies in the neutralgas.Future work includes a complete analysis in order to explain many still unex-plained effects, the addition of a grid at the input to the discharge pipe, and an attemptto measure directly the expected but unconfirmed enhanced plasma loss rate caused bythe turbulence. The grid is being added, since it is possible that it will have an effecton the very low frequency (large-scale length) fluctuations.G. A. GarosiQPR No. 89 108(XI. GASEOUS ELECTRONICS)References1. G. A. Garosi, "Effects of Hydrodynamic Turbulence on a Weakly Ionized ArgonPlasma," Quarterly Progress Report No. 86, Research Laboratory of Electronics,M.I.T. , July 15, 1967, pp. 129-134.2. R. L. Kronquist, "Microwave Scattering from an Electron-Beam Produced Plasma,"Quarterly Progress Report No. 82, Research Laboratory of Electronics, M. I. T.,July 15, 1966, pp. 109-114.3. J. O. Hinze, Turbulence (McGraw-Hill Book Company, Inc., New York, 1959),p. 41.4. V. L. Granatstein, "Structure of Wind-Driven Plasma Turbulence as Resolved byContinuum Ion Probes," Phys. Fluids 10, 1236 (1967).5. H. M. Schulz III, "Interactions of Electrons and Acoustic Waves in a Plasma,"Ph.D. Thesis, M.I.T., 1967.6. V. M. Zakharova et al., Soviet Phys. - Tech. Phys. 5, 411 (1960).7. J. O. Hinze, ibid., p. 220.QPR No. 89 109

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