Contains reports on two research projects.U. S. Navy (Office of Naval Research) under Contract Nonr-1841-(42)Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 36-039-AMC-03200(E

Gentle, K. W.

Schulz, H. M., III

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IX. PHYSICAL ACOUSTICSAcademic and Research StaffProf. K. U. IngardProf. L. W. Dean IIIDr. K. W. GentleGraduate StudentsR. H. Katyl W. M. Manheimer J. A. RossJ. L. Macon H. M. Schulz IIIA. ACOUSTIC WAVE AMPLIFICATIONContinued work on the problem of acoustic-wave amplification in a plasmal, 2 hasled to the realization that the electron gas should be treated isothermally. The amplifi-cation mechanism, as described by Ingard,l is a coherent heating of the neutral gas by3the electrons, which are constrained to move in phase with the neutrals and ions. Acalculation based on the fluid equations for the three-component system yields in theisothermal-electron limit the dispersion relationk = (w/c)(1+i/o-)-/ (1)where c is the adiabatic speed of sound for the neutral gas, and T is an amplificationtime. This agrees with the initial result of Ingard,2k = (w/c)(1-i/ l) 1/2, (2)in the limit WT >> 1, but not for w-r 1. In fact, one finds that (2) is valid only whenRe k = w/c, but since T is such a large number (10 - 2 sec r 1 sec), an experimentaldistinction between (1) and (2) would be difficult to achieve.Acoustic losses establish a threshold conditionFT < 1 (3)for the observation of an amplified wave. For propagation parallel to a cylindricalboundary of radius r, one findsF = (2P/pr2)1/2 + (W/c) 2 (7/3p) (4)for a monatomic gas of viscosity r and density p. The dispersion relation actuallyobserved under the expected quasi-adiabatic conditions, from an expansion of (1),This work was supported principally by the U. S. Navy (Office of Naval Research)under Contract Nonr-1841-(42); and in part by the Joint Services Electronics Programs(U. S. Army, U. S. Navy and U. S. Air Force) under Contract DA 36-039-AMC-03200(E).QPR No. 82(IX. PHYSICAL ACOUSTICS)would bek z (w/c) - i(1/ZcT)(1-r'T).1. Lateral Acoustic InstabilityContinuing work on the problem, described previously, 4 ' 5 of understanding why aconstricted argon discharge kinks when the current is modulated at a lateral acousticresonant frequency has led to a simple mechanism for explaining the effect. One mayestimate the ionization rate, by intuition, asR = YNe(P+Ne) N n exp (-aNn/E),where N and N are the densities of electrons and neutrals, E is the electric field, ande na, 3, and y are positive constants. This model has the desired properties1. OR/aE > 02. aR/aN > 03. aR/aN < 0nfor aN /E < 1for aNn/E > 1.If the modulation is sufficient to make both properties Z and 3 realized during separateparts of the modulation cycle, the discharge will minimize E, thereby minimizing itspower dissipation, by selecting the high-gas-density region when E is large and the low-gas-density region when E is small. Thus the path known to be favorable to theFig. IX-1.60 70 80 90z/2 (kHz2)Longitudinal structure in the mode (nm) = (01),as evidenced by the lateral acoustic instability.QPR No. 82(IX. PHYSICAL ACOUSTICS)production of an acoustic wave is also preferred energetically in the presence of thatwave. The path is stationary because the gas density and electric field at a given spatiallocation are periodic in time. The increase in path length serves to limit the degree ofdisplacement.The spatial regularity of the discharge path 5 allows one to plot the wavelength kagainst modulation frequency v. This is done in Fig. IX-1 for the lowest mode (n = 0,2 -m = 1), which displays through the linear relation between v and 6 the very definiteexcitation of a series of longitudinal modes based on the fundamental frequency v 0 1 . The-2line has slope c-2, c being the speed of sound.2. Acoustic Modulation of Microwave TransmissionBerlande, Goldan, and Goldstein 6 have described an experiment in which the micro-wave transmission coefficient T of a decaying cryogenic helium plasma is demonstrablymodulated by the sound produced by the decay of the electron temperature. An analysisnow being conducted on this experiment seems to indicate that(i) The electron temperature does not decay to the gas temperature (4. 20K), but toa temperature (~30 0 *K) determined by the microwave signal used in making the measure-ment.(ii) The initial electron density (-2 X 1011 cm - 3 ) and temperature (-3 X 104 "K) arealso unknown, so that quantitative agreement between theory and experiment can onlybe achieved by curve fitting.1.0 -0.9 -T0.8 -0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6TIME (msec)Fig. IX-2. Acoustic modulation of the microwave transmission coefficientof a decaying cryogenic plasma: theoretical plot for the param-eters indicated in the text.QPR No. 82 89(IX. PHYSICAL ACOUSTICS)(iii) The insensitivity of the acoustic amplitude to the size of the pulse generatingthe plasma may be due in part to an increase in gas temperature, which would defeatthe purpose of raising the electron density and temperature by means of the larger pulse.A theoretical curve with parameters as indicated in (i) and (ii) above, chosen so asto fit the experimental data, is shown in Fig. IX-2. The decay of the plasma is governedmainly by recombination rather than by diffusion. The transmission coefficient can beshown to be given approximately byT = exp (-wwca/c 2),where a is the length of the plasma,frequency. The plasma frequency wpphase with each other by the acousticc is the speed of light, and w/27 is the microwaveand the collision frequency Oc are modulated inwave.H. M. Schulz IIIReferences1. U. Ingard, Phys. Rev. 145, 41 (1966).2. H. M. Schulz III, Quarterly Progress Report No. 81, Researchtronics, M. I. T. , April 15, 1966, p. 43.3. U. Ingard and K. W. Gentle, Phys. Fluids 8, 1396 (1965).4. S. D. Strickler and A. B. Stewart, Phys. Rev. Letters 11, 5275. H. M. Schulz III and K. W. Gentle, Quarterly Progress ReportLaboratory of Electronics, M. I. T. , April 15, 1966, p. 44.6. J. Berlande, P. D. Goldan, and L. Goldstein, Phys. Letters 5,B. ERRATUM: LATERAL ACOUSTIC INSTABILITYLaboratory of Elec-(1963).No. 81, Research51 (1964).In Quarterly Progress Report No. 81, p. 45, Fig. VI-2, the photograph on the left-hand side marked "MODULATED" should read UNMODULATED.H. M. Schulz III, K. W. GentleQPR No. 82

Physical Acoustics

Contains reports on two research projects.U.S. Navy (Office of Naval Research) under Contract Nonr-1841-(42)Joint Services Electronics Programs (U.S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 36-039-AMC-03200(E

Macon, J. L.

VI. PHYSICAL ACOUSTICSAcademic and Research StaffProf. K. U. IngardProf. L. W. Dean IIIGraduate StudentsR. H. Katyl W. M. Manheimer J. A. RossJ. L. Macon H. M. Schulz IIIA. POSSIBILITY OF ION-WAVE AMPLIFICATION IN A PLASMAThe energy-transfer mechanism proposed by Ingard I for the amplification of acous-tic waves in a weakly ionized gas has been applied to the amplification of ion-acousticwaves in a fully ionized gas. Of importance in the calculation is the assumption, sup-ported by recent experimental observations,2 that the electron temperature remainsconstant during the period of an ion-acoustic oscillation. If the ions are treated adia-batically except for the coherent heating by the electrons, and if the various possibleion-acoustic loss terms are ignored, an amplification is discovered which is of orderTi/T e (i. e., of the order of the ion-electron temperature ratio) times the amplificationcalculated for acoustic waves in a weakly ionized gas having the same electron densityand temperature. This result can be understood from elementary considerations, anda note discussing the calculation in somewhat more detail has been submitted for publi-cation in The Physics of Fluids.H. M. Schulz IIIReferences1. U. Ingard, Phys. Rev. 145, 41 (1966).2. I. Alexeff and W. D. Jones, Phys. Rev. Letters 15, 286 (1965).B. SOUND AMPLIFICATION IN PLASMASPreliminary experimental evidence has been obtained in support of the theoryadvanced by Ingard I that sound waves are amplified as they pass through a plasma. Thisresults from an in-phase heating of the neutrals by the hot electron gas. The experimen-tal configuration is the following. A cold Helium discharge at a pressure of 16 mmHg wasmaintained in a long cylindrical tube, 2" in diameter, which contains a speaker at oneend and a microphone at the other. The speaker is so constructed that the maximumThis work was supported principally by the U.S. Navy (Office of Naval Research)under Contract Nonr-1841-(42); and in part by the Joint Services Electronics Programs(U.S. Army, U.S. Navy and U.S. Air Force) under Contract DA 36-039-AMC-03200(E).QPR No. 83(VI. PHYSICAL ACOUSTICS)- , ,, *--- DISCHARGE ON- DISCHARGE OFFT=45 0 K p=17mmHgT= 360*K p=16mmHg1000 1200Fig. VI-1. Cavity response vs frequency for a discharge power of 340 watts(E=1600 V, I=210 ma). Pressure is not calibrated.displacement of the diaphragm can be measured electronically while it vibrates. Thisknown sound pressure source is then used to excite vibrations within the cylindricalcavity, and the resulting pressure at the other end of the tube is measured. The fre-quencies used are in the 1-2 kc range.Figure VI-1 gives the results of a typical set of measurements. With the dischargeon, the resonance peak for the second normal mode shifted from 1325 Hz to 1540 Hz.This is caused by the increase in neutral temperature when the discharge is turned on.Of significance is the fact that the peak is higher and the preceding trough is lower forthe discharge ON curve. This indicates that the net attenuation rate is smaller with thedischarge ON than it is with the discharge OFF. This is presumed to result from theelectron amplification.Details of these results are given in the author's thesis.2J. L. MaconReferencesU. Ingard, Phys. Rev. 145, 41 (1966).J. L. Macon, S.M. Thesis, M.I.T., September 1966.QPR No. 83A.0 * 01600FREQUENCY Hz/,\

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