Contains reports on five research projects.U. S. Navy (Office of Naval Research) under Contract Nonr-1841(42

Dean, L. W., III

Gentle, K. W.

Ingard, K. Uno

Johnson, L. E.

Maling, G. C., Jr.

Matchett, G. A.

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VIII. PHYSICAL ACOUSTICSProf. K. U. Ingard T. J. Kinzer III M. C. Poppe, Jr.Dr. L. W. Dean III G. C. Maling, Jr. J. W. Ryon IIIK. W. Gentle W. M. Manheimer H. L. Willke, Jr.L. E. Johnson G. A. Matchett J. M. WittingA. MAGNETOHYDRODYNAMIC INSTABILITIES IN A LOW-DENSITY LIQUIDCONDUCTORThe first experiments in magnetohydrodynamic instabilities were probably performedby Northrupl in 1907. The "pinch effect," an instability in which the conductor constrictsitself until severed, was observed by Hering2 in electrolytic refining and was suggestedto Northrup. Northrup reported detailed observations of this effect in mercury and alsoreported stable "pinches" that reached equilibrium before breaking the current.The present work has been devoted to detailed investigations of this pinch effect ina liquid conductor. Our experiment employed a rectangular glass trough, approximately10 inches long and 0. 5 inch wide, filled 1 inch deep with an alloy of sodium and potas-sium that is liquid at room temperature. The alloy was covered with mineral oil. Cur-rents up to 1000 amps could be passed through the column and the results observed andphotographed.Because the alloy was covered with a fluid of almost the same density, the restoringpressure for surface deformations was slight. The result was a system that was quitesusceptible to magnetic forces and instabilities. It is therefore a possible model of adense, high-current plasma. 3Several experimental parameters were varied. The entire range of available cur-rents was investigated, from currents below 300 amps at which the conductor was stableto the high currents at which conduction lasted only one-tenth of a second. In additionto the normal column of uniform cross section and homogeneous fields, initial pertur-bations in the surface, constrictions in the trough, and external magnetic fields ofvarying degrees of inhomogeneity were employed. Photographic records of the motionof the fluid under these circumstances gave considerable information about the mecha-nism and details of the motion.In addition to the experimental work, some approximate theories of the pinch weredeveloped. Although we made no attempt to solve the complete equations of motion,enough progress was made in computing the forces caused by the interaction of the cur-rent with its own magnetic field to provide a stability criterion and to give considerableinsight into the phenomena. From both experimental and theoretical results, the depthof the pinch was found to grow exponentially with time. Such unstable pinches wereThis work was supported in part by the U. S. Navy (Office of Naval Research) underContract Nonr-1841(42).(VIII. PHYSICAL ACOUSTICS)observed for all currents above 400 amps, the threshold of instability as experimentallydetermined and theoretically indicated. However, the time constant of the growing expo-nential is a complex function of current, dimensions of the conductor, and shape of thepinch for which no functional dependence is given.A homogeneous fluid conductor is most certainly unstable with respect to small per-turbations when the current exceeds a certain critical value. Careful examination ofthe experiments and theory indicate also that if the conductor is unstable for small per-turbations, it will be even more unstable for large constrictions. We concluded that nostable pinches will be formed in a homogeneous conductor.A paper with a more detailed description of these studies is in preparation.K. W. Gentle, U. IngardReferences1. E. E. Northrup, Some newly observed manifestations of forces in the interiorof an electric conductor, Phys. Rev. 24, 474 (1907).2. C. Hering, A practical limitation of resistance furnaces, the pinch phenomenon,Trans. Am. Electrochem. Soc. 11, 329 (1907).3. B. Lehnert and G. Sjbgren, A liquid conductor model of the hollow pinch,Nuclear Energy: Part C 1, 121-123 (1960).B. GENERATION OF SHOCK WAVES BY EXPLODING WIRESA high-voltage facility for the study of exploding wires and similar phenomena hasbeen completed. It consists of 8 banks, each with sixteen 3. 75-4F Sprague 10-kv oil-bath discharge capacitors, giving a total of 60 FF for each bank. The capacitors areconnected with a large sheet of aluminum which forms the ground plate of the back. Ter-minals of a capacitor bank are connected to large metal sheets separated by a mylarsheet. The capacitors are charged. The discharge is triggered by means of a gapswitch that is caused to break down by means of a trigger pulse of 15 kv.Shock waves produced by exploding wires in air at atmospheric pressure have beenstudied. Copper wires 1. 5 inches long and ranging in diameter from 0. 3 mm to 0. 7 mmhave been used. The voltage on the wires has been varied from 2 kv to 5. 5 kv. Theenergy spectrum of the shock waves has been determined up to a frequency of 50 kc,and the efficiency of energy conversion to the shock wave has been measured. We foundthat a maximum power efficiency of approximately 3 per cent was obtained for a diam-eter of 0. 5 mm when the voltage was 5 kv. The duration of the "N-type" wave wasapproximately 0. 5 msec, and the maximum pressure measured at a distance of 30 cmwas approximately 0. 1 atmosphere.A paper on these studies is in preparation.L. E. Johnson, U. Ingard(VIII. PHYSICAL ACOUSTICS)C. MAGNETICALLY DRIVEN SHOCK WAVES IN SOLID CONDUCTORSPreliminary experiments on the excitation of magnetically driven shock waves in con-ducting solids have been undertaken. The end of a copper bar has been placed in themagnetic field of a single-turn coil through which a large current (approximately60, 000 amps) was discharged. The other end of the bar was attached to a quartz-crystaltransducer. Shock waves in the bar were observed, and the attenuation of these waveswas measured in copper. The generation of shock waves in electrolytes is now beingattempted, in the same manner.U. IngardD. SOUND PROPAGATION IN Cu3AuThe alloy Cu 3 Au exhibits an order-disorder transition at a critical temperature of390 0 C. As the temperature is raised, the ordering of atoms in the lattice decreasesslowly at first, then rapidly, and vanishes altogether at the critical temperature.Previous measurements 1 at the critical temperature have shown that the attenuationof a 600-kc sound wave is approximately 0. 05 nepers per cm. More recent measure-ments indicate that the attenuation at 2 mc may be more than ten times this amount.More exact measurements will be made when the problem of how to couple the soundwave to the sample over the necessary range of temperature has been solved.L. W. Dean III, G. A. MatchettReferences1. P. M. Scop, An Investigation of Order-Disorder Transitions in Cu3Au by Acous-tic Techniques, S. B. Thesis, Department of Physics, M. I. T., May 25, 1959.E. FIELD MEASUREMENTS OF SOUND PROPAGATION OVER GROUNDField measurements performed to check some theoretical calculations on the influ-ence of a plane boundary on sound propagation in an inhomogeneous moving medium havebeen completed. In order to simplify comparison of experiment with theory, we decidedthat the measurements should be performed over a large rigid boundary. The mainparking lot of Lincoln Laboratory, M. I. T., was used for the experiments describedbelow.Tape recordings of the received sound pressure level were made as a function ofthe distance from an electromagnetic horn driver. Both driver and microphone wereplaced 4 ft above the ground level. Frequencies of 500, 1000, and 2000 cps were used,and measurements were made on three different days. The rms data follow the theo-retical curves reasonably well, except in the minima of the pressure pattern at which(VIII. PHYSICAL ACOUSTICS)the effect of the turbulence is to raise the rms level, as discussed in Quarterly ProgressReport No. 64 (page 59). The fluctuations, however, are much more irregular thanthose obtained in the R. L. E. anechoic chamber. In order to try to obtain better corre -lation with the theoretical calculations, other statistical properties of the received signal(for example, the standard deviation) are being calculated.G. C. Maling, Jr., U. Ingard

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