Second Sound in Solid Helium-3

Abstract

VOLUME 22, NUMBER 15 PHYSICAL REVIEW LETTERS 14APRIL1969 and the linearized Boltzmann equation solved for the perturbed velocity distribution. The current density can then be calculated and related back to the electric field by means of Maxwell's equations so determining the coefficients a n . For a) «w. and a Maxwellian velocity distribution in the unperturbed state,where B(a) is the amplitude of the magnetic field at x = ±a, c 0 is the most probable speed of electrons, Z(|) is the plasma dispersion function, 7 and £ zz 2av(i-(x)/v)('nc ( fi)~1. The electromagnetic field and the current distributions are then determined, leading to a value for R. In making these calculations we put i>= ^en + ^ei> where the electron-ion collision frequency u e i was obtained from an expression for the resistivity of a fully ionized plasma given by Spitzer. 8 The theory confirms the presence of a critical frequency and density for which R is much greater than predicted by cold plasma theory. Theoretical values of R are shown in Fig. 1 for a frequency near the critical value. Despite the plane geometry used in the theoretical treatment, the theory gives a good description of the observed field penetration. On the other hand, the coldplasma theory in plane geometry giveswhich is plotted in Fig. 1 for the same value of <x)/v ( en* The results show a monotonic increase of R with increasing N (similar to the Besselfunction expression given earlier) and do not agree with the experiment.For densities greater than that corresponding to the maximum of R the theory shows that in general \B\ does not decrease monotonically from the plasma surface to the central plane. This has been observed by Demirkhanov, Kadysh, and Khodyrev. 4 The theory of Weibel 3 for the anomalous skin effect in a semi-infinite plasma also predicts analogous behavior in that the amplitudes of the field vectors do not decrease steadily from the plasma boundary.Other experiments have been carried out with plasmas of different radii and also with steady state plasmas for which the plasma parameters could be determined more accurately. These results will be described in a later publication.We wish to thank Mr. A. G. Allender for computational work.An experiment on temperature pulse propagation in a bcc crystal of 3 He grown at 95.9 atm shows the existence of second sound in the solid below about 0.58°K. In the temperature range 0.42°K<T<0.58°K, reflections of the received pulses were observed. In the range 0.58°K<r< 1.2°K, the temperature pulses were observed to propagate diffusively.The phenomenon of second sound in solids has been observed previously 1 in experiments on temperature pulse propagation in crystals of hep 4 He. The purpose of this Letter is to report pre-liminary results of an experiment in which temperature pulses were observed to propagate as second sound in a crystal grown from high-purity 3 He. 764

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