Phonon propagation in liquid⁴He: the dependence on injected power and pressure

Abstract

The propagation of phonons in liquid 4He is considered as a function of the number of phonons injected, the ambient pressure, the propagation distance and the ambient temperature. It is shown that there are four main groups of behaviour. The first and simplest is at high pressures, P>19 bar, where apart from some phonon-roton scattering near the heater, the propagation is ballistic and independent of distance and temperature for T<0.3 K. the second group is at low pressures and low injected phonon densities, where the behaviour is dominated by spontaneous decay and can be modelled satisfactorily. The third group is at low pressures and moderate injected phonon densities, where there is interaction within the beam between the high- and low-frequency phonons. The fourth group is at low pressures and high injected phonon densities, where interactions within the beam are so strong that there is frequency up-conversion to both medium and high phonon energies. The up-conversion process is suggested to be a combination of three- and four-phonon processes. At low pressures, the high-frequency phonons are attenuated by scattering with thermal phonons; however, the dependence of the attenuation on ambient temperature decreases as the injected phonon density increases, because the up-conversion reduces the effective distance for decay processes.

Dissipation in an Ideal Monoatomic Superfluid

“…of an I.M.S., the elementary excitations are almost only phonons. As the phonon creation and annihilation processes are very rare in helium II at high pressures [15], we conclude that the assumption that helium II (at low temperatures and high pressures) behaves as an ideal fluid is solidly motivated, even when dissipative processes are taken into account.…”

“…This behaviour agrees with some experiments which evidence that, for low temperatures and high pressures, helium II behaves as a gas of non-interacting quasi-particles. Indeed, in [15] it is shown that for sufficiently high values of pressure the phenomena of phonon creation and destruction are absent and that the phonon propagation is ballistic. Furthermore in [16] it is shown that the mobility of ions in liquid helium II increases as the temperature is lowered.…”