Formation of a Mesa Shaped Phonon Pulse in Superfluid 4He

Abstract

We present a theory for the formation of a mesa shaped phonon pulse in superfluid 4 He. Starting from the hydrodynamic equations of superfluid helium, we obtain the system of equations which describe the evolution of strongly anisotropic phonon systems. Such systems can be created experimentally. The solution of the equations are simple waves, which correspond to second sound in the moving phonon pulse. Using these exact solutions, we describe the expansion of phonon pulses in superfluid helium at zero temperature. This theory gives an explanation for the mesa shape observed in the measured phonon angular distributions. Almost all dependencies of the mesa shape on the system parameters can be qualitatively understood.

Creation of high-energy phonons in superfluidH4eand the dependence of their angular distribution on heater size

“…Such possibilities of the lateral expansion of the cool l-phonon pulse are analyzed in Ref. 32 and predict a widening of the l-phonon mesa width with distance.…”

“…There is another model for the later development of the mesa that does not involve any h-phonons 32 and so applies after the period of intense h-phonon creation. The model only involves the behavior of a cool low-energy phonon beam where there are no h-phonons, which is after the pulse has propagated a few millimeters from the heater.…”