Formation of a mesa shaped phonon pulse in superfluid $^4$He

TL;DR

This paper develops a hydrodynamic theory explaining the formation of a distinctive mesa-shaped phonon pulse in superfluid helium-4, linking experimental observations with exact solutions of wave equations.

Contribution

It introduces a new theoretical framework based on hydrodynamics to describe anisotropic phonon pulse evolution and explains the observed mesa shape in phonon distributions.

Findings

The theory reproduces the mesa shape observed experimentally.

Exact solutions describe second sound in moving phonon pulses.

Dependencies of the mesa shape on system parameters are qualitatively understood.

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.