Creation of high-energy phonons by four-phonon processes in anisotropic phonon systems of HeII

Abstract

The problem of the creation of high-energy phonons (h-phonons) by a pulse of low-energy phonons (l-phonons) moving from a heater to a detector in superfluid helium is solved. The rate of h-phonon creation is obtained, and it is shown that the h-phonons created occupy a much smaller solid angle in momentum space than the l-phonons. An analytical expression for the creation rate of h-phonons, along the symmetry axis of a pulse, is derived. It allows us to get useful approximate analytical expressions for the creation rate of h-phonons. The time dependences of the parameters describing the l-phonon pulse are obtained. This shows that half of the initial energy of l-phonon pulse can be transferred into h-phonons. The results of the calculations are compared with experimental data, and we show that this theory explains a number of experimental results. The value of the momentum that separates the l- and h-phonon subsystems is found.