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 created h-phonons occupy a much smaller solid angle in momentum space, than the l-phonons. An analytical expression for the creation rate of h-phonon, along the symmetry axis of a pulse, are derived. It allows us to get useful approximate analytical expressions for the creation rate of h-phonons. The time dependences of the parameters which describe 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, which separates the l-and h-phonon subsystems, is found.

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

“…However, it is apparent from the figure that initially the h-phonon creation rate rapidly increases as it depends strongly on the energy density of the l-phonons. 29 The ratio slowly decreases at high-power densities probably due to more scattering of the h-phonons within the denser l-phonon pulse before they leave it. This scattering within the pulse, by 4pp, reduces the number of h-phonons within the pulse and consequently the number that escape the pulse.…”

“…This is consistent with the theory of h-phonon creation which showed that h-phonons are produced in the central core of the l-phonons within a few millimeters of the heater. 5,29 After the h-phonons have stopped being created, the l-phonons, propagating near to the heater normal, are cool but still strongly interacting. Any development of the l-phonon system which would change the width of the angular distribution and the width of the mesa, can only be due to the effects within the l-phonon pulse and does not involve the h-phonons.…”

“…7 In the first paper on the mesa, 6 it was proposed that the mesa shape was related to the creation of high-energy phonons: Immediately after the heater pulse, the low-energy phonons have an angular distribution of energy which is highest along the direction normal to the heater and decreases as the angle to the normal increased. As the h-phonon creation rate is a strong function of energy density, 29 broadly speaking, above a certain energy density h , there is increasing h-phonon creation and below it, little h-phonon creation. So h-phonons are created in directions near to the heater normal.…”