High-energy phonon creation from cold phonons in pulses of different length in He II

We have carried out a theoretical investigation of the experimentally observed phenomenon that long-lived high-energy (h) phonons are generated by a moving cloud of low-energy (l) phonons. The h phonons are created from the l phonons by four phonon processes $(4pp)$ and they are lost from the trailing edge of the l phonon cloud, because they have a lower velocity than the l phonons, and form the h phonon cloud. We obtain a set of equations which completely describe these phenomenon. The solution of these equations accounts for the high efficiency of the conversion process: a major part of the energy in the l phonons can be converted to h phonons within the propagation time of the pulse $(<{10}^{\ensuremath{-}4}\mathrm{s}).$ In short pulses $(<{10}^{\ensuremath{-}7}\mathrm{s})$ the h phonons escape as soon they are created, but in long pulses the h phonon density increases within the l cloud. It is shown that in long phonon pulses there can be a suprathermal number of h phonons within the l cloud. The theory describes the cooling of pulses of different length due to energy being transformed into h phonons. It also accounts well for the important characteristics of h phonon generation which is an unusual example of energy transferring from low-energy to high-energy states.