The Density of High Energy Phonons Created from a Low Energy Phonon Pulse in Liquid 4He

We calculate the energy density of high energy phonons created from a pulse of low energy phonons spatially confined to a narrow cone. We include the tangential expansion of the propagating pulse and the interactions between high energy phonons within the pulse as well with low energy phonons. The expansion of the pulse causes it to cool so much that the creation of high energy phonons stops within 3 mm of the heater. The decay rate of high energy phonons governs the dynamic equilibrium inside the pulse. The magnitude of the high energy phonons, emitted by the pulse into the cold liquid helium, is calculated for different length pulses. It is found that small heaters can produce short pulses of high energy phonons from relatively long injected pulses.