Angular distribution of phonons from a planar heater in superfluidHe4: Pressure and power dependence

Abstract

We have measured the angular distribution of phonons propagating in liquid $^{4}\mathrm{He}$ which are created by a planar heater. The angular distribution varies considerably with pressure in the range $0--20\phantom{\rule{0.3em}{0ex}}\text{bars}$. At small angles to the heater normal, the angular distribution shows a mesa shape at $P=0$. At $6<P<12\phantom{\rule{0.3em}{0ex}}\text{bars}$ a large cusplike peak replaces the mesa shape and the peak gradually disappears at higher pressures. At larger angles to the heater normal, the signal is very small at $P=0$ and grows slowly until $P\ensuremath{\sim}15\phantom{\rule{0.3em}{0ex}}\text{bars}$ when it grows rapidly. At $P>19\phantom{\rule{0.3em}{0ex}}\text{bars}$ the overall angular distribution is cosinelike. The behavior is explained in terms of phonon interactions amongst the injected phonons, that take place in the liquid helium when there is anomalous phonon dispersion. The interactions change the energy of the phonons and this is detected by the phonon-energy sensitive bolometer. Modeling of the results indicates that at small angles to the heater normal, there is thermalization of the low energy phonons and the creation of high energy phonons, which decreases in the range $7.5<P<15\phantom{\rule{0.3em}{0ex}}\text{bars}$. At larger angles to the heater normal, $>20\ifmmode^\circ\else\textdegree\fi{}$, phonons with energy below the pressure-dependent critical energy only spontaneously decay. We find that the injected phonon spectrum can be approximately characterized by a Bose-Einstein spectrum with a temperature $\ensuremath{\sim}0.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which is nearly independent of heater power.