Parametric generation of second sound in superfluid helium: Linear stability and nonlinear dynamics - art. no. 054506

We report experimental studies of parametric excitation of second sound (SS ) by first sound (FS) in superfluid helium in a resonance cavity. The resul ts on several topics in this system are presented: (i) The linear propertie s of the instability, namely, the threshold, its temperature and geometrica l dependencies, and the spectra of SS just above the onset were measured. T hey were found to be in good quantitative agreement with the theory. (ii) I t was shown that the mechanism of SS amplitude saturation is due to the non linear attenuation of SS via three wave interactions between the SS waves. Strong low-frequency amplitude fluctuations of SS above the threshold were observed. The spectra of these fluctuations had a universal shape with expo nentially decaying tails. Furthermore, the spectral width grew continuously with the FS amplitude. The role of three and four wave interactions are di scussed with respect to the nonlinear SS behavior. The first evidence of Ga ussian statistics of the wave amplitudes for the parametrically generated w ave ensemble was obtained. (iii) The experiments on simultaneous pumping of the FS and independent SS waves revealed several effects. Below, the insta bility threshold, the SS phase conjugation as a result of three wave intera ctions between the FS and SS waves was observed. Above the threshold two in teresting effects were found: a giant amplification of the SS wave intensit y and strong resonance oscillations of the SS wave amplitude as a function of the FS amplitude. Qualitative explanations of these effects are suggeste d.