Nonlinear and Critical Second Sound in Helium -4

Experimental studies of the nonlinear evolution in time of planar second-sound pulses in superfluid ^4He have been carried out very near the lambda-transition. Second sound pulses have been observed as close as 2 times 10^{-7} in reduced temperature, and their evolution in time is studied by the use of a pulse-echo technique. Within limits, this time evolution is shown to be well described by the solutions of Burgers' equation. The model used to describe these pulses is described in detail, including the treatment of the heater and detector boundaries. A method for extracting the linear second sound velocity and damping from these nonlinear pulses is described. The understanding of the nonlinear behavior of second sound near T_lambda is important to the study of critical phenomena in ^4He. In particular, the nonlinearities present in second sound propagation diverge at the transition, so that sufficiently near T_lambda the amplitudes required for the propagation of linear sound become unmeasurably small. The second sound velocity is related to the superfluid density and is therefore of interest in the study of static critical phenomena, while the second sound damping is of interest in the study of dynamic critical phenomena. All methods used to date for extracting these quantities have relied on the existence of a regime where linear second sound can still be generated and detected; the method described herein does not suffer from this limitation and allows for the study of second -sound damping and velocity into the nonlinear regime. In part II of this work, new results are presented for these quantities for reduced temperatures as small as 3 times 10^{-7}, and a comparison with existing theories is made. This study required temperature stability and measurement on the nano-Kelvin level, and a detailed description is given of the methods involved. In particular, a new thermometer is described, as well as a new method for measuring T_lambda. Finally, a number of suggestions are made for future work. I demonstrate that studies of the effect of a heat flux on the critical behavior of ^4 He are possible, using this method, very near to T_lambda. It is also possible to study the "breakdown" of superfluidity, or the dynamics of superfluid turbulence, very near the transition with the use of very large amplitude second sound pulses. New phenomena in this regime are reported and connections with previous work away from T_lambda are made.