Evolution of superfluid vortex line density behind a heat (second-sound) pulse in helium II

Abstract

A new probe for superfluid vortex line density with a response time of 400 /is and a spatial resolution of 1 mm was developed and used to investigate the growth and decay of superfluid vortex lines during the passage of a heat pulse. The evolution process turns out to be in accordance with existing theories. PACS numbers: 67.40.Pm, 67.40.Vs One of the most striking features of liquid-helium II is its high thermal conductivity, resulting from an internal convection process that can be described in terms of Tisza's two-fluid model as formulated by Landau. x According to this model the fluid consists of two components, each having its own density and velocity field. An important case of flow is that generated by injecting a heat flux into the fluid. Heat is transported solely by the normal fluid component, whereas the superfluid moves so as to provide no net mass flux of the whole liquid: counterflow. For small heat fluxes the only dissipation is caused by the viscosity of the normal fluid component. Early experiments of Gorter and Mellink 2 on temperature and pressure gradients in flows in tubes showed an extra dissipation that could be described by an additional friction force in the equations of motion, and is related to the appearance of superfluid vortex lines, as was later shown by Hall and Vinen. 3,4 This feature has often been investigated in steadystate pipe flows, which are now quite well understood as far as the dependence of the total amount of vortex line density (VLD) (i.e., length of vortex line per unit volume) on temperature and heat flux is concerned, 5 whereas substantial uncertainties remain regarding the growth of the vortex tangle and its motion. 6,7 Therefore we used heat pulses to get a closer insight into the resulting temporal evolution of the vortex line density.Our experimental apparatus is a square tube of 2.6 x2.6-cm 2 cross section and 8-cm height made of Lucite located vertically in a Dewar. The second-sound shock waves are generated by means of a chromium thin-film heater at the bottom of the tube. The VLD, L, is deduced by measuring its effect on the damping of second sound. The additional attenuation due to the vortex lines is given by 8 a's ~ (BK/6C2)L, where B is a mutual friction coefficient, K -10 ~3 cm 2 /s is the quantum of circulation, and C2 is the speed of second sound.The VLD probe consists of two plane parallel glass plates (12x12x0.1 mm 3 ) fixed at a distance of 1 mm from one another forming a resonator (Fig. 1). On one plate a thin-film heater (1x2 mm 2 ) consisting of vapordeposited chromium acts as a second-sound pulse emitter. Facing it on the other plate, the bolometer consisting of a thin evaporated layer of gold and tin 9 (1 xO.02 mm 2 ) is located. At the beginning of a measurement, an electric pulse is applied to the heater located at the bottom of the channel, producing a primary heat pulse of duration tn and heat flux Q. After a certain delay time taking into account the time of flight to the probe, a short probe pulse (*///> -10 jus, 6/>-3 W/cm 2 ) is relea...

Temperature overshoot due to quantum turbulence during the evolution of moderate heat pulses in He II

“…Selected typical experimental findings are correlated with theoretical calculations based on a simple model deduced for the case of steady flow in tubes. Some previous results have been already published by Fiszdon & Schwerdtner (1989) and Schwerdtner, Stamm & Schmidt (1989).…”

Three dimensionality of pulsed second-sound waves in He II

“…Nonlinear theory about second sound wave was first developed by Temperley [3], and was then extended by Khalatnikov [4,5] whose prediction was proven by the experimental demonstration of Dessler and Fairbank [6]. Planar second sound wave has been frequently used to probe quantized vortices for its relatively simple geometry, and extensive study concerning this topic has been carried out in recent decades [7][8][9][10]. It has been shown that second sound wave interacts with self-generated quantized vortices as it propagates along a wave guide.…”

Looking at electrons

“…At 1.65 K, ␣ / ␤ is measured 24 to be 109 s cm −2 , and the counterflow velocity is nearly the same as the velocity of the normal fluid. Equation ͑12͒ then gives a line density of 3 ϫ 10 5 cm −2 .…”