HPD and Superfluid Hydrodynamics Yury Mukharsky Low Temperature Laboratory, Helsinki University of Technology Kapitza Institute Landau Institute Ioffe Institute J. S. Korhonen, Y. Kondo, M. Krusius, Ü. Parts, E. V. Thuneberg Yu. M. Bunkov, V. V. Dmitriev G. E. Volovik E. B. Sonin HPD and counterflow • Magnetic field Þ anisotropy of rs Þ interaction with vs. H n ll n Minimized at equilibrium by adjusting v R. In the HPD Counterflow suppresses the HPD. Interaction of HPD with vortices. Vortex motion • Vortex core rotates and rocks. j • Rocking motion causes the dissipation h H b Interaction of HPD with vortices. When vortex end are pinned – twisting. Twisted vortex is more rigid and rocks less. When the vortex move – the ends are free. Effect of field tilting Tilting the field orients the vortex: No twisting Reduced rocking motion. Smaller dissipation. • If we twist less? – Rocking motion is less suppressed. • Difference in absorption smaller • Shorted HPD – weaker twist. Cosmic-like soliton. Connects two half-quantum vortices. Olivier Avenel, Eric Varoquaux CEA-DRECAM, Service de Physique de l'Etat Condense, Centre d'Etudes de Saclay, France CNRS-Laboratoire de Physique des Solides, Universite Paris-Sud, Orsay, France The cell: •Weak link: xSD(H=0)=7 mm • 198 0.10x0.10 mm holes separated by 2 mm in SiliconNitride membrane ~0.1 mm thick. Membrane: 75x60 mm, Ra=16 mm, R k=0.03 mm •Part of the membrane where edge effects can be strong is highlighted with yellow. xs Measurements Technique. •Flexible diaphragm+Fluid inertia=Resonator •Position of the diaphragm (equivalent Flexible Diaphragm to the charge of the capacitor) is Cap. plate recorded. Orifice Pos. Sensor The current through the orifice/parallel path is determined as derivative of the diaphragm location. The pressure across the orifice is proportion Cd The phase across the orifice is P L1 f proportional to the integral of Pel L2 (orifice) pressure: Amplitude of phase oscillations µ amplitude of diaphragm. Measurement technique - rotation •Rotation changes the phase across the weak link. •Phase is determined by solving Flexible Diaphragm plate Cap. plate. Orifice Can be graphically represented by Pos. Sensor intersection of loadline with J(f). The dependence has period: 0.842 WÅ=5.6 10-5 rad/sec. W Inductance of the orifice is inversely proportional to J¢(f). As rotation changes the frequency P L kx L1 f changes. el current Driven oscillations 1/L1 Response to ambient vibrations Max. f. Min. f 1/L2 f kx Measurements Technique - rotation. •Rotation results in the circulation in the sensing loop. Thus the rotation changes phase drop Flexible Diaphragm Cap. plate. plate across the weak link. Orifice Pos. Sensor Earth - rotating platform. Change in rotation - reorient apparatus W relative to the Earth. Effect has been calibrated in 4He experiments: with 4.9 cm2 two-turn loop we use, the Earth rotation produces circulation ~0.85 k3. P kx f el Data Analysis k4 Large amplitude frequency (f0) Precision in the bias. p-shift. •Bias does not change much after going through Tc, if it does not jump by k3/2 •We assign bias ~0 to the case which happens more often (see below). T effect explains most of the scatter show on the picture to the left (local overheating Bias at fixed T, P and magnetic of the inner cell while at nominally stable field. T). p-shifted states. Explanations? p-solitons? Vortex? Salomaa-Volovik, 1988 Very large energy. Bind cores of double-core vortex. Thought to be unstable in bulk (are they?) T-dependence of the circulation. • Bias is stable after each cooldown (save for some time-drift, see below. There are some minor variations from one cooldown to another. • However there is strong temperature dependence – as T changes between ~0.99 and 0.5 Tc the bias changes by almost k3 at P=0.2 bar and much stronger at P=10 bar. • At 10 bar the effect is much stronger with 2 amp current in the field coil. “Mirror” I(f). •Often apparently the same state can have 0 or p bias. •Not predicted by theory? – Changing n to –n will not do. 0.3 0.2 0.1 (f/f0) -1 2 0.0 -0.1 -0.2 0.0 0.1 0.2 k 0.3 0.4 0.5 Cosmiclike solitons • Have been predicted by Salomaa and Volovik. Though to be conecting cores of double-cores vortex, but have have been observed in free state. • Solitons are thought to be unstable. But are they in toroidal geometry? For example – rotation of the torus may provide p/2 phase shift along it. Will then the soliton be stable configuration? Phase change • We think that the observed p-shift can be provided by 1 or more solitons, crossing the flow loop. • Alternative explanation – a single vortex pinned in a position exactly in the middle of the flow channel seems Why soliton? 100 gauss Coils Explanation of T-dependence •Heat leak to inner cell, due, for example to heat release from Stycast or eddy heating in silver increases Ag fountain pressure there and causes normal current flow from the inner cell Stycast Q vs and counterflow of superfluid into it. vn Q •As observed, the circulation should diverge towards Tc. •Change of the sign (weak), however, remains unexplained. Summary • A number (~8) of different current-phase relations (CPR) are observed. • Under certain conditions most of these relations are observed shifted by p. • The shift appears to be unrelated to the shape of the CPR and does not change when CPR changes. • We argue that the most probable cause is a cosmic-like soliton(s) crossing the sensing loop. • Temperature dependence of the trapped circulation can be explained by thermomechanical effects. • This has important implication for superfluid gyroscopes – heat leaks and temperature stability become important. • It appears that there is no remnant vorticity in the cell.
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