HPD and Superfluid Hydrodynamics by yurtgc548


									HPD and Superfluid Hydrodynamics

         Yury Mukharsky
  Low Temperature Laboratory, Helsinki University of
  Kapitza Institute
  Landau Institute
  Ioffe Institute
J. S. Korhonen, Y. Kondo, M. Krusius, Ü. Parts, E. V.
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.

                                         ll            n
Minimized at equilibrium by adjusting                      v

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

                   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
         • Difference in absorption
•   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.

                    Measurements Technique.
                                           •Flexible diaphragm+Fluid
                                           •Position of the diaphragm (equivalent
                      Flexible Diaphragm
                                           to the charge of the capacitor) is
                         Cap. plate        recorded.
                        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
                         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.
                                                          Inductance of the orifice is inversely
                                                             proportional to J¢(f).
                                                           As rotation changes the frequency
                            P         L    kx      L1   f changes.
          current                                               Driven oscillations
                    1/L1                                        Response to ambient vibrations
Max. f.                               Min. f
             1/L2                              f

          Measurements Technique -
                                        •Rotation results in the circulation in
                                        the sensing loop.
                                        Thus the rotation changes phase drop
                   Flexible Diaphragm
                      Cap. plate.
                            plate       across the weak link.
                     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.

              kx                   f
   Data Analysis


Large amplitude frequency (f0)
Precision in the bias.
                                      •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.

  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
•   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.



                (f/f0) -1



                            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

            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
               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.

          Q                   •As observed, the circulation should
                              diverge towards Tc.

                              •Change of the sign (weak),
                              however, remains unexplained.
•   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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