Download Quantum Turbulence in Superfluid 3He at Ultra Low Temperatures.

Quantum Turbulence in Superfluid 3He-B
at Ultra Low Temperatures.
D.I.Bradley
D.O.Clubb
S.N.Fisher
A.M.Guenault
A.J.Hale
R.P.Haley
M.R.Lowe
C.Mathhews
G.R.Pickett
R.Rahm
K.Zaki
I.E.Miller
M.G.Ward
•Introduction
•Vibrating Wires in superfluid 3He-B
•Observation of Turbulence
•The Spatial Extent of Turbulence
•Direct measurements of Andreev scattering from Turbulence
•Grid Turbulence
3He
Phase Diagram
Superfluid phases formed by
Cooper pairs with S=1, L=1
Vortices in the B-phase
Formed by a 2p phase shift around the core
superfluid flows around core with velocity,
vS=k/2pr
vortices are singly quantised with
circulation :
k=h/2m3
Superfluid is distorted in the core,
core size depends on pressure: x0~ 65nm to 15nm
Decrease in damping at higher temperatures implies that the
damping from thermal quasiparticles is reduced.
i.e. thermal quasiparticles are prevented from scattering with
the detector wire.
Quasiholes propagate through flow field
Quasiparticles Andreev Scattered into Quasiholes
with very small momentum transfer
Fraction of flux Reflected
=0.5*[1-exp(-pFv(r)/kBT)]
v(r)=k/2pr, k=h/2m3
Shadow half Width
= pFk/2pkBTln2
~8mm @ 100mK
(vortex core size
x0 ~ 65nm @low P)
Flow barrier independent of temperature below .22Tc
Flow barrier decreases above .22Tc
The heat input to the radiator
(applied heat and heat leak) is
balanced by a beam of ballistic
quasiparticle excitations
emitted from the radiator
orifice.
In the presence of vortices,
the change in width
parameter is proportional to
the fraction of excitations
Andreev reflected.
Simple Estimate of vortex Line Density
Take a thin slab of homogeneous vortex tangle of
unit area, line density L and thickness dx
Mean qp energy =kBT
Qps are Andreev scattered if pFv(r)> kBT
v(r)=k/2pr, so qps scattered if they approach within a distance, r ~ kpF /2pkBT
Probability of qp passing within distance r of a vortex core is L dx r
Fraction of qps Andreev scattered after traveling dx through tangle, Ldx kpF /2pkBT
Total fraction transmitted through tangle of thickness x is exp(-x/l),
l~ 2pkBT / LkpF
Decay time of vortex tangle
VWR measurements show the tangle disperses in ~ 3-4s
From Simulations by C.F.Barenghi and D.C.Samuels, PRL 89 155302 (2002)
Tangle disperses
by evaporating
small rings of
size R~L-1/2
Rings form after a time t~1/(Lk) [~0.3s for our line densities]
The tangle then expands at the self induced velocity of the rings, vR
Time scale for tangle to disperse ~ S0/ vR
~5s for our line densities
Grid Mesh:
11mm rectangular wires,
40mm square holes.
Summary
Turbulence in 3He-B Generated by VWRs:
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Generated above pair-breaking critical velocity vC=vL/3 ~ 9mm/s @ P=0
Spatial extent ~2mm
Line densities up to ~5x107m-2, line spacing ~ 150mm
Disperses on a time scale of a few seconds, explained by ‘ring evaporation’
Turbulence in 3He-B Generated by a Vibrating Grid:
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Generated above a velocity ~ 1mm/s
Estimated Spatial extent ~2mm
Estimated Line densities up to ~5x108m-2, line spacing ~ 50mm
Disperses on a time scale of: seconds above ~4mm/s
<0.1s at lower velocities
(sharp cross-over at 3.5 mm/s)
- Possible explanation: The Grid is only generating fast propagating vortex rings at
low velocities which become turbulent at high velocities.