Quantum Turbulence in Superfluid 3 He-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 Introduction Vibrating Wires in superfluid 3He-B Observation of Turbulence The Spatial Extent of Turbulence Direct measurements of Andreev scattering from Turbulence Grid Turbulence G.R.Pickett R.Rahm K.Zaki I.E.Miller M.G.Ward

3 He Phase Diagram Superfluid phases formed by Cooper pairs with S=1, L=1

Vortices in the B-phase Formed by a 2  phase shift around the core superfluid flows around core with velocity, v S =  /2  r vortices are singly quantised with circulation :  =h/2m 3 Superfluid is distorted in the core, core size depends on pressure:  0 ~ 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(-p F v(r)/k B T)] v(r)=  /2  r,  =h/2m 3 Shadow half Width = p F  /2  k B Tln2 ~8  100  K (vortex core size  0 ~ P)

Flow barrier independent of temperature below.22T c

Flow barrier decreases above.22T c

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.

Take a thin slab of homogeneous vortex tangle of unit area, line density L and thickness  x Probability of qp passing within distance r of a vortex core is L  x r Mean qp energy =k B T Qps are Andreev scattered if p F v(r)> k B T v(r)=  2  r, so qps scattered if they approach within a distance, r ~  p F /2  k B T Simple Estimate of vortex Line Density Fraction of qps Andreev scattered after traveling  x through tangle, L  x  p F /2  k B T Total fraction transmitted through tangle of thickness x is exp(-x/ ), ~  2  k B T / L  p F

Decay time of vortex tangle From Simulations by C.F.Barenghi and D.C.Samuels, PRL (2002) Tangle disperses by evaporating small rings of size R~L -1/2 Rings form after a time  ~1/(L  ) [~0.3s for our line densities] The tangle then expands at the self induced velocity of the rings, v R Time scale for tangle to disperse ~ S 0 / v R ~5s for our line densities VWR measurements show the tangle disperses in ~ 3-4s

Grid Mesh: 11  m rectangular wires, 40  m square holes.

Summary Turbulence in 3 He-B Generated by VWRs: Generated above pair-breaking critical velocity v C =v L /3 ~ P=0 Spatial extent ~2mm Line densities up to ~5 x 10 7 m -2, line spacing ~ 150  m Disperses on a time scale of a few seconds, explained by ‘ring evaporation’ Turbulence in 3 He-B Generated by a Vibrating Grid: Generated above a velocity ~ 1mm/s Estimated Spatial extent ~2mm Estimated Line densities up to ~5x10 8 m -2, line spacing ~ 50  m 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.