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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: • • • • 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: • • • • 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.