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Focus: Detecting vortices/turbulence in pure superfluid 4 He at T << 1 K. Message: Ions (microscopic probe particles) can be injected into helium, manipulated and detected. They are attracted to vortex cores and can be trapped by them Hence, by observing: - loss of ions, - deflection of current, - time-dependent variaytion of current, one can learn about the presence and dynamics of vortices – even at low temperatures. Plan: 1. Ions in helium – tutorial 2. Results of preliminary experiments at Manchester 3. Trapping cross-section 4. Time constants for vortex relaxation Injected ions in superfluid helium as detectors of quantized vortices Andrei Golov Warwick, 8 December 2005

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- Injected ions (attracted to vortex lines) - Second sound (requires normal component) - Local pressure and temperature sensors (early stage) The ion technique is: 1.Create and send ions through the test volume. 2.If there are vortices, some ions will be trapped and move with vortices: The loss of ions and deflected currents tell about the density of vortex lines and their motion. Detectors of vortices in superfluid 4 He: Ions helped to prove that vortices are discrete continuous defects: - Carreri, Scaramuzzi, Thomson, McCormick (1960): first observation of a vortex tangle; - Carreri, McCormick, Scaramuzzi (1962): trapping of -ve ions by a vortex array; - Packard and Saunders (1972): entry of vortices one by one;

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Ω = 0.30 – 0.86 s -1

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S.I.Davis, P.C.Hendry, P.V.E.McClintock, H.Nichol, in “Quantized Vortex Dynamics and Superfluid Turbulence”, ed. C.F.Barenghi, R.J.Donnelly and W.F.Vinen, Springer (2001). Physica B 280, 43 (2000); T = 22 - 70 mK To interpret, need to know the trapping cross-section and lifetime

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Negative ion: bare electron in a bubble (Atkins 1959) : p0 bar 25 bar R - 17 Å 12 Å m - 243 m He 87 m He (Ellis, McClintock 1982) Positive ion: cluster ion (“snowball”) (Ferrell 1957) : p0 bar 25 bar R + 7 Å 9 Å m + ~30 m He ~50 m He Injected ions: structure Ions - spherical probe particles that can be pulled by external force. Proved extremely useful for studies of excitations and vortices in liquid He. By changing pressure and species, one can cover R = 7–17 Å, m/m He = 30-240.

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C.C.Grimes and G.Adams, Phys. Rev. B 1990; Phys. Rev. B 1992 A.Ya.Parshin and S.V.Pereverzev, JETP Lett. 1990 Radius of negative ions: IR spectroscopy

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Ion–vortex interaction (rigid vortex) Energy of interaction = missing kinetic energy of superflow Calculated binding energy ΔV (p = 0): Negative ions: ΔV ~ 60 K Theory: Parks and Donnelly (1966): Donnelly & Roberts (1969): Berloff, Roberts (2000) slope ~ 10 K / 10 Å = 1 K/Å e.g. eE = 10 -3 K/Å at E = 10 V/cm

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How to inject ions? - radioactive ionization (α or β) sources (easy to use but can’t be switched off: excess heating) - sharp metal tips (radius of curvature ~ 100 -1000 Å ): - 100V + 400V field emission: negative ions field ionization: positive ions β

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Tungsten tips: etching A. Golov and H. Ishimoto, J. Low Temp. Phys. 113, 957 (1998). Currents ~ 10 pA at voltage ~ - 80 V

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Ions: mobility D.R.Allum, P.V.E.McClintock, A.Phillips, R.M.Bowley, Phil. Trans. R. Soc. A284, 179 (1977) R.Zoll. Phys. Rev. B 14, 2913 (1976) ~ 2.0 K p = 0v L = 60 m/s p = 25 bar v L = 46 m/s At our fields E ~ 20-30 V/cm, ions cross our cell in ~ 1 ms.

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Vortex nucleation by a fast ion at v c ~ R -1 Experiment: Rayfield and Reif (1964) McClintock, Bowley, Nancolas, Stamp, Moss (1980, 1982, 1985) Theory for V c : C.M.Muirhead, W.F.Vinen, R.J.Donnelly, Phil. Trans. R. Soc. A311, 433 (1984) Simulations: T.Winiecki and C.S.Adams, Europhys. Lett. 52, 257 (2000) Berloff abd Roberts (2000) Depending on the pull and friction, the ion will then either stay with the ring or leave At T < 1K, vortex rings are produced: - pure 4 He: at p < 12 bar; - impure 4 He (even at ~10 -7 3 He): always V - * (with traces of 3 He)

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Ion-ring complex At our voltages ~ 100 V, rings grow to ~ 10 -4 cm. They cross the cell in ~ 1 s.

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Ion–vortex interaction (rigid vortex) Energy of interaction = missing kinetic energy of superflow Calculated binding energy ΔV (p = 0): Negative ions: ΔV ~ 60 K Theory: Parks and Donnelly (1966): Donnelly & Roberts (1969): Berloff, Roberts (2000) slope ~ 10 K / 10 Å = 1 K/Å e.g. eE = 10 -3 K/Å at E = 10 V/cm E

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Theory: Brownian particle in a gas of rotons. Solid line: stochastic model (Donnelly & Roberts,1969) Dashed line: Monte-Carlo calculations σ = 10 -6 – 10 -4 cm

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Cross-section for ion-rings σ ~ 2 R 0 ~ E = 4 10 -5 cm – 2 10 -4 cm T-independent for T < 0.5 K PRL 17, 1088 (1966)

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What if T < 1 K? Near a rigid vortex line, an ion will hardly thermalize in the well, at least when being pulled normal to the vortex line. ΔVΔV v = v L, KE v = v L When the ion is pulled parallel to the line, trapping is more likely: σ ~ 1 / cosθ, hence should be measured at all angles, not only θ = 0. Especially if we are going to sample a tangle, not an array of parallel lines. P KE (v L ) ΔV 0180K~60K 20 bar 60K~20K

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What if vortex line is not rigid? Capture of a stationary ion from distance ~ R: Kelvin waves help remove excess energy N.G.Berloff and P.H.Roberts, Phys. Rev. B 63, 024510 (2000). More calculations are needed to figure out how a moving ion will interact with the vortex. As stretching a vortex line by just 10 Å increases its energy by some 30 K, this indeed might help.

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If captured: chances of escape In low fields, E << 10 4 V/cm, long sentence if T < 1.6 K (p = 1 bar) T < 1.3 K (p = 15 bar) At T < 1 K the trapping lifetime seems to shorten again (Douglas, Phys. Lett. 28A, 560 (1969) – a mystery so far) While trapped, ions can slide along the vortex line, but the mobility is reduced compared to the bulk value Donnelly, Glaberson, Parks (1967), Ostermeier and Glaberson (1976)

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4.5 cm Vortices in superfluid 4 He below 100 mK Aims: - to measure the cross-section of ion capture by vortex lines, -to study the vortex dynamics at T < 100 mK Rotating cryostat is used to produce an array of parallel vortex lines: inter-vortex spacing ~ 0.2 - 0.3 mm (density n = 2 10 3 cm -2 ) P.M. Walmsley, A.A. Levchenko, S. May, L. Chan, H.E. Hall, A.I. Golov Ion source Collector

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Charging of vortices by a horizontal current Measuring the total trapped charge Setup 1

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Simultaneous measurements (by both collectors) of the current due to the trapped ions sliding vertically and bulk current detected horizontally Setup 2

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Measuring bulk mobility Measuring ion mobility along vortex lines Setup 3

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T = 60 mK, p = 1.2 bar -190 V 20 min Current to top collector Current to side collector

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Temperature sweep from 1.3 K to 0.1 K

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Three different regimes ion-rings? ions no trapping rotation -190 V

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Trapping cross section -190 V I(L)/I 0 = exp(-nσL), n = 2Ω/κ Hence, σ = κ/2LΩ* Experiment: Ω* ~ 1 rad/s Thus, σ ~ 210 -4 cm (i.e. ion-ring complex) Ω*Ω*

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Relaxation at different Ω starting rotation stopping rotation top side -190 V

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Relaxation at T = 60 mK and 1.2 K starting rotation stopping rotation top side -190 V

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Specifics of 4 He Re s = Ω R 2 / κ = 5,000 Re n = Ω R 2 /ν = 50,000 (for Ω = 1 rad/s & R = 2.25 cm) Underdamped Kelvin waves at all T (unless very near T c ) No nucleation problem (due to remanent vortices): v c = 0 Dissipation mechanisms: T > 1 K, mutual friction + normal viscosity; T < 1 K, Kelvin wave cascade, reconnections, ring emission …

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Vortex relaxation from HVBK (T>1 K)

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0.01 t 0 = 500 s

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No mutual friction Vinen Equation:

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Simulations of the evolution of a vortex tangle in a rotating cube (Finne et al., Nature (2003))

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Conclusions: 1. Success – one can detect vortices by ions down to 30 mK 2. So far only vortex rings, but one can work even with them 3. Dynamics of spin-up and spin-down probed at various T 4. At T 1 K 5. Need more measurements

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