1. 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

2. - 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;

3. Ω = 0.30 – 0.86 s -1

7. 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

8. 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.

9. 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

10. 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

11. 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

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

14. 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.

15. 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)

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

17. 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

18. 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

19. 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)

20. 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

21. 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.

22. 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)

23. 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

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

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

26. Measuring bulk mobility Measuring ion mobility along vortex lines Setup 3

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

28. Temperature sweep from 1.3 K to 0.1 K

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

30. 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*

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

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

33. 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 …

34. Vortex relaxation from HVBK (T>1 K)

35. 0.01 t 0 = 500 s

36. No mutual friction Vinen Equation:

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

39. 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