Focus: Detecting vortices/turbulence in pure superfluid 4 He at T << 1 K. Message:

1. Warwick, 8 December 2005 Injected ions in superfluid helium as detectors of quantized vorticesAndrei Golov Focus: Detecting vortices/turbulence in pure superfluid 4He 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

2. Detectors of vortices in superfluid 4He: • - Injected ions (attracted to vortex lines) • - Second sound (requires normal component) • - Local pressure and temperature sensors (early stage) • The ion technique is: • Create and send ions through the test volume. • 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. 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. T = 22 - 70 mK Physica B 280, 43 (2000); To interpret, need to know the trapping cross-section and lifetime 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).

8. Injected ions: structure Negative ion: bare electron in a bubble (Atkins 1959) : p 0 bar 25 bar R- 17 Å 12 Å m- 243mHe 87mHe (Ellis, McClintock 1982) Positive ion: cluster ion (“snowball”) (Ferrell 1957) : p 0 bar 25 bar R+ 7 Å 9 Å m+ ~30 mHe ~50mHe 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/mHe= 30-240.

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

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 slope ~ 10 K / 10 Å = 1 K/Å e.g. eE = 10-3 K/Å at E = 10 V/cm Theory: Parks and Donnelly (1966): Donnelly & Roberts (1969): Berloff, Roberts (2000)

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): β field emission: negative ions - 100V field ionization: positive ions + 400V

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

14. ~ 2.0 K 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) p = 0 vL= 60 m/s p = 25 bar vL= 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 vc~ R-1 V-* (with traces of 3He) Depending on the pull and friction, the ion will then either stay with the ring or leave Experiment: Rayfield and Reif (1964) McClintock, Bowley, Nancolas, Stamp, Moss (1980, 1982, 1985) Theory for Vc: 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) • At T < 1K, vortex rings are produced: • pure 4He: at p < 12 bar; • impure 4He (even at ~10-73He): always

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 E slope ~ 10 K / 10 Å = 1 K/Å e.g. eE = 10-3 K/Å at E = 10 V/cm Theory: Parks and Donnelly (1966): Donnelly & Roberts (1969): Berloff, Roberts (2000)

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

19. Cross-section for ion-rings PRL 17, 1088 (1966) σ ~ 2 R0 ~ E = 4 •10-5 cm – 2 •10-4 cm T-independent for T < 0.5 K

20. ΔV v = vL v = vL, KE 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. P KE (vL) ΔV 0 180K ~60K 20bar 60K ~20K 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.

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 << 104 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. Collector 4.5 cm Ion source Vortices in superfluid 4He below 100 mK P.M. Walmsley, A.A. Levchenko, S. May, L. Chan, H.E. Hall, A.I. Golov • 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 • 103 cm-2)

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

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

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

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

28. Temperature sweep from 1.3 K to 0.1 K

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

30. -190 V Trapping cross section I(L)/I0 = exp(-nσL), n = 2Ω/κ Hence, σ = κ/2LΩ* Experiment: Ω* ~ 1 rad/s Thus, σ ~ 2•10-4 cm (i.e. ion-ring complex) Ω*

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

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

33. Specifics of 4He Res = ΩR2/ κ = 5,000 Ren = ΩR2/ν = 50,000 (for Ω = 1 rad/s & R = 2.25 cm) Underdamped Kelvin waves at all T (unless very near Tc) No nucleation problem (due to remanent vortices): vc= 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 t0 = 500 s

36. No mutual frictionVinen 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 mK2. So far only vortex rings, but one can work even with them3. Dynamics of spin-up and spin-down probed at various T4. At T < 100 mK vortices relax nearly as quickly as at T > 1 K 5. Need more measurements