1. 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 (and will stay trapped forever if T<1K). Hence, by observing: - loss of ions, - deflection of current, - time-dependent fluctuations of current, one can learn about the presence and behaviour of vortices. Plan: 1. Ions in helium – tutorial. 2. Select experimental results with either rectilinear arrays of vortices or vortex tangles. 3. Ongoing Manchester (+ Birmingham-Lancaster) programme. Focus: Detecting vortices/turbulence in pure superfluid 4 He at T < 100 mK. R.J.Donnelly, Quantized Vortices in Helium II, Cambridge University Press, 1991. J.T.Tough, “Superfluid Turbulence” in Progress in Low Temperature Physics, vol. VIII, 1982. Injected ions in superfluid helium as detectors of quantized vortices Andrei Golov Miramare – Trieste, 6-10 June, 2005

2. In superfluid 4 He: - Second sound (requires normal component) - Injected ions (attracted to vortex lines) In superfluid 3 He: - spin: NMR - nature of quasiparticles: Andreev reflection - anisotropy ( 3 He-A): ultrasound, torsional oscillator, ions Known detectors of vortices Main interest: detecting vortices/turbulence in pure superfluid 4 He at T < 100 mK.

3. What to do The technique is: 1.Create and send ions through the test volume. 2.If there are vortices, some ions will be trapped: - if not all ions made it through, this tells about vortex density - also, the trapped space charge can be detected We don’t want to: - nucleate new vortices - affect the shape and dynamics of existing vortices Example: Awschalom, Milliken, Schwartz (1984)

4. 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 in bulk He and vortices. By changing pressure and species, one can cover R = 7–17 Å, m/m He = 30-240.

5. C.C.Grimes and G.Adams, Phys. Rev. B 1990; Phys. Rev. B 1992 A.Ya.Parshin and S.V.Pereverzev, JETP Lett. 1990 A. Golov, Z. Phys. D (1994) Radius of negative ions: IR spectroscopy liquid 4 He solid 4 He and 3 He

6. How to inject ions? - radioactive ionization (α or β) sources (easy to use but can’t be switched off: excess heating) Example: 3 H emits β-particles of average energy 5 KeV - sharp metal tips (radius of curvature ~ 100-1000 Å ): - 200V + 400V field emission: negative ions field ionization: positive ions β

7. Tungsten tips: etching A. Golov and H. Ishimoto, J. Low Temp. Phys. 113, 957 (1998).

9. Ions: bulk 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

10. Vortex nucleation by a moving 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, the ion will then either stay with the ring or leave: We don’t need new vortices, hence: For positives: any pressures OK, For negatives: p > 13 bar OK.

11. Ion–vortex interaction (rigid vortex) Energy of interaction = missing kinetic energy of superflow (roughly proportional to ion’s volume) Calculated binding energy ΔV (p=0): Positive ions: ΔV = 16 - 46 K Negative ions: ΔV = 55 - 66 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

12. Chances of escape (Brownian particle in a well) In low fields, E << 10 4 V/cm, no escape at low T : - for negatives, at T < 1.7 K, - for positives, at T < 0.8 K. 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) High field E > 10 4 V/cm might help liberate the ion:

13. Chances of getting captured Theory: Donnelly (1965): ion near vortex (at high T) – Brownian motion in potential well Donnelly and Roberts (1969): capture diameter d ~ kT/eE Experiment (capture diameter d): Careri, McCormick, Scaramuzzi (1962): below T=1.7K, -ve is captured (d ~ 10 -5 cm at T=1.37K), but +ve is not. Tanner, Springett, Donnelly (1965), Schwartz and Donnelly (1966). Tanner (1966) Phys Rev 152, 121. Springett (1967) Phys Rev 155, 139. At high T > 1 K, (viscous regime): a particle is bound to collapse into the well within d ~ E -1 Ostermeier and Glaberson (1974) (1975a); Williams and Packard (1978) At T < 1K capture diameter drops rapidly (p.t.o.)!

14. Theory: Brownian particle in a gas of rotons. Solid line: stochastic model (Donnelly & Roberts,1969) Dashed line: Monte-Carlo calculations

15. 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. -ve at p~20 bar (v L =50 m/s, m = 100 m 4 ): KE = 60 K vs. ΔV~20K ΔVΔV v = v L, KE v = v L When the ion is pulled parallel to the line, trapping is likely. ionpKE(v L ) ΔV -ve0180K~55K -ve25bar45K~20K +ve030K20-40K +ve25bar30K40-80K

16. What if T < 1 K? When an ion is pulled parallel to the vortex line, trapping is likely v < v L v = 0 v = v L v = 0 or

17. 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.

18. Cons and Pros of using ions Invasive/non-invasive: vortex shape distortion, relaxation time changed when charged? Conflicting requirements: - to enhance capture rate: need low E - to enhance sensitivity (space-charge limited): high E For: high sensitivity to small quantities: can detect n~10 6 cm -3 or less: 0.1 mm between ions Against: Coulomb repulsion: space-charge effects

19. Some experiments with ions and vortices in 4 He Capture of ions by an array of vortices: Rotating cryostat, radioactive source - Carreri, McCormick, Scaramuzzi (1962): trapping of -ve ions by a vortex array; - Tanner, Springett, Donnelly (1965), Schwartz and Donnelly (1966): -ve and +ve, T<0.5K; - Donnelly, Glaberson, Parks (1967): trapping diameter, mobility along lines; - Packard and Saunders (1972): entry of lines one by one; - Williams, Yarmchuk, Gordon, Packard (1975, 1979, 1982): visualization of vortex arrays; - Ostermeier and Glaberson (1974, 1975, 1976), Williams and Packard (1978): ion capture cross- section at lowest T (~1 K) so far. Detection of turbulence (ion losses, deflection, time resolution): Counterflow, radioactive source : Carreri, Scaramuzzi, Thomson, McCormick (1960): first observation of a vortex tangle; Awschalom, Schwarz (1983): proof of existence of remnant vortices, detection of turbulence. Sitton, Moss (1969, 1972) Ashton, Northby (1973, 1975, 1977) Scwartz and Smith (1980), Awschalom, Milliken, Schwarz (1984): pulsed ions – line density resolution in space and time Hoch, Busse, Moss (1975, 1977), Ostermeier, Cromar, Kittel, Donnelly (1980), Smith and Tejwani (1984): time-fluctuations in the line density Ultrasaound, radioactive source Carey, Rooney, Smith (1978), Schwarz and Smith (1981), Milliken, Schwarz, Smith (1982) Vibrating grid, field emission tip Davis, Hendry, McClintock (2001) – decay of turbulence at T<100mK To interpret these we often need to know the capture cross-section!

20. Ω = 0.30 – 0.86 s -1

24. 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);

25. Lancaster-Manchester program: Vortices in superfluid 4 He below 100 mK Aim: studies of the turbulence in superfluid 4 He at T < 100 mK, i.e. when the normal component is virtually absent. Manchester: rotating cryostat will be used to produce: - an array of parallel vortex lines of known density, - superflow in an annulus (for example, through a grid). Lancaster: a grid, towed through liquid 4 He, will produce turbulence. Will use ions to detect vortices. Manchester: A.I. Golov, P.M. Walmsley, A.A. Levchenko, S. May, H.E. Hall in collaboration with W.F. Vinen (Birmingham) and P.V.E. McClintock et al. (Lancaster)

26. We are going to measure the cross-section of ion capture by vortex lines in superfluid 4 He well below 100 mK. A homogeneous array of vortex lines of variable density will be created in the rotating cryostat, and the charge, accumulated on the vortices after the exposure to the transverse current of negative ions, will be measured. A cell is built to measure trapping of negative ions drifting past parallel or perpendicular array of straight vortex lines in liquid 4 He at pressure of some 20 bar and temperature 10 - 100 mK. The ion mobility along the lines and in bulk will be measured too. If this works, the dynamics of vortex array creation and annihilation during starting (stopping) of the rotation will be probed too. Ion source Collector 4.5 cm

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

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

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

30. The End