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 4He 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

In superfluid 4He:- Second sound (requires normal component)- Injected ions (attracted to vortex lines)

In superfluid 3He: - spin: NMR- nature of quasiparticles: Andreev reflection- anisotropy (3He-A): ultrasound, torsional oscillator, ions

Known detectors of vortices

Main interest: detecting vortices/turbulence in pure superfluid 4He at T < 100 mK.

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)

Negative ion: bare electron in a bubble (Atkins 1959) :p 0 bar 25 bar R- 17 Å 12 Åm- 243 mHe 87 mHe (Ellis, McClintock 1982)

Positive ion: cluster ion (“snowball”) (Ferrell 1957) : p 0 bar 25 bar R+ 7 Å 9 Åm+ ~30 mHe ~50 mHe

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/mHe= 30-240.

0 10 20 30 40 50 60 70 80 90 100

10

12

14

16

18

Re , A

Pressure, atm

C.C.Grimes and G.Adams, Phys. Rev. B 1990; Phys. Rev. B 1992

A.Ya.Parshin and S.V.Pereverzev, JETP Lett. 1990A. Golov, Z. Phys. D (1994)

Radius of negative ions: IR spectroscopy

liquid 4He

solid 4He and 3He

How to inject ions?

- radioactive ionization (α or β) sources (easy to use but can’t be switched off: excess heating)Example: 3H 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

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

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=0 vL= 60 m/s

p=25 bar vL= 46 m/s

Vortex nucleation by a moving ion at vc~ R-1

0 5 10 15 20 250

10

20

30

40

50

60

70

80

VLV

-

V+

V (

m/s

)P (bar)

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)

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.

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 KNegative ions: ΔV = 55 - 66 K

Theory:

Parks and Donnelly (1966):

Donnelly & Roberts (1969):

Berloff, Roberts (2000)

slope ~ 10 K / 10 Å = 1 K/Åe.g. eE = 10-3 K/Å at E = 10 V/cm

Chances of escape (Brownian particle in a well)

In low fields, E << 104 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 valueDonnelly, Glaberson, Parks (1967), Ostermeier and Glaberson (1976)

High field E > 104 V/cm might help liberate the ion:

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.)!

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

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 (vL=50 m/s, m = 100 m4): KE = 60 K vs. ΔV~20K

ΔV

v = vL, KE

v = vL

When the ion is pulled parallel to the line, trapping is likely.

ion p KE(vL) ΔV

-ve 0 180K ~55K

-ve 25bar 45K ~20K

+ve 0 30K 20-40K

+ve 25bar 30K 40-80K

What if T < 1 K?

When an ion is pulled parallel to the vortex line, trapping is likely

v < vL

v = 0v = 0

v = vL

v = 0v = 0

or

What if vortex line is not rigid?

Capture of a stationary ion from distance ~ R: Kelvin waves help remove excess energyN.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.

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~106 cm-3 or less: 0.1 mm between ions

Against: Coulomb repulsion: space-charge effects

Some experiments with ions and vortices in 4HeCapture 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 timeHoch, Busse, Moss (1975, 1977), Ostermeier, Cromar, Kittel, Donnelly (1980), Smith and Tejwani (1984): time-fluctuations in the line density

Ultrasaound, radioactive sourceCarey, Rooney, Smith (1978), Schwarz and Smith (1981), Milliken, Schwarz, Smith (1982)

Vibrating grid, field emission tipDavis, Hendry, McClintock (2001) – decay of turbulence at T<100mK

To interpret these we often need to know the capture cross-section!

Ω = 0.30 – 0.86 s-1

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);

Lancaster-Manchester program: Vortices in superfluid 4He

below 100 mK

Aim: studies of the turbulence in superfluid 4He 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 4He, 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)

We are going to measure the cross-section of ion capture by vortex lines in superfluid 4He 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 4He 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

Charging of vortices by a horizontal current

Measuring the total trapped charge

Setup 1

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

Setup 2

Measuring bulk mobilityMeasuring ion mobility along vortex lines

Setup 3

The End