Focus: Detecting vortices/turbulence in pure superfluid 4 He at T
description
Transcript of Focus: Detecting vortices/turbulence in pure superfluid 4 He at T
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
Injected ions in superfluid helium as detectors of quantized vortices
Andrei Golov
Warwick, 8 December 2005
- 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 4He:
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;
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);
T = 22 - 70 mK
To interpret, need to know the trapping cross-section and lifetime
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 and vortices in liquid He .
By changing pressure and species, one can cover R = 7–17 Å, m/mHe= 30-240.
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
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/Åe.g. eE = 10-3 K/Å at E = 10 V/cm
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
Tungsten tips: etching A. Golov and H. Ishimoto, J. Low Temp. Phys. 113, 957 (1998).
Currents ~ 10 pA at voltage ~ - 80 V
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 = 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.
Vortex nucleation by a fast 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 and friction, the ion will then either stay with the ring or leave
At T < 1K, vortex rings are produced:
- pure 4He: at p < 12 bar;
- impure 4He (even at ~10-7 3He): always
V-* (with traces of 3He)
Ion-ring complex
At our voltages ~ 100 V, rings grow to ~ 10-4 cm. They cross the cell in ~ 1 s.
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/Åe.g. eE = 10-3 K/Å at E = 10 V/cm
E
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
Cross-section for ion-rings
σ ~ 2 R0 ~ E = 4 •10-5 cm – 2 •10-4 cm
T-independent for T < 0.5 K
PRL 17, 1088 (1966)
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.
ΔV
v = vL, KE
v = vL
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 (vL) ΔV
0 180K ~60K
20bar 60K ~20K
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.
If captured: chances of escape
In low fields, E << 104 V/cm, long sentence ifT < 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 valueDonnelly, Glaberson, Parks (1967), Ostermeier and Glaberson (1976)
4.5 cm
Vortices in superfluid 4He 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 • 103 cm-2)
P.M. Walmsley, A.A. Levchenko, S. May, L. Chan, H.E. Hall, A.I. Golov
Ion source
Collector
Charging of vortices by a horizontal current
Measuring the total trapped chargeSetup 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
T = 60 mK, p = 1.2 bar
-190 V20 min
Current to top collector
Current to side collector
Temperature sweep from 1.3 K to 0.1 K
Three different regimes
ion-rings? ions no trapping
rota
tion
-190 V
Trapping cross section
-190 VI(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*
Relaxation at different Ω
starting rotation stopping rotation
top
side
-190 V
Relaxation at T = 60 mK and 1.2 K
starting rotation stopping rotation
top
side
-190 V
Specifics of 4He
Res = Ω R2/ κ = 5,000 Ren = Ω R2/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 …
Vortex relaxation from HVBK (T>1 K)
0.01 t0 = 500 s
No mutual friction
Vinen Equation:
Simulations of the evolution of a vortex tangle in a rotating cube
(Finne et al., Nature (2003))
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 < 100 mK vortices relax nearly as quickly as at T > 1 K
5. Need more measurements