focus: detecting vortices/turbulence in pure superfluid 4 he at t
DESCRIPTION
Warwick, 8 December 2005. Injected ions in superfluid helium as detectors of quantized vortices Andrei Golov. Focus: Detecting vortices/turbulence in pure superfluid 4 He at TTRANSCRIPT
![Page 1: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/1.jpg)
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
![Page 2: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/2.jpg)
- 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;
![Page 3: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/3.jpg)
Ω = 0.30 – 0.86 s-1
![Page 4: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/4.jpg)
![Page 5: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/5.jpg)
![Page 6: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/6.jpg)
![Page 7: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/7.jpg)
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
![Page 8: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/8.jpg)
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.
![Page 9: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/9.jpg)
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
![Page 10: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/10.jpg)
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
![Page 11: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/11.jpg)
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
![Page 12: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/12.jpg)
Tungsten tips: etching A. Golov and H. Ishimoto, J. Low Temp. Phys. 113, 957 (1998).
Currents ~ 10 pA at voltage ~ - 80 V
![Page 13: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/13.jpg)
![Page 14: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/14.jpg)
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.
![Page 15: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/15.jpg)
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)
![Page 16: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/16.jpg)
Ion-ring complex
At our voltages ~ 100 V, rings grow to ~ 10-4 cm. They cross the cell in ~ 1 s.
![Page 17: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/17.jpg)
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
![Page 18: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/18.jpg)
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
![Page 19: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/19.jpg)
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)
![Page 20: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/20.jpg)
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
![Page 21: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/21.jpg)
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.
![Page 22: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/22.jpg)
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)
![Page 23: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/23.jpg)
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
![Page 24: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/24.jpg)
Charging of vortices by a horizontal current
Measuring the total trapped chargeSetup 1
![Page 25: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/25.jpg)
Simultaneous measurements (by both collectors) of the current due to the trapped ions sliding vertically and bulk current detected horizontally
Setup 2
![Page 26: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/26.jpg)
Measuring bulk mobilityMeasuring ion mobility along vortex lines
Setup 3
![Page 27: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/27.jpg)
T = 60 mK, p = 1.2 bar
-190 V20 min
Current to top collector
Current to side collector
![Page 28: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/28.jpg)
Temperature sweep from 1.3 K to 0.1 K
![Page 29: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/29.jpg)
Three different regimes
ion-rings? ions no trapping
rota
tion
-190 V
![Page 30: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/30.jpg)
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*
![Page 31: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/31.jpg)
Relaxation at different Ω
starting rotation stopping rotation
top
side
-190 V
![Page 32: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/32.jpg)
Relaxation at T = 60 mK and 1.2 K
starting rotation stopping rotation
top
side
-190 V
![Page 33: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/33.jpg)
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 …
![Page 34: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/34.jpg)
Vortex relaxation from HVBK (T>1 K)
![Page 35: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/35.jpg)
0.01 t0 = 500 s
![Page 36: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/36.jpg)
No mutual friction
Vinen Equation:
![Page 37: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/37.jpg)
![Page 38: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/38.jpg)
Simulations of the evolution of a vortex tangle in a rotating cube
(Finne et al., Nature (2003))
![Page 39: Focus: Detecting vortices/turbulence in pure superfluid 4 He at T](https://reader036.vdocuments.net/reader036/viewer/2022062409/568145bd550346895db2c882/html5/thumbnails/39.jpg)
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