Unstable states of the superfluid confined between rotating spheres
The unstable states (including those related to self-accelerations of pulsars) in which the mutual friction causes an irreversible motion of vortices is considered.
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Zitieren: | Unstable states of the superfluid confined between rotating spheres / A. Gongadze, L. Kiknadze, Yu. Mamaladze, S. Tsakadze // Физика низких температур. — 2003. — Т. 29, № 8. — С. 840-841. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-1288942018-01-15T03:03:48Z Unstable states of the superfluid confined between rotating spheres Gongadze, A. Kiknadze, L. Mamaladze, Yu. Tsakadze, S. Квантовые жидкости и квантовые кpисталлы The unstable states (including those related to self-accelerations of pulsars) in which the mutual friction causes an irreversible motion of vortices is considered. 2003 Article Unstable states of the superfluid confined between rotating spheres / A. Gongadze, L. Kiknadze, Yu. Mamaladze, S. Tsakadze // Физика низких температур. — 2003. — Т. 29, № 8. — С. 840-841. — Бібліогр.: 7 назв. — англ. 0132-6414 PACS: 67.40.Vs http://dspace.nbuv.gov.ua/handle/123456789/128894 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Квантовые жидкости и квантовые кpисталлы Квантовые жидкости и квантовые кpисталлы |
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Квантовые жидкости и квантовые кpисталлы Квантовые жидкости и квантовые кpисталлы Gongadze, A. Kiknadze, L. Mamaladze, Yu. Tsakadze, S. Unstable states of the superfluid confined between rotating spheres Физика низких температур |
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The unstable states (including those related to self-accelerations of pulsars) in which the mutual friction causes an irreversible motion of vortices is considered. |
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Article |
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Gongadze, A. Kiknadze, L. Mamaladze, Yu. Tsakadze, S. |
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Gongadze, A. Kiknadze, L. Mamaladze, Yu. Tsakadze, S. |
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Gongadze, A. |
| title |
Unstable states of the superfluid confined between rotating spheres |
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Unstable states of the superfluid confined between rotating spheres |
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Unstable states of the superfluid confined between rotating spheres |
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Unstable states of the superfluid confined between rotating spheres |
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Unstable states of the superfluid confined between rotating spheres |
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unstable states of the superfluid confined between rotating spheres |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2003 |
| topic_facet |
Квантовые жидкости и квантовые кpисталлы |
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http://dspace.nbuv.gov.ua/handle/123456789/128894 |
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Unstable states of the superfluid confined between rotating spheres / A. Gongadze, L. Kiknadze, Yu. Mamaladze, S. Tsakadze // Физика низких температур. — 2003. — Т. 29, № 8. — С. 840-841. — Бібліогр.: 7 назв. — англ. |
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Физика низких температур |
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2025-07-09T10:10:59Z |
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2025-07-09T10:10:59Z |
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Fizika Nizkikh Temperatur, 2003, v. 29, No. 8, p. 840–841
Unstable states of the superfluid confined between
rotating spheres*
A. Gongadze, L. Kiknadze, Yu. Mamaladze, and S. Tsakadze
E.A. Andronikashvili Institute of Physics of the Georgian Academy of Sciences
6 Tamarashvili Str., Tbilisi 380077, Georgia
E-mail: yum@iph.hepi.edu.ge; yum270629@yahoo.com
Received December 19, 2002
The unstable states (including those related to self-accelerations of pulsars) in which the mu-
tual friction causes an irreversible motion of vortices is considered.
PACS: 67.40.Vs
Introduction
The concentric spheres with radii R1 and R2 rotat-
ing with the constant or variable angular velocity �
are considered. Both equilibrium and metastable
states of this system are the solutions of the equations
of vortex dynamics with the given velocity and zero
mutual friction between vortices and the normal com-
ponent. This force realizes the transitions from one
equilibrium or metastable state to another at the
change of angular velocity. But there also exist such
configurations of vortices, which cannot stay stable
even if the variation of the velocity of rotation was in-
terrupted.
In this publication of our report at CWS-2002 the
part devoted to equilibrium and metastable rotation
(see [1]) is omitted. This paper is dedicated to the
mechanism of unstable processes and to the difference
between double-cylinder and double-sphere devices.
Breaking and connection of vortices
The clear example of the difference between the
coaxial cylinders and spheres is the generation
of the first vortices. Fetter [2] had shown that the
vortex generation begins at the outer cylinder at
� � � ln ( )2 2C / mRd (d R R� �2 1, R R R /� �( ) ,1 2 2
C � 1), but the generated vortex has no equilibrium
position in the space between the cylinders until � ex-
ceeds the value � ln ( )d/a /md2. Therefore, the vorti-
ces move to the inner cylinder, annihilate on it, and
leave there the circulation. In contrast to this, in the
case of spheres the part of the axis of rotation is placed
in liquid, a vortex has the equilibrium position there if
� > � ln ( )2 2 2R/a / mR [1], and that is less than the
critical velocity of vortex generation at the equator of
the outer sphere: � ln( )2 2 2C / mR d. In this situation
all generated vortices have their equilibrium positions
in the vicinity of the axis of rotation and move to them
being broken in two parts.
The same processes of vortex breaking and the op-
posite processes of two vortex connection happen
when vortices displace to their equilibrium positions
or when the metastable vortex cluster [3] expand or
compress according to variations of the angular velo-
city.
The mechanism of these processes is shown in
Fig. 1. Its left part shows what happens when a vortex
approaches the inner sphere from the area r R� 1. At
first the interaction of the vortex with the sphere
(«with the own image») manifests itself in the nearest
part of the vortex to the equator which begins to dis-
tort. The prominent part of the vortex line and its im-
age make «the leading pair». The sequence of the fol-
lowing events is represented by Fig. 1 (left): the
above-mentioned part of the vortex interacting with
its image stretches along the equator, moves faster and
faster, approaches the wall nearer and nearer, and an-
© A. Gongadze, L. Kiknadze, Yu. Mamaladze, and S. Tsakadze, 2003
* The report was submitted at the 3rd International Workshop on Low Temperature Microgravity Physics (CWS-2002).
nihilates in it. So the vortex breaks in two parts, and
the edges of two remaining vortices find their equilib-
rium positions, not shown in Fig. 1.
The second picture of Fig. 1 (right) shows what
happens when a vortex approaches the equator of the
inner sphere from the area r R� 1. Then a vortex ap-
proaches the equator simultaneously with its continu-
ation situated on the other side of the equator. Here,
being perpendicular to the surface, the ends of the vor-
tices form the leading pair. They move along the equa-
tor, approach each other and annihilate. The remain-
ing parts of vortices join and form one vortex outside
the inner sphere.
Thus, opposite processes of vortex breaking and
connection at the equator of the inner sphere do not
represent the sequence of similar events observed in
reverse order. The leading pairs, their orientation, and
the directions of their gathering are different.
Annihilation of outgoing vortices
The position near the equator of the outer sphere is
also where the equilibrium rotation of a vortex with
the vessel and the normal component is impossible.
The vortex may appear here, e.g., as a result of decel-
eration of almost freely rotating double-sphere. Then
the interaction with its own image becomes decisive,
and a vortex leaves the vessel moving along and to the
equator. It is known that the mutual friction results in
time dependence ( )t t /
an �
1 2 for compressing linear
dimensions: the distance from the vortex to the wall of
the cylinder [4], and the radius of the ring [5] (tan is
the moment of annihilation). Freely rotating vessel re-
sponds to the changes of liquid angular momentum
(which is proportional to the area outlined by the vor-
tex and the wall) by the change of rotation velocity.
The result is the self-accelerations superimposed on
general deceleration of the vessel. In the case of a cy-
linder d /dt t t /
� � �
�( )an
1 2 [4] in accordance with
Packard’s idea that the annihilation of vortices may be
the reason of pulsar self-accelerations (starquakes)
[6]. But a pulsar is a sphere, and in this case it is possi-
ble to represent the annihilating vortex as something
like a small compressing ring. Then the self-accelera-
tion also would happen but the derivative d /dt�
would be finite. However, this statement requires
more detailed consideration.
Conclusions
More detailed observations of the pulsars self-ac-
celerations, modeling experiments (like [7]), and
more detailed theoretical studies are desirable to com-
pare the date, to discuss the similarity and difference
between the cylindrical and spherical models and pul-
sars, and to distinguish between the processes taking
place in the pulsar solid crust and the neutron liquid
pierced by vortices.
Acknowledgments
This work was partly supported by INTAS (Net-
work OPEN 97-1643) and by Grant 2.17.02 of Geor-
gian Academy of Sciences. We thank the Organizing
Committee of CWS-2002 for the support of atten-
dance of one of us (Yu.M.) at the workshop, Prof.
W. Glaberson for discussions about experimental pos-
sibilities connected with the creation of freely rotating
device and Prof. G. Kharadze for his interest and at-
tention.
1. L. Kiknadze and Yu. Mamaladze, J. Low Temp. Phys.
127, 271 (2002).
2. A.L. Fetter, Phys. Rev. 153, 285 (1967).
3. Y. Kondo, J. Korhonen, and M. Krusius, Proceedings
of LT-19, PG.G10 (1991); Y. Kondo, A. Gongadze,
Y. Pattz, Y. Korhonen, M. Krusius, and O. Lou-
nasmaa, Physica B178, 90 (1992); A.D. Gongadze and
G.E. Vachnadze, Zh. Eksp. Teor. Fiz. 109, 471
(1996).
4. L.V. Kiknadze and Yu.G. Mamaladze, Zh. Eksp. Teor.
Fiz. 75, 607 (1978).
5. C.F. Barenghi, R.J. Donnelly, and W.F. Vinen, J. Low
Temp. Phys. 52, 189 (1983).
6. B.E. Packard, Phys. Rev. Lett. 28, 1080 (1972).
7. J.S. Tsakadze and S.J. Tsakadze, Usp. Fiz. Nauk 115,
503 (1975); J. Low Temp. Phys. 39, 649 (1980); S.J.
Tsakadze, Fiz. Nizk. Temp. 6, 674 (1980).
Equilibrium, metastable, and unstable states of the superfluid confined between rotating spheres
Fizika Nizkikh Temperatur, 2003, v. 29, No. 8 841
Fig. 1. The sequence of events during the breaking of a
vortex moving to the axis of rotation (left), and the be-
ginning of the connection of two vortices outgoing from
the inner sphere (right).
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