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Submitted on 1 Jan 1978
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THE SCREENING EFFECT AND NUCLEATION OF
CORELESS VORTICES IN SUPERFLUID 3He-A IN
STATIONARY AND ROTATION CONTAINERS
T.-L. Ho
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-21
THE SCREENING EFFECT AND NUCLEATION OF CORELESS VORTICES
IN SUPERFLUID 3He"A IN STATIONARY AND ROTATION CONTAINERS+
T.-L. Ho
Physios Department, University of Illinois at Urbana-Champaign
Vvbana, Illinois 61801>U.S.A.
Résumé.- Le minimum absolu de l'énergie libre, pour 3He-A ayant une circulation superfluide à grande surface, contient une couche en surface de tourbillons sans noyau. Par conséquent, le paramètre d'ordre est une constante dans son ensemble. On discute de l'action semblable dans un tore rotatif. On utilise la forme intégrale de l'équation V x v pour élucider ces effets, de même que le mécanisme de formation en noyau de tourbillons sans noyau. On indi-que les effets susceptibles d'être observés.
Abstract.- For ^Ee-A in stationary containers with a large surface superfluid circulation, the absolute minimum of the free energy contains a surface layer of coreless vortices. As a result, the order parameter in the bulk is a constant. Similar effect in a rotating torus is discussed. The integral form of the V x vs equation is used to elucidate these effects as
well as the mechanism of nucleation of coreless vortices. Observable effects are mentioned.
The integral form of the v x v equation in
3He-A l\l is established. Let %i be the surface of
a unit sphere describing all possible directions of the texture 2. It is found that the circulation
1(C) = —7- / v . ds around any closed contour G n « s
obeys the geometrical rule : 1(C) = y (D); where D = y(C) is the image of the space loop C under the mapping i on Sp, and p(D) is the area on Sj: enclo-sed by D. From this circulation formula, the follo-wing results are obtained :
A) The mechanism of the nucleation of co-reless vortices is understood. It uncovers another stronge property of 3He-A : a vortex ring of finite size can be nucleated continuously out from a u n i -form superflow. Nucleation of coreless vortices turns out to be the origin of the instability of superflow. Ill
B) The screening effect of surface vorti-ces in stationary containers : It is found that when the surface circulation is large, coreless vortices tends to nucleate near the surfaces so as to screen out the surface circulation — a phenome-non that bears striking resemblance to the Meissner effect in superconductivity. This screening effect, when appears, will reduce the supercurrent in the bulk, hence the angular momentum of the fluid, al-most down to zero.Whether the full development of surface vortices is prevented by the existence of
tResearch supported in part by U.S. National Science Foundation Grant NSF DMR 76-24011.
any metastable state during the course of nuclea-tion can be detected experimentally by comparing
3
the angular momentum carried by He-A with that by 3
He-B. The former is expected to be much smaller when the screening effect occurs.
3
(C) For He-A in rotating containers with zero surface superfluid circulation, the tendency to reduce a sufficiently large v - v in the bulk
' 6 n s
will give rise to a textural distortion, accompa-nied by a change in the moment of inertia of the fluid. Such a process can be understood in terms of vortex nucleation. For toroidal containers (or annu-li) with not too small inner radius, vortex textures exactly like those in (B) will be formed to reduce
3
the velocity difference. The rotation of He-A is then essentially the same as those of classical fluids. The superfluid is not super at all.
Details of (A) and (B) are given in refe-rence /3/. (C) is a straightforward extension of the results therein.
References
/I/ Mermin.N.D. and Ho,T.Phys.Rev.Lett.36 (1976) 594
lit Bhattacharyya,Ho,T-L, and Mermin.N.D., Phys. Rev. Lett. 39 (1967) 1290,1691 /3/ Ho,T-L , Corless Vortices in 3He-A, to be
published.
