Vortex Mutual Friction in Rotating SuperfluidHe3-B

Abstract

We have measured the resistive and reactive mutual friction coefficients B and B' in rotating superfluid 'He-B at pressures of 1.6, 10, 20, and 29.3 bars. Near T, , Bp"/p diverges as (T, -T)", with a = -0.7, and B'p"/p -2 tends to zero. Coefficients d~~a nd d, that relate the force to v"vc, the relative velocity of normal Quid and vortex lines show relaxation-dissipation behavior tending slightly towards resonant dissipation. Within our experimental error there is no clear indication of the expected vortex core transition in our data at 20 and 29.3 bars.PACS numbers: 67.57. De, 67.57.Fg In a rotating superAuid in the interaction of quantized vortices with the normal fluid (or thermal excitations) manifests itself as a force of mutual friction between the two fluids. In equilibrium at angular velocity 0, the force F", on unit volume of normal Quid isthe suffix J denotes a component perpendicular to A. In a type II superconductor there is a similar mutual friction force mediated by quantized fiux lines; in this case the resistive and reactive forces represented by the dimensionless coefficients B and B' contribute to the longitudinal resistivity and Hall effect, respectively, in the fIux Row state. There has recently been considerable interest in the change of sign of the Hall effect for high-T;, superconductors, observed on cooling through T, in an applied field [1]. Mutual friction gives a contribution to the Hall effect of the appropriate sign to explain this if B'p"/p -2 ) 0; we show below that the opposite ineqUality holds in He-B, as predicted by Kopnin, Ivlev, and Kalatsky [2] for superconductors with an isotropic Fermi surface. Mutual friction has been extensively studied in He [3], but so far there are only limited measurements of B in superguid He [4,5]. The present experiments are the first in He designed to measure B' as well, and thus obtain complete information. We report here the results of an extensive series of measurements on the B-phase; measurements so far in the A phase are markedly less reproducible, presumably because of textural problems. Theory [6] predicts that for singular vortices the friction should be dominated by the interaction between excitations bound to the vortex core and free excitations. Consequently, the mutual friction is expected to provide valuable information on vortex core structures. Bur experimental cell, which is mounted on the nuclear refrigeration stage of a rotating cryostat [7], is shown very schematically in Fig. 1. A circular Kapton diaphragm separated two disk-shaped regions of liquid, each nominally 100 p, m thick. The roof of the cell has six electrodes set into it by means of which the modes of the diaphragm may be driven and detected electrostatically.The modes that are of interest are those with a single nodal line along the diameter. Motion of the diaphragm then displaces superAuid as indicated in the figure, while the normal fIuid is held at rest by its viscosity to a very good approximation.The frequency of these modes is of order 50 Hz at T = 0 and v...

Comment on “Transverse Force on a Quantized Vortex in a Superfluid”

“…The forces on the vortex have been recently measured in superfluid 3 He-B in a broad temperature range [2]. A general expression for a balance of forces acting on the vortex with circulation k moving with velocity v V is [3] …”

“…The measured ratio of two reactive parameters d Ќ D 0 ͞kr s [2] reproduces at low T the result d Ќ ഠ 0 observed in the limit T ø T c [4]. When T increases, d Ќ first becomes negative, then after reaching the minimum at T ϳ 0.4T c it increases, changes sign, and smoothly approaches The reason is that the formalism of TAN does not incorporate the kinetic properties of fermions localized in the vortex core and interacting with heat-bath fermions.…”

Observations on Superfluid Meniscus in Rotating3He-B

“…[9]). [4] have made extensive measurements on mutual friction in 3He-B over a wide temperature range. We have drawn a dashed curve in Fig.…”

Superfluid 3He-B Vortex Simulations inside a Rotating Cylinder

“…Here the coefficients α and α have been obtained from the experiments 7,8 and v n is the undisturbed normal fluid velocity far from the vortex core.…”