Superconducting vibrating reed applied to flux-line pinning. I. Theory

Journal Article · Thu May 01 04:00:00 EDT 1986 · J. Low Temp. Phys.; (United States)

DOI:https://doi.org/10.1007/BF00683764· OSTI ID:5567307

Brandt, E H; Esquinazi, P; Neckel, H

A theoretical treatment is given of a superconducting reed clamped at one end and performing flexural vibrations in a homogeneous longitudinal magnetic field B/sub a/. When the flux lines are rigidly pinned the reed behaves like an ideal diamagnet whose bending disorts the external field. This generates a magnetic restoring force (line tension) proportionalB/sup 2//sub a/ which is independent of the reed thickness d, whereas the mechanical restoring force (stiffness) is proportional d/sup 3/. Therefore, the resonance frequency w/2..pi.. of a thin superconducting reed increases drastically when a field B/sub a/ is applied, or for a given B/sub a/, when the reed is cooled below its critical temperature T/sub c/. With decreasing pinning strength (characterized by Labusch's parameter ..cap alpha..) the resonance frequency decreases, w/sup 2/..-->..w/sup 2/: w/sup 2//sub p//sub i//sub n/ where w/sup 2//sub p//sub i//sub n/ proportional ..cap alpha../sup -1/, and an attenuation GAMMA/sub v/proportional..cap alpha../sup -2/ occurs due to the viscous motion of flux lines. For larger vibration amplitudes an additional, amplitude-dependent damping GAMMA/sub h/proportional..cap alpha../sup -3/ occurs due to the hysteretic losses caused by elastic instabilities during flux motion.

• Research Organization: Max-Planck-Institute fuer Metallforschung, Institute fuer Physik, Stuttgart, West Germany
• OSTI ID: 5567307
• Journal Information: J. Low Temp. Phys.; (United States), Journal Name: J. Low Temp. Phys.; (United States) Vol. 63:3; ISSN JLTPA
• Country of Publication: United States
• Language: English

Related Subjects

656102* -- Solid State Physics-- Superconductivity-- Acoustic
Electronic
Magnetic
Optical
& Thermal Phenomena-- (-1987)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BENDING
DAMPING
DIAMAGNETISM
DIFFERENTIAL EQUATIONS
ELASTICITY
EQUATIONS
EQUATIONS OF MOTION
HYSTERESIS
INSTABILITY
INTEGRAL EQUATIONS
MAGNETIC FIELDS
MAGNETIC FLUX
MAGNETISM
MECHANICAL PROPERTIES
OSCILLATION MODES
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
PLATES
RESONANCE
SUPERCONDUCTORS
TENSILE PROPERTIES
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE