The design of a very high-Q superconductor electromechanical clock

Abstract

We discuss the properties of an electromechanical oscillator whose operation is based upon the cyclic, quasiconservative conversion between gravitational potential, kinetic, and magnetic energies. The system consists of a strong-pinning type-II superconductor square loop subjected to a constant external force and to magnetic fields. The loop oscillates in the upright position at a frequency that can be tuned in the range 10-1000 Hz, and has induced in it a rectified electrical current. The emphasis of this paper is on the evaluation of the major remaining sources of losses in the oscillations. We argue that such losses should be associated with the viscous vibration of pinned flux lines in the superconductor Nb-Ti wire, provided the oscillator is kept under vacuum and the magnetic field is sufficiently uniform. Losses of similar or greater magnitude would be associated with dragging of the loop against the He atmosphere remaining in the evacuated cryostat. We discuss how other different sources of loss would become negligible for such operational conditions, so that a very high quality factor Q exceeding 10 10 might in principle be reached by the oscillator. The prospective utilization of such oscillator as a low-frequency high-Q clock is analyzed.

The Precise Determination of Mass through the Oscillations of a Very High-Q Electromechanical System

“…The FLs will remain pinned, only slightly displaced from their equilibrium positions in the absence of that ripple field. The losses will be negligible for all practical effects, as calculated for a case study in [5]. This latter reference brings a detailed numerical example, in which a loop of mass of about 0.5 gram, subjected to a field difference B 0 of 0.3 T, will oscillate at 178 Hz frequency with an amplitude of oscillations of about 8 μm.…”

“…However, as we show hereafter it has been possible to design a system in which all dissipative processes can be diminished to the point that the application of Equation (4) becomes realistic. This system has been devised and previously analyzed in detail by Schilling [5,6] (although its equations of motion had independently been published much earlier by Saslow [7]), and consists of a type-II superconducting rectangular loop of mass m, subjected to magnetic fields and gravity. In this section, we present the main results obtained from the analysis of the loop motion, including the proposal of a new relation between the loop mass and the total energy which follows from Equation (4).…”

“…The need for two fields is explained in Section 3. These fields should be homogeneous upon the loop wire within a tolerance discussed in [5], assuming also that any sidewise drift motion is entirely negligible. The tridimensional equivalent of this system, comprising three mutually perpendicular rectangular oscillating loops subjected to the field of a magnetized sphere has recently been discussed in the Letter [8], and utilized as a resonator as part of a quantum magneto-mechanical device.…”

“…It is clear that such equations are equivalent to the ones in Section 1 for the spring-load system, with ω replaced by Ω. It is possible then to combine (5) and (6) to obtain an equation for the current i(t), which flows within a very thin layer close to the wires surface [5]:…”

“…The design of the system has been discussed in [5,6], but we describe here the main details. However, this discussion does not include further details on the experimental techniques to be adopted in the measurement of the magnetic flux produced by the loop and of its position and speed, which lay beyond the scope of this paper and should be considered in due course.…”