A study of a superconducting magnetic levitation system for an absolute determination of the magnetic flux quantum

Abstract

A study of the equilibrium positions of a superconducting magnetic levitation system which substitutes an electromagnetic energy for a mechanical energy is in progress for the absolute determination of the magnetic flux quantum «1>0' The study on a preliminary system at ppm-level resolution has been done and the reproducibility of the trajectory turned out to be of the order of 10 ppm. The problems of the present system and ideas for the next system at the sub-ppm level are discussed.(2) corner cube reflector Laser Interferometerwhere k is the flux-to-current conversion factor and n; is the order of the SQUID.The vertical position z, of the center of gravity of M is measured by a laser interferometer. Sets of data (ie' z.) as a function of cI> describe the equilibrium trajectory of the system. It is assumed that there exists a unique equilibrium trajectory as long as the attitude of M is stable and the Meissner effect of the system holds.The total energy U of the system is the sum of the magnetic energy of the system and the gravitational potential energy of M. The difference in U between two points (epf, i el , Zel) and (cI>h, i eh , Zeh) arises from the energy supplied by the current driver I d during the flux-up from cI>l to 4>h. This energy injected under a quasi-static flux-up condition can be obtained by the integration of i e over cI>I to cI>h on the equilibrium trajectory, sõ 4>h i e dcI> = ! (cI>h i eh -cI>li el) + mg (Zeh -Zel) (3) 4>[ where g is the gravitational acceleration.Introducing the expressions for cI> and i e in terms of 4>0 Fig. 1. Superconducting magnetic levitation system.The body M is levitated by the force due to the Meissner effect when cI> is large enough. When cI> is kept constant (is = 0), M reaches the equilibrium position which depends on cI>.The system in equilibrium will now be dealt with, and quantities in equilibrium are indicated with the suffix "e." The coil current i, is measured by a SQUID ammeter (CSQ) which is calibrated with a Josephson voltage reference and a calibrated resistor aswhere N is the number of cI>0 linking C. II. THEORYA superconducting magnetic levitation system is composed of a superconducting floating body M with mass m, a superconducting coil C, and the Josephson junction J irradiated with a microwave frequency 1as shown in Fig. 1. The flux cI> linking C increases when the bias current is of J is set on the first Shapiro step ( V] = 1cI>0) by the drive current i d controlled by the SQUID ammeter (VSQ) so that the EMF of C corresponds to 1cI>0.This process may be called flux-up, and cI> is obtained by the integration oflover the flux-up period T as

Watt balance experiments for the determination of the Planck constant and the redefinition of the kilogram

“…However, every direct energy conversion suffers from energy losses, which would need to be quantified at the level of several parts in 10 9 , which is very demanding. Experiments of this type, in the form of magnetic levitation of a superconducting body, have been carried out but were subsequently abandoned for this reason [27]. Direct energy conversion should therefore be avoided.…”

“…It remains to be seen whether the joule balance approach is simpler or capable of achieving smaller uncertainties. Another related technique is superconducting magnetic levitation [27] in which electromagnetic energy is converted into potential energy of a superconducting floating body above a superconducting coil. This experiment determines the flux quantum 0 = h/2e, but from the definition of the fine-structure constant (equation ( 11)) it follows that…”

The watt balance: determination of the Planck constant and redefinition of the kilogram

“…However, every direct energy conversion suffers from energy losses, which would need to be quantified at the level of several parts in 10 9 , which is very demanding. Experiments of this type, in the form of magnetic levitation of a superconducting body, have been carried out but were abandoned for this reason [15]. Direct energy conversion should therefore be avoided.…”

Estimation of Uncertainties Caused by Elastic Deformations in a Superconducting Levitation System

“…The best condition for precision measurement of mechanical energy is that when f (z) = 1, which corresponds to acceleration-free displacement, and the process of displacement appears to be quasi-static if the body has zero velocity at point zl [3]. In this case, the magnetic force merely increases the potential energy of the body in the gravitational field and A = mg (zhzl).…”

“…It is a topical task, therefore, to review the systematic errors that may arise when electromechanical system experiments are made under the most favourable conditions in an upto-date metrological laboratory. Devices which use the levitation of a superconducting body [3,41 constitute one such system.…”