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The London moment (after
Fritz London Fritz Wolfgang London (March 7, 1900 – March 30, 1954) was a German physicist and professor at Duke University. His fundamental contributions to the theories of chemical bonding and of intermolecular forces (London dispersion forces) are today c ...
) is a
quantum-mechanical Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qu ...
phenomenon whereby a spinning superconductor generates a magnetic field whose
axis An axis (plural ''axes'') is an imaginary line around which an object rotates or is symmetrical. Axis may also refer to: Mathematics * Axis of rotation: see rotation around a fixed axis *Axis (mathematics), a designator for a Cartesian-coordinate ...
lines up exactly with the spin axis. The term may also refer to the magnetic moment of any rotation of any superconductor, caused by the electrons lagging behind the rotation of the object, although the field strength is independent of the
charge carrier density Charge carrier density, also known as carrier concentration, denotes the number of charge carriers in per volume. In SI units, it is measured in m−3. As with any density, in principle it can depend on position. However, usually carrier concentr ...
in the superconductor.


Gravity Probe B

A magnetometer determines the orientation of the generated field, which is
interpolated In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a n ...
to determine the axis of rotation. Gyroscopes of this type can be extremely accurate and stable. For example, those used in the Gravity Probe B experiment measured changes in gyroscope spin axis orientation to better than 0.5
milliarcseconds A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The n ...
(1.4 degrees) over a one-year period. This is equivalent to an
angular separation Angular distance \theta (also known as angular separation, apparent distance, or apparent separation) is the angle between the two sightlines, or between two point objects as viewed from an observer. Angular distance appears in mathematics (in ...
the width of a human hair viewed from 32 kilometers (20 miles) away. The GP-B gyro consists of a nearly-perfect spherical rotating mass made of
fused quartz Fused quartz, fused silica or quartz glass is a glass consisting of almost pure silica (silicon dioxide, SiO2) in amorphous (non-crystalline) form. This differs from all other commercial glasses in which other ingredients are added which chang ...
, which provides a dielectric support for a thin layer of
niobium Niobium is a chemical element with chemical symbol Nb (formerly columbium, Cb) and atomic number 41. It is a light grey, crystalline, and ductile transition metal. Pure niobium has a Mohs hardness rating similar to pure titanium, and it has si ...
superconducting Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
material. To eliminate friction found in conventional bearings, the rotor assembly is centered by the electric field from six electrodes. After the initial
spin-up Spin-up refers to the process of a hard disk drive or optical disc drive accelerating its platters or inserted optical disc from a stopped state to an operational speed. The period of time taken by the drive to perform this process is referred to ...
by a jet of helium which brings the rotor to 4,000
RPM Revolutions per minute (abbreviated rpm, RPM, rev/min, r/min, or with the notation min−1) is a unit of rotational speed or rotational frequency for rotating machines. Standards ISO 80000-3:2019 defines a unit of rotation as the dimensi ...
, the polished gyroscope housing is evacuated to an ultra-high vacuum to further reduce drag on the rotor. Provided the suspension electronics remain powered, the extreme rotational symmetry, lack of friction, and low drag will allow the angular momentum of the rotor to keep it spinning for about 15,000 years. A sensitive DC SQUID magnetometer able to discriminate changes as small as one
quantum In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizati ...
, or about 2 Wb, is used to monitor the gyroscope. A precession, or tilt, in the orientation of the rotor causes the London moment magnetic field to shift relative to the housing. The moving field passes through a superconducting pickup loop fixed to the housing, inducing a small electric current. The current produces a voltage across a shunt resistance, which is resolved to
spherical coordinates In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' meas ...
by a microprocessor. The system is designed to minimize
Lorentz Lorentz is a name derived from the Roman surname, Laurentius, which means "from Laurentum". It is the German form of Laurence. Notable people with the name include: Given name * Lorentz Aspen (born 1978), Norwegian heavy metal pianist and keyboa ...
torque on the rotor.


Magnetic field strength

The magnetic field strength associated with a rotating superconductor is given by: :B=-\frac\ \omega where ''M'' and ''Q'' are the mass and the charge of the superconducting charge carriers respectively. For the case of Cooper pairs of electrons, ''M=2me'' and ''Q=2e''. Despite the electrons existing in a strongly-interacting environment, ''me'' denotes here the mass of the bare electrons (as in vacuum), and not e.g. the effective mass of conducting electrons of the normal phase.


Etymology

Named for the physical scientist
Fritz London Fritz Wolfgang London (March 7, 1900 – March 30, 1954) was a German physicist and professor at Duke University. His fundamental contributions to the theories of chemical bonding and of intermolecular forces (London dispersion forces) are today c ...
, and
moment Moment or Moments may refer to: * Present time Music * The Moments, American R&B vocal group Albums * ''Moment'' (Dark Tranquillity album), 2020 * ''Moment'' (Speed album), 1998 * ''Moments'' (Darude album) * ''Moments'' (Christine Guldbrand ...
as in magnetic moment.


See also

* Barnett effect


References

{{DEFAULTSORT:London Moment Quantum mechanics