# Multipole

Also found in: Dictionary, Medical, Wikipedia.

## multipole

[′məl·tə‚pōl]
(electromagnetism)
One of a series of types of static or oscillating distributions of charge or magnetization; namely, an electric multipole or a magnetic multipole.

## Multipole

a characteristic of a system of electric charges (“poles”) that has a definite symmetry. At a distance R from such a system (if R is sufficiently great compared to the system’s dimensions r), the static or variable electromagnetic field generated by the system can be visualized as a superposition of multipole fields of various orders / (a zero-order multipole is a charge, a first-order multipole is a dipole, a second-order multipole is a quadrupole, a third-order multipole is an octupole, and so on). For static fields the potential of an lth order multipole (the 2’-pole) decreases as 1/R l + 1 (if R « r) and also has a specific angular dependence. At distances R that are much greater than the wavelength of the emitted waves (in the wave zone), the variable (radiated) fields of oscillating multipoles of any order have an identical dependence on R (they vary as 1/ R) and can be distinguished only by their angular dependence, which is the same as that of static multipoles.

The magnitude and angular distribution of a multipole field, as well as the energy of its interaction with an external field, are determined by the multipole moment. If all multipole moments up to the order I —1 are equal to zero, the moment of the order L is independent of the selection of the coordinate origin within the system.

In the case of a static system of charges ei, located at points ri (with coordinates xia, where ɑ = 1, 2, 3), the potential ɸ(R) of a constant electric field at point R is

For large R (Rri), the potential may be represented as a series in powers of ri/R

where the scalar e = Σiei is the total charge of the system, the vector da = Σiexia is its dipole moment, and the tensor dαβ = Σiei (3xαβxαβ - ri2δαβ) is the quadrupole moment (where α, β = 1, 2, 3 and δαβ is the Kronecker symbol, which is equal to 1 for α = β and 0 for α ɸ β); the quantities Ya, Yαβ, and so on depend only on the direction of the vector R and are expressed in terms of spherical harmonics of the appropriate order I. In the simplest case a dipole field is generated by two charges of equal magnitude but opposite sign; a quadrupole field is generated by four charges of equal magnitude placed at the vertexes of a parallelogram such that each side connects charges of opposite sign; an octupole field is generated by eight charges in the vertexes of a parallelepiped, with each edge connecting opposite charges; and so on.

Magnetic multipoles are used to describe the magnetic properties of a system. Since magnetic charges do not exist, the resolution of vector potential, which is analogous to the resolution of the scalar potential Ф, starts with the magnetic dipole.

The resolution of a variable field by multipoles plays an important role in classical radiation theory and antenna theory. This approach is particularly useful in the quantization of the radiation field. The wave function of a radiation field of the 2’-pole is an eigenfunction of the operator of an angular momentum, with an eigenvalue of l: such a multipole radiates photons only with moment l.

The concept of a multipole is also used in describing variable acoustic, gravitational, and other fields.

### REFERENCES

Landau, L. D., and E. M. Lifshits. Teoriia polia, 6th ed. Moscow, 1973. (Teoreticheskaia fizika, vol. 2.)
Frenkel’, la. I. Elektrodinamika: Sobr. izbr. trudov, vol. 1. Moscow-Leningrad, 1956.
Akhiezer, A. I., and V. B. Berestetskii. Kvantovaia elektrodinamika, 3rd ed. Moscow, 1969.

V. P. PAVLOV

References in periodicals archive ?
A calculation of the borehole thermal resistance using the multipole method can there fore take into account the uncertainty related to both the pipe spacing and the grout thermal conductivity.
the multipole method of Bennet and Claesson [6]), it includes the dynamics of the grout and the authors propose models for coaxial, single- and double-U-type system.
Key words: Thick disk, Rayleigh, epicyclic frequency, and multipole.
Vassiliou, "The fast multipole method (FMM) for electromagnetic scattering problems," IEEE Trans.
As mentioned earlier, it is assumed here that the spheres are small enough so that the multipole expansion of the electric field can be approximated with the first dipole mode.
This assembly has been implemented in the magnetic systems of various devices, for instance in the case of permanent magnet brushless machines employing multipole Halbach magnetized rotors (Zhu and Howe, 2001).
This field is a function of both the applied and multipole fields in the media.
Claesson and Hellstrom examine steady-state borehole heat transfer using the multipole method.
Introduced in February, the Schlumberger SonicScope 475 multipole sonic-while-drilling service is a unique logging-while-drilling service that provides multipole measurements to consistently and reliably deliver compressional and shear data in all environments.
The push-pull connector is available in a wide range of body styles, sizes and configurations, including multipole contacts from two to 42 poles.
Schlumberger--SonicScope[R] Multipole Sonic-While-Drilling Service;

Site: Follow: Share:
Open / Close