Quadrupole magnet

A quadrupole magnet is an arrangement of four magnetic poles, where the north and the south poles are opposite each. Mathematics enters the magnetic quadrupole field in the multipole expansion of the magnetic field as a second non-zero term. For a basic sketch see also the electric quadrupole.

In accelerator physics quadrupole magnets are used for focusing the particle beam accelerators and beamlines. This exploits that its magnetic field transverse to the beam direction, a gradient, ie, position-dependent field strength and flux density, so that also depends on the force acting on the particles Lorentz force from the resort.

Shape of the magnetic field

It is the direction of the beam axis, and the two transverse directions. To the desired beam axis ( the orbit ), so to is the flux density of the quadrupole field is zero. It grows outward with a constant gradient of, ie

If the equipotential surfaces, ie the surfaces of the iron yoke, are hyperbolic in shape. The proportionality constant is called this quadrupole.

Application of accelerator technology

A quadrupole magnet always acts in a direction transverse to the particle beam focusing while defocused in the other transverse direction; that is, a horizontally focusing quadrupole magnet is defocused vertical and vice versa. In order to achieve an overall focus, so hold the beam, one must, therefore, an array of quadrupoles build, the focus turns in a given direction (F) and defocusing ( D), ( eg, FDFD, FFDD or FODO with O as drift ). It is the same principle of strong focusing, as it is also used in the dipole magnets of modern cyclotrons and synchrotrons for example.

The focus is necessary, since the particles generally have an angle of divergence relative to the beam axis. If you do not use focusing parts, sooner or later they ran against the wall of the vacuum chamber and went with it lost.

Due to the quadrupole magnets the particles, the so-called betatron oscillations to oscillate around the desired trajectory. During the construction and configuration of an accelerator must be taken to ensure that the amplitude of these oscillations is never so large that the particles run into the wall. Among other things, this is the job of the so-called beam optics.

Application in the physical analysis

Through special arrangements of quadrupole complicated, each superimposed fields can be generated, which produce at defined locations in areas that have the zero field, what with magnetic resonance imaging offers advantages in studies of objects.

666714
de