Dipole magnet

A dipole magnet is a magnet with a positive or north and a negative or south pole (see magnetism ). Most magnets ( permanent magnets and electromagnets ) are dipole magnets.

The term is mainly used in the field of particle accelerators where other magnet configurations, e.g. B. quadrupole magnets are used. Dipole magnets in accelerators are electromagnets made from a U-shaped iron yoke. Coils are wound around the ends of the yoke . A magnetic field that can be regulated by the current flow is created in the gap between the ends .

Basics

Sketch of a dipole magnet as used in accelerator physics

Dipole magnet arrangement of the Advanced Photon Source in the Argonne National Laboratory

Calculated magnetic field of a dipole magnet. A relatively homogeneous and strong field is created in the gap between the two cylinder magnets.

In particle accelerators , dipole magnets are used to generate a magnetic field to deflect the beam, which is why they are also referred to as deflection magnets . The field can be homogeneous (i.e., spatially constant) or inhomogeneous for focusing purposes; The decisive factor is the surface of the pole pieces with parallel or non-parallel planes. The particle movement under the Lorentz force takes place on a path whose curvature is perpendicular to the field. If the field is homogeneous, for example in the classic cyclotron , the path is an arc of a circle.

In accelerators for high particle energies such as synchrotrons and storage rings , due to the technical feasibility, not a single large magnet is used, but many smaller magnets, so-called sector magnets . In such systems there is no circular path, instead there are field-free straight sections between the magnets. These offer space for acceleration elements, interaction zones in colliding beam experiments or for wigglers or undulators for generating synchrotron radiation .

The iron cores of the magnets are saturated at a magnetic flux density of approx. 2  Tesla . If higher magnetic flux densities are required, for example because a larger radius of curvature is not possible for reasons of space, superconducting magnets without cores must be used. The current densities in superconducting magnets can reach values ​​of several kA / mm ² . Although part of the conductor cross-section is required for copper (to stabilize the superconductor) and thermal insulation, the average net current density over the entire cross-section of the winding is significantly higher than with conventional copper windings. The ohmic losses ( electricity heat , copper losses) drop to zero.

In the case of superconducting magnets, no equipotential surfaces almost fixed by pole shoes or yoke ends form the field. Instead, the superconductors in the coil must be arranged in such a way that the mean current distribution in it is proportional to the cosine of the angle around the beam axis.

Connections

With a constant cross-section of the magnetic path (yoke + air gap) , the magnetic flux density in the air gap, which is decisive for the deflection angle and thus the orbital radius of charged particle beams , is approximately: ${\displaystyle B}$

${\displaystyle B={\mu _{0}}{\mu _{r}}\cdot {\frac {I\cdot n}{{\mu _{r}}{l_{1}}+{l_{2}}}}}$

with - magnetic field constant - permeability number of the yoke material - electric current through the coil - number of turns of the coil - air gap of the yoke - iron path of the yoke
${\displaystyle {\mu _{0}}}$
${\displaystyle {\mu _{r}}}$
${\displaystyle I}$
${\displaystyle n}$
${\displaystyle {l_{1}}}$
${\displaystyle {l_{2}}}$

It can be seen from this that

• the yoke must be as compact as possible (short iron path length)
• the permeability number of the yoke material should be as high as possible.

The great influence of the air gap can also be seen. The air gap cannot be made arbitrarily small because it i. A. the vacuum tube for the particle beam must accommodate.
The heat loss (which increases with the square of the electrical current) often requires water cooling .

In order to fill the winding cross-section of the yoke as effectively as possible, so that the iron path can remain as short as possible, copper strips or rectangular conductors are often used instead of round wires.

The deflection angle of a beam of charged particles is proportional to the flux density and also the length of the field flown through - one reason that such magnets often weigh many tons and the air gaps develop huge forces that have to be intercepted.

See also

• Deflection magnet
• Deflection system
• Quadrupole magnet
• dipole
• Multipole

literature

• Horst Stöcker: Pocket book of physics. 4th edition, Verlag Harry Deutsch, Frankfurt am Main, 2000, ISBN 3-8171-1628-4
• Richard P. Feynman, Robert B. Leighton, Matthew Sands: Lectures on Physics. 3rd edition, Oldenbourg Verlag, Munich Vienna, 2001, ISBN 3-486-25589-4