Sextupole magnets consist of groups of six magnet

Magnet

A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, and attracts or repels other magnets.A permanent magnet is an object...

s set out in an arrangement of alternating north and south magnetic poles

Magnet

A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, and attracts or repels other magnets.A permanent magnet is an object...

 arranged around an axis. They are used in particle beam

Particle beam

A particle beam is a stream of charged or neutral particles which may be directed by magnets and focused by electrostatic lenses, although they may also be self-focusing ....

 control in particle accelerators.

The design of sextupoles using electromagnet

Electromagnet

An electromagnet is a type of magnet in which the magnetic field is produced by the flow of electric current. The magnetic field disappears when the current is turned off...

s generally involves six steel

Steel

Steel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten...

 pole tips of alternating polarity. The steel is magnetised by a large electric current

Electric current

Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

 that flows in the coils of wire wrapped around the poles.

Sextupoles in particle accelerators

At the energies reached in high energy particle accelerator

Particle accelerator

A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

s, magnetic deflection is more powerful than electrostatic, and use of the magnetic term of the Lorentz force

Lorentz force

In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...

:

is enabled with various magnets that make up 'the lattice' required to bend, steer and focus

Strong focusing

In accelerator physics strong focusing or alternating-gradient focusing is the principle that the net effect on a particle beam of charged particles passing through alternating field gradients is to make the beam converge...

 a charged particle beam.

The quadrupole magnet

Quadrupole magnet

Quadrupole magnets consist of groups of four magnets laid out so that in the multipole expansion of the field the dipole terms cancel and where the lowest significant terms in the field equations are quadrupole. Quadrupole magnets are useful as they create a magnetic field whose magnitude grows...

s used to focus and combine the beam have the unfortunate property that their focusing strength (describable by a focal length

Focal length

The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...

) is dependent on the energy of the particle being focused—high energy particles having longer focal lengths than those with lower energy. Since all realistic beams have some, non-negligible, energy spread, any focusing scheme that relies purely on quadrupole magnets will result in the size of the beam "blowing up" with distance.

In linear accelerators this is due to the under- or over-focusing of the particles, while in storage rings it is related to the chromaticity

Chromaticity

Chromaticity is an objective specification of the quality of a color regardless of its luminance, that is, as determined by its hue and colorfulness ....

 of the ring (the tendency for off-energy particles to have different values for the betatron

Betatron

A betatron is a cyclotron developed by Donald Kerst at the University of Illinois in 1940 to accelerate electrons, but the concepts ultimately originate from Rolf Widerøe and previous development occurred in Germany through Max Steenbeck in the 1930s. The betatron is essentially a transformer with...

 phase advance per orbit).

Typically this is controlled with the addition of sextupolar fields to the lattice.

Sextupolar fields have a focal length that is inversely proportional to the distance from the centre of the magnet with which the particle passes. This is similar to the action of a quadrupole, whose effect on the beam may be described as a bending whose strength depends on the distance from the centre of the magnet.

If a sextupole is placed at a point at which the particles in the beam are arranged by their energy offset (i.e. a region of non-zero dispersion

Dispersion (materials science)

In materials science, dispersion is the fraction of atoms of a material exposed to the surface. In general:where D is the dispersion, NS is the number of surface atoms and NT is the total number of atoms of the material...

), then the sextupole can be set at a strength that ensures that particles of all reasonable energy offsets are focused to the same point. This will negate the tendency of the quadrupole lattice to disperse the beam.

Problems

Sextupolar fields are non-linear (i.e. they depend on the product of the sizes of the transverse displacements), and have terms which depend on both the horizontal and vertical offsets (i.e. they are coupled).

This leads to equations of motion that cannot be solved for the general case, thus requiring approximations to be used when calculating their effects on the beam.

In addition, the quadrature dependence of the sextupole kick on the transverse offset of the beam, can lead to high amplitude particles being kicked far from the beam axis and being lost on the beam-pipe walls. Due to this mechanism, the addition of sextupole fields to an accelerator lattice will limit the dynamic aperture

Dynamic aperture

Dynamic aperture is a term in acoustics used very much like aperture in photography. The arrays in side-scan sonar can be programmed to transmit just a few elements at a time or all the elements at once. The more elements transmitting, the narrower the beam and the better the resolution.The ratio...

 or acceptance

Acceptance

Acceptance is a person's agreement to experience a situation, to follow a process or condition without attempting to change it, protest, or exit....

 of the accelerator.

See also

• Charged particle beam
  Charged particle beam
  A charged particle beam is a spatially localized group of electrically charged particles that have approximately the same velocity . The kinetic energies of the particles are typically measured in keV or MeV, much larger than the energies of particles at ambient temperature...
  
  
• Dipole magnet
  Dipole magnet
  A dipole magnet, in particle accelerators, is a magnet constructed to create a homogeneous magnetic field over some distance. Particle motion in that field will be circular in a plane perpendicular to the field and collinear to the direction of particle motion and free in the direction orthogonal...
  
  
• Electron optics
  Electron optics
  Electron optics deals with the focusing and deflection of electrons using magnetic and/or electrostatic fields.- Electron properties :Electrons are charged particles . The electron also has an associated spin of + 1/2...
  
  
• Halbach cylinder
• Quadrupole magnet
  Quadrupole magnet
  Quadrupole magnets consist of groups of four magnets laid out so that in the multipole expansion of the field the dipole terms cancel and where the lowest significant terms in the field equations are quadrupole. Quadrupole magnets are useful as they create a magnetic field whose magnitude grows...