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[[Image:Aust.-Synchrotron,-Sextupole-Focusing-Magnet,-14.06.2007.jpg|250px|right|thumb|Sextupole electromagnet as used within the [[storage ring]] of the [[Australian Synchrotron]] to [[Focus (optics)|focus]] and steer the [[electron]] beam]]
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[[Image:Magnetic field of an idealized sextupole.svg|thumb|right|250px|Field lines of an idealized sextupole magnet in the plane transverse to the beam direction]]
'''Sextupole magnets''' consist of groups of six [[magnet]]s set out in an arrangement of alternating north and south [[magnet|magnetic poles]] arranged around an axis.<ref name="XFEL" /> They are used in [[particle beam]] control in [[particle accelerators]].<ref name="XFEL">{{cite web|url=http://xfelinfo.desy.de/en/lexikon.sextupolmagnet/2/index.html|title=Sextupole magnet|date=NA|publisher=The European X-Ray Laser Project (XFEL)|accessdate=2008-09-17}}</ref>


The design of sextupoles using [[electromagnet]]s generally involves six [[steel]] pole tips of alternating polarity. The steel is magnetised by a large [[electric current]] that flows in the coils of wire wrapped around the poles.
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==Sextupoles in particle accelerators==
{{main|Strong focusing}}
At the energies reached in high energy [[particle accelerator]]s, magnetic deflection is more powerful than electrostatic, and use of the magnetic term of the [[Lorentz force]]:
 
: <math>\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}),</math>
 
is enabled with various magnets that make up 'the lattice' required to bend, steer and [[strong focusing|focus]] a charged particle beam.
 
The [[quadrupole magnet]]s used to focus and combine the beam have the unfortunate property that their focusing strength (describable by a [[focal length]]) 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 ring]]s it is related to the [[chromaticity]] of the ring (the tendency for off-energy particles to have different values for the [[betatron]] 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 center 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 center 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 (materials science)|dispersion]]), 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 (Accelerator Physics)|dynamic aperture]] or [[Beam emittance#Acceptance|acceptance]] of the accelerator.
 
==See also==
*[[Charged particle beam]]
*[[Dipole magnet]]
*[[Electron optics]]
*[[Halbach cylinder]]
*[[Quadrupole magnet]]
*[[Multipole magnet]]
 
==References==
{{reflist}}
 
[[Category:Accelerator physics]]
[[Category:Types of magnets]]

Latest revision as of 07:29, 3 March 2014

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