en>Michael Hardy at 19:29, 13 December 2012

2012-12-13T19:29:04Z

New page

Multipole magnets are magnets built from multiple individual magnets, typically used to control [[Charged particle beam|beams of charged particles]]. Each type of magnet serves a particular purpose.

* [[Dipole magnet]]s are used to bend the trajectory of particles
* [[Quadrupole magnets]] are used to focus particle beams
* [[Sextupole magnet]]s are used to correct for [[chromaticity (accelerator)|chromaticity]] introduced by quadrupole magnets <ref>http://cas.web.cern.ch/cas/Bulgaria-2010/Talks-web/Brandt-1-web.pdf</ref>

==Magnetic field equations==

The magnetic field of an ideal multipole magnet in an accelerators is typically modeled as having no (or a constant) component parallel to the nominal beam direction (<math>z</math> direction)
and the for the transverse components can be written as complex numbers:<ref>http://cas.web.cern.ch/cas/Belgium-2009/Lectures/PDFs/Wolski-1.pdf</ref>

<math>
B_y + i B_x = C_n \cdot ( x + iy )^{n-1}
</math>

where <math>x</math> and <math>y</math> are the coordinates in the plane transverse to the nominal beam direction. <math>C_n</math> is a complex number specifying the orientation and strength of the magnetic field. <math>B_x</math> and <math>B_y</math> are the components of the magnetic field in the corresponding directions. Fields with a real <math>C_n</math> are called 'normal' while fields with <math>C_n</math> purely imaginary are called 'skewed'.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ First few multipole fields
|-
!n
!name
!magnetic field lines
!example device
|-
| 1 || [[dipole magnet|dipole]] || [[File:Magnetic field of an idealized dipole.svg|thumb]] || [[Image:Hetdipole.jpg|thumb|250px]]
|-
| 2 || [[quadrupole magnet|quadrupole]] || [[File:Magnetic field of an idealized quadrupole.svg|thumb]] || [[Image:Aust.-Synchrotron,-Quadrupole-Focusing-Magnet,-14.06.2007.jpg|thumb|250px]]
|-
| 3 || [[sextupole magnet|sextupole]] || [[File:Magnetic field of an idealized sextupole.svg|thumb]] || [[Image:Aust.-Synchrotron,-Sextupole-Focusing-Magnet,-14.06.2007.jpg|thumb|250px]]
|}

==References==
{{Reflist}}

[[Category:Types of magnets]]
[[Category:Accelerator physics]]

Excursion probability - Revision history

en>Michael Hardy at 19:29, 13 December 2012