Multipole magnets are magnets built from multiple individual magnets, typically used to control beams of charged particles. Each type of magnet serves a particular purpose.
- Dipole magnets are used to bend the trajectory of particles
- Quadrupole magnets are used to focus particle beams
- Sextupole magnets are used to correct for chromaticity introduced by quadrupole magnets 
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 ( direction) and the for the transverse components can be written as complex numbers:
where and are the coordinates in the plane transverse to the nominal beam direction. is a complex number specifying the orientation and strength of the magnetic field. and are the components of the magnetic field in the corresponding directions. Fields with a real are called 'normal' while fields with purely imaginary are called 'skewed'.
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