Multipole magnet

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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.

Magnetic field equations[edit]

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 (z direction) and the for the transverse components can be written as complex numbers:[2]

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

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

First few multipole fields
n name magnetic field lines example device
1 dipole
Magnetic field of an idealized dipole.svg
2 quadrupole
Magnetic field of an idealized quadrupole.svg
3 sextupole
Magnetic field of an idealized sextupole.svg