# Multipole magnet

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

The magnetic field of an ideal multipole magnet in an accelerator is typically modeled as having no (or a constant) component parallel to the nominal beam direction (${\displaystyle z}$ direction) and for the transverse components can be written as complex numbers:[2]

${\displaystyle B_{y}+iB_{x}=C_{n}\cdot (x+iy)^{n-1}}$

where ${\displaystyle x}$ and ${\displaystyle y}$ are the coordinates in the plane transverse to the nominal beam direction. ${\displaystyle C_{n}}$ is a complex number specifying the orientation and strength of the magnetic field. ${\displaystyle B_{x}}$ and ${\displaystyle B_{y}}$ are the components of the magnetic field in the corresponding directions. Fields with a real ${\displaystyle C_{n}}$ are called 'normal' while fields with ${\displaystyle C_{n}}$ purely imaginary are called 'skewed'.

First few multipole fields
n name magnetic field lines example device
1 dipole