# Magnetic Sector¶

A charged particle (mass m and charge q) with velocity **v** perpendicular to a uniform magnetic
field **B** will (by the Lorentz Force Law) experience a
centripetal force , sustaining a circular motion of
radius R in the plane perpendicular to the magnetic field [4] [3] .
This equation is called the **cyclotron formula** [1] [2],
and it may be rewritten as , thereby showing that the
**gyroradius** [2], R, is proportional to momentum, if charge is constant.
A uniform magnetic field
therefore can act as a **momentum analyzer** (in contrast to electric fields used in
kinetic energy analyzers like in the Hemispherical Deflection Analyzer (HDA)).

A **magnetic sector** is a type of mass analyzer using
a static magnetic field to deflect particles in this way along a roughly circular
arc. It is characterized by a **deflection angle** and **radius** .
For background/theory, particularly on focusing properties in design, see [5]
[6] [7].

See also Hemispherical Deflection Analyzer (HDA), which is combined with a magnetic sector in a double focusing magnetic sector.

## SIMION specific¶

See SIMION Example: magnet (mag90.iob) for a simple 3D simulation with cylindrical poles
and fringing fields. SIMION Example: magnetic_sector (added in 8.1.1.0) is a more
extensive example, which examines focusing properties of various magnetic sector
geometries (inclined and conical, 2D and 3D)
with full control of parameters. The HIPIRMS course [8] includes
other SIMION magnetic sector models and discussions.
The Short ASMS Course (`courses\short`

) (Session 2) has a brief look at
sectors.
SIMION simulations of sectors are
illustrated in the discussions in [6]. Magnetic poles with approximately infinite
permeability and treated with scalar magnetic potential are the easiest to handle
(see Magnetic Potential).

## References¶

[1] | http://scienceworld.wolfram.com/physics/Cyclotron.html |

[2] | (1, 2) Wikipedia:Gyroradius |

[3] | SIMION 8.1 printed manual. Section 2.2 “Basic Ion Optics Concepts”. |

[4] | David Jeffery Griffiths. Introduction to electrodynamics. G:M8XvAAAAMAAJ. 1999. Prentice Hall. ISBN:978-0-13-805326-0. Section 5.1 “The Lorentz Force Law”. |

[5] | Helmut Liebl. Applied charged particle optics. November 2007. Springer. G:XqRFZX0ssRMC ISBN:978-3-540-71924-3 springer. Chapter 3. Magnetic Deflection. |

[6] | (1, 2) Mikhail Yavor. Advances in Imaging and Electron Physics: Optics of Charged Particle Analyzers.
Volume 157 of Advances in Imaging and Electron Physics.
G:ntYf2V-pbIgC. 24 July 2009. Academic Press. ISBN:978-0-12-374768-6.
Chapter 5. Static Magnetic Charged Particle Analyzers. |

[7] | Jürgen H. Gross. Mass Spectrometry: A Textbook. G:xHOQiaquq24C. 6 April 2011. springer. ISBN:978-3-642-10709-2. Section 4.3. Magnetic Sector Instruments. See also http://www.ms-textbook.com/. |

[8] | HIPIRMS http://hipirms.org/ has SIMION course notes and examples related to magnetic sectors. Topic 3 and Session 3 are on magnetic sectors. d3_lecture.ppt - summary on magnetic sector theory. |

[9] | Wikipedia:Sector_instrument |