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 .
This equation is called the cyclotron formula ,
and it may be rewritten as , thereby showing that the
gyroradius , 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
See also Hemispherical Deflection Analyzer (HDA), which is combined with a magnetic sector in a
double focusing magnetic sector.
See SIMION Example: magnet (mag90.iob) for a simple 3D simulation with cylindrical poles
and fringing fields. SIMION Example: magnetic_sector (added in 184.108.40.206) 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 includes
other SIMION magnetic sector models and discussions.
The Short ASMS Course (courses\short) (Session 2) has a brief look at
SIMION simulations of sectors are
illustrated in the discussions in . Magnetic poles with approximately infinite
permeability and treated with scalar magnetic potential are the easiest to handle
(see Magnetic Potential).
Figure: SIMION Example: magnetic_sector - 90 degree 3D sector (with fringe fields)
and inclined 26.56 degree entrance/exit angles
to achieve symmetric stigmatic focusing.