Example:
Magnetic Quadrupole Lens
Introduction
• This is an example model of a system of magnetic
quadrupoles for use in a nuclear accelerator
• The beam consists of Be5+ ions, traveling through three
consecutive magnetic quadrupoles with the velocity
0.01c.
• The quadrupole triplet acts as a lense, focusing the
beam in the transversal plane.
3D Geometry
iron
magnets
N inward
S inward
2D Geometry
iron
M
magnet
Cross section of the 3D geometry
Results
• The magnetic field distribution.
Results
• The magnetic field distribution and approximately
hyperbolic contour lines for the magnetic potential.
Particle Tracing
• The force on an ion is given by
F  qv  B
drift (1m)
Q1 (1m)
Q3 (1m)
Q2 (2m)
• Particle tracing in 2D is done with a logic expression reversing
the polarity of the force when the ions are in Q2.
Results
• Magnetic field and ion trajectories.
Results
Q1
Q2
Q3
drift
1 cm
3 cm
• Ions starting from R = 3 cm all arrive within R = 1 cm.
Results 3D
• Magnetic field and ion trajectories.
Results 3D
• Ion trajectories only. Color scale shows local force on
each ion.