Subatomic Physics

22 Accelerators
large numbers of rare isotopes by bombarding a variety of targets with beams of
stable ions accelerated with a linac.
2.5 Beam Optics
In the description of linacs we have swept many problems under the rug, and we shall
leave most of them there. However, one question must occur to anyone thinking
about a machine that is a few km in length: How can the beam be kept well
collimated? The beam of a flashlight, for instance, diverges, but it can be refocused
with lenses. Do lenses for charged particle beams exist? Indeed they do, and we shall
discuss here some of the elementary considerations, using the analogy to ordinary
optical lenses. In light optics, the path of a monochromatic light ray through a
system of thin lenses and prisms can be found easily by using geometrical optics. (4)
Consider, for instance, the combination
of a positive and a negative
thin lens, with equal focal
lengths f and separated by a distance
d (Fig. 2.7). This combination
is always focusing, with an
overall focal length given by
2 f
fcomb = . (2.20)
d
In principle one could use electric
or magnetic lenses for the guidance
of charged particle beams.
The electric field strength required
for the effective focusing of
high-energy particles is, however,
impossibly high, and only magnetic
elements are used.
Figure 2.7: The combination of a focusing
and a defocusing thin lens with
equal focal lengths is always focusing.
The deflection of a monochromatic (monoenergetic) beam by a desired angle, or the
selection of a beam of desired momentum, is performed with a dipole magnet, as
shown in Fig. 2.8. The radius of curvature, ρ, can be computed from the Lorentz
equation, (5) which gives the force F exerted on a particle with charge q and velocity
v in an electric field E and a magnetic field B:
�
F = q E + 1
�
v × B . (2.21)
c
4See, for instance, E. Hecht, Optics, 4th. Ed., Addison-Wesley, San Francisco, 2002.
5Jackson, Eq. (6.113).