24
An Introduction to Beam Physics
FIGURE 1.18: The principle of the cyclotron, with top view on the left
and side view on the right. (From E. O. Lawrence, US Patent 1,948,384, 1932
[40].)
The basic idea of the cyclotron is similar to that of the microtron, except
that the RF cavity is used more efficiently by providing acceleration twice or
even more times per turn, and the orbits roughly follow concentric circles.
The concept of the cyclotron is shown schematically in Fig. 1.18 [40].
According to eq. (1.9), the revolution frequency is
ω =
q
γm 0
B,
(1.11)
and the momentary radius of the orbit is
r =
p
qB
.
(1.12)
This entails very similar restrictions regarding relativistic effects as in the case
of the microtron; as before, any deviation from constancy of the magnetic
field prevents continuous injection of the beam and hence leads to a noncontinuous outgoing beam. But because the orbits are nearly concentric, it is
possible to at least partly compensate the relativistic effects by increasing
B radially in such a way that the revolution frequency in eq. (1.11) stays
constant. This kind of cyclotrons is called the isochronous cyclotron. If it
is necessary to accelerate different particles in the same machine, then that
entails that the actual field profile has to be adjustable, which is usually
achieved by having one or several trim coils. The superconducting K1200
cyclotron at the National Superconducting Cyclotron Laboratory (NSCL) at
Michigan State University, Michigan, USA, allows for such corrections of the
profile of the magnetic field.
An Introduction to Beam Physics
FIGURE 1.18: The principle of the cyclotron, with top view on the left
and side view on the right. (From E. O. Lawrence, US Patent 1,948,384, 1932
[40].)
The basic idea of the cyclotron is similar to that of the microtron, except
that the RF cavity is used more efficiently by providing acceleration twice or
even more times per turn, and the orbits roughly follow concentric circles.
The concept of the cyclotron is shown schematically in Fig. 1.18 [40].
According to eq. (1.9), the revolution frequency is
ω =
q
γm 0
B,
(1.11)
and the momentary radius of the orbit is
r =
p
qB
.
(1.12)
This entails very similar restrictions regarding relativistic effects as in the case
of the microtron; as before, any deviation from constancy of the magnetic
field prevents continuous injection of the beam and hence leads to a noncontinuous outgoing beam. But because the orbits are nearly concentric, it is
possible to at least partly compensate the relativistic effects by increasing
B radially in such a way that the revolution frequency in eq. (1.11) stays
constant. This kind of cyclotrons is called the isochronous cyclotron. If it
is necessary to accelerate different particles in the same machine, then that
entails that the actual field profile has to be adjustable, which is usually
achieved by having one or several trim coils. The superconducting K1200
cyclotron at the National Superconducting Cyclotron Laboratory (NSCL) at
Michigan State University, Michigan, USA, allows for such corrections of the
profile of the magnetic field.