1 Accelerators, Colliders and Their Application
9
Fig. 1.5 The principle of the
cyclotron
Fig. 1.6 Balance of forces in
a cyclotron
and, rearranging, we can define the magnetic rigidity—the reluctance of the beam
to be bent in a curve:
BB =
mv
e
, if v c.
(1.2)
In the relativistic regime if we replace the classical momentum, mv, by the
relativistic momentum, p = γ mv, with γ being the Lorentz factor, we obtain the
equation, valid in the relativistic regime:
BB =
p
e
.
(1.3)
By good fortune the radius of the orbit in a cyclotron is proportional to the
velocity and the frequency of revolution this being the inverse of the time of
9
Fig. 1.5 The principle of the
cyclotron
Fig. 1.6 Balance of forces in
a cyclotron
and, rearranging, we can define the magnetic rigidity—the reluctance of the beam
to be bent in a curve:
BB =
mv
e
, if v c.
(1.2)
In the relativistic regime if we replace the classical momentum, mv, by the
relativistic momentum, p = γ mv, with γ being the Lorentz factor, we obtain the
equation, valid in the relativistic regime:
BB =
p
e
.
(1.3)
By good fortune the radius of the orbit in a cyclotron is proportional to the
velocity and the frequency of revolution this being the inverse of the time of