Elementary Particles
383
step with the circulating particles. Machines based on this idea are called synchrocyclotrons. A further modification was to change the magnetic field as well as
the pulse frequency so as to keep the protons in circular orbits of approximately
the same radius (magnetic field must increase as the velocity of the protons
increases) and to keep the pulse frequency in step with the particles. Such an
accelerator is called the synchrotron, and is capable of providing proton beams
of an energy of a few GeV (GeV = 10
9
eV).
One of the problems of synchrotrons is the focussing of the particles. If
there is no focussing, particles with velocities slightly different from the average
velocity will spread out and only a few particles with the final energy will be
obtained. In velocity focussing the particles are kept together by adjusting the
timing of the pulses. In spatial focussing, the particles are kept together (though
they perform small oscillations) by controlling spatial variation of the magnetic
field. An important advance in the accelerators was introduced by what is known
as strong focussing. This was achieved by using magnet sections with alternating
magnetic field gradients—that is the magnetic field increases radially in one
section and decreases in the next sections. This allows one to obtain focussing
in both radial and axial directions and to reduce the radial and axial oscillations.
Synchrotrons using strong focussing are called alternating-gradient synchrotrons
(AGS) (see Fig. 10.5) and have been used to obtain protons of energies of about
30 GeV.
High-energy beams of electrons have been obtained by linear accelerators
(where the radiation loss in the energy due to radial acceleration, synchrotron
radiation, is avoided), and beams of photons have been obtained from the
synchrotron radiation of electrons, e
–
– e
+
annihilation, etc.
Colliding Beams
For the production of heavy particles and the observation of interactions at
high energies, it is advantageous to work with colliding beams of energetic
particles. To see this, consider a collision between two particles of mass m
each. The effective energy for a process may be standardized in terms of the
total energy in the centre of mass (cm) system (P tot = 0 in the cm system). If one
of the particles is at rest and the other is moving with an energy E (E includes
kinetic energy and rest energy) and momentum p, the total cm energy E t is
given by
2
2
1
t
E
c
=
2 2
2
1 (
)
E mc
c
+
-p. p
= 2m
2
c
2
+ 2Em
(10.43)
383
step with the circulating particles. Machines based on this idea are called synchrocyclotrons. A further modification was to change the magnetic field as well as
the pulse frequency so as to keep the protons in circular orbits of approximately
the same radius (magnetic field must increase as the velocity of the protons
increases) and to keep the pulse frequency in step with the particles. Such an
accelerator is called the synchrotron, and is capable of providing proton beams
of an energy of a few GeV (GeV = 10
9
eV).
One of the problems of synchrotrons is the focussing of the particles. If
there is no focussing, particles with velocities slightly different from the average
velocity will spread out and only a few particles with the final energy will be
obtained. In velocity focussing the particles are kept together by adjusting the
timing of the pulses. In spatial focussing, the particles are kept together (though
they perform small oscillations) by controlling spatial variation of the magnetic
field. An important advance in the accelerators was introduced by what is known
as strong focussing. This was achieved by using magnet sections with alternating
magnetic field gradients—that is the magnetic field increases radially in one
section and decreases in the next sections. This allows one to obtain focussing
in both radial and axial directions and to reduce the radial and axial oscillations.
Synchrotrons using strong focussing are called alternating-gradient synchrotrons
(AGS) (see Fig. 10.5) and have been used to obtain protons of energies of about
30 GeV.
High-energy beams of electrons have been obtained by linear accelerators
(where the radiation loss in the energy due to radial acceleration, synchrotron
radiation, is avoided), and beams of photons have been obtained from the
synchrotron radiation of electrons, e
–
– e
+
annihilation, etc.
Colliding Beams
For the production of heavy particles and the observation of interactions at
high energies, it is advantageous to work with colliding beams of energetic
particles. To see this, consider a collision between two particles of mass m
each. The effective energy for a process may be standardized in terms of the
total energy in the centre of mass (cm) system (P tot = 0 in the cm system). If one
of the particles is at rest and the other is moving with an energy E (E includes
kinetic energy and rest energy) and momentum p, the total cm energy E t is
given by
2
2
1
t
E
c
=
2 2
2
1 (
)
E mc
c
+
-p. p
= 2m
2
c
2
+ 2Em
(10.43)