6 Design and Principles of Synchrotrons and Circular Colliders
257
is limiting the achievable beam energy in a hadron collider is the magnetic field to
be provided by the dipole magnets in order to bend the particle beam on a circular
trajectory. The radius of curvature of a particle in a dipole field is given by
1
ρ
m
−1
=
eB
p
p = 0.2998
B [T ]
p [GeV /c]
where ρ is the radius of curvature, B is the magnetic field, e is the elementary
charge and p is the particle momentum. The quantity Bρ is called the rigidity
[65, 66]. The beam rigidity determines the B-field required to bend the beam on
a circular trajectory with given bending radius. The maximum achievable B-field
being limited to about 2 Tesla for normal conducting magnets, today’s high-energy
hadron colliders use superconducting bending magnets.
The quasi absence of synchrotron radiation leads to another feature of hadron
colliders, which is the fact that there is no synchrotron radiation damping and the
transverse emittance is hence determined and preserved throughout the injector
chain. Emittance blow up, e.g. via injection mismatch, is therefore critical.
6.8.2 Proton-Antiproton Colliders
A machine with one single vacuum chamber, e.g. the Super Proton Synchrotron SPS
(“SppbarS in this operation mode) in the 1980s or the Tevatron can accomplish the
acceleration of protons and antiprotons.
During the years 1981–1987, the CERN SPS was operated as a proton-antiproton
collider, providing high energy collisions for two major experiments located in
adjacent sextants of the accelerator. This operation was first with three dense
bunches of protons in collision with three rather weak bunches of antiprotons,
with no separation of the beams at the unused crossing points. After increasing
the antiproton production rate, six bunches per beam were used. The SPS has
normal conducting bending magnets and a circumference of 6.9 km. The beam
energy provided by the SPS as proton-antiproton collider was 315 GeV [67, 68].
The SppS was the first hadron collider operating with bunched beams. Before the
commissioning of the machine it was debated if it was possible to collide proton
and antiproton bunches, or if the beams would become unstable due to the presence
of the beam-beam interaction without damping as in e + e − colliders. Its success
demonstrated the feasibility of high energy hadron colliders [69].
Higher energy was achieved by the Tevatron, using superconducting magnets
with a maximum B field of 4.5 T. The circumference of the machine is 6.28 km;
comparable to that of the SPS. In the final stage of operations (“run II”), beams are
injected at 150 GeV and accelerated to 980 GeV. The bunches (36+36) circulate
in the same aperture, the protons clockwise and the antiprotons anticlockwise. The
machine has a lattice with four dipoles followed by a quadrupole, with a total of
772+2 dipoles and 90+90 quadrupoles, plus a number of corrector magnets.
257
is limiting the achievable beam energy in a hadron collider is the magnetic field to
be provided by the dipole magnets in order to bend the particle beam on a circular
trajectory. The radius of curvature of a particle in a dipole field is given by
1
ρ
m
−1
=
eB
p
p = 0.2998
B [T ]
p [GeV /c]
where ρ is the radius of curvature, B is the magnetic field, e is the elementary
charge and p is the particle momentum. The quantity Bρ is called the rigidity
[65, 66]. The beam rigidity determines the B-field required to bend the beam on
a circular trajectory with given bending radius. The maximum achievable B-field
being limited to about 2 Tesla for normal conducting magnets, today’s high-energy
hadron colliders use superconducting bending magnets.
The quasi absence of synchrotron radiation leads to another feature of hadron
colliders, which is the fact that there is no synchrotron radiation damping and the
transverse emittance is hence determined and preserved throughout the injector
chain. Emittance blow up, e.g. via injection mismatch, is therefore critical.
6.8.2 Proton-Antiproton Colliders
A machine with one single vacuum chamber, e.g. the Super Proton Synchrotron SPS
(“SppbarS in this operation mode) in the 1980s or the Tevatron can accomplish the
acceleration of protons and antiprotons.
During the years 1981–1987, the CERN SPS was operated as a proton-antiproton
collider, providing high energy collisions for two major experiments located in
adjacent sextants of the accelerator. This operation was first with three dense
bunches of protons in collision with three rather weak bunches of antiprotons,
with no separation of the beams at the unused crossing points. After increasing
the antiproton production rate, six bunches per beam were used. The SPS has
normal conducting bending magnets and a circumference of 6.9 km. The beam
energy provided by the SPS as proton-antiproton collider was 315 GeV [67, 68].
The SppS was the first hadron collider operating with bunched beams. Before the
commissioning of the machine it was debated if it was possible to collide proton
and antiproton bunches, or if the beams would become unstable due to the presence
of the beam-beam interaction without damping as in e + e − colliders. Its success
demonstrated the feasibility of high energy hadron colliders [69].
Higher energy was achieved by the Tevatron, using superconducting magnets
with a maximum B field of 4.5 T. The circumference of the machine is 6.28 km;
comparable to that of the SPS. In the final stage of operations (“run II”), beams are
injected at 150 GeV and accelerated to 980 GeV. The bunches (36+36) circulate
in the same aperture, the protons clockwise and the antiprotons anticlockwise. The
machine has a lattice with four dipoles followed by a quadrupole, with a total of
772+2 dipoles and 90+90 quadrupoles, plus a number of corrector magnets.