Subatomic Physics

2.8. Colliding Beams 31
or with Eqs. (2.25) and (2.26),
W 2 =(E c.m.
a + Ec.m. b ) 2 =(E lab
a + mbc 2 ) 2 − (p lab
=2E lab
a mbc 2 +(m 2 a + m2b )c4 .
a c)2
(2.31)
Equation (2.31) connects W 2 , the square of the total c.m. energy, to the laboratory
energy. With E lab
a ≫ mac 2 ,mbc 2 , the energy W becomes
W ≈ (2E lab
a mbc 2 ) 1/2 . (2.32)
Only the energy available in the c.m. frame is useful for producing new particles or
exploring internal structure. Equation (2.32) shows that this energy, W ,increases
only as the square root of the laboratory energy at high energies.
2.8 Colliding Beams
The price for working in the laboratory system is high, as is stated plainly by
Eq. (2.32). If the machine energy is increased by a factor of 100, the effective
gain is only a factor of 10. In 1956, Kerst and his colleagues and O’Neill therefore
suggested the use of colliding beams to attain higher energies. (13)
Two proton beams of 21.6 GeV colliding head-on would be equivalent to one 1
TeV accelerator with a fixed target. The main technical obstacle is intensity; both
beams must be much more intense than the ones available in normal accelerators
in order to produce sufficient events in the regions where they collide.
The solution to this problem came in part from progress in vacuum technology,
and in beam storage and cooling, techniques that are described further below. As
an example, Fig. 2.12 shows the colliding beam arrangement at CERN, where an
electron–positron collider (LEP) of 2×50 GeV was completed in 1989 and ran until
2000, and where the next Large Hadron Collider will soon start running. At DESY
in Hamburg, the HERA electron-proton collider was constructed in the 1990’s.
Electrons are accelerated to 28 GeV, protons to 820 GeV in the same tunnel, with
the proton accelerator on top of the electron one. The proton accelerator uses
superconducting magnets with coils cooled to liquid helium temperatures, whereas
the electron ring uses normal magnets.
2.9 Superconducting Linacs
A limiting factor in obtaining beams at the highest energies is the maximum attainable
strength of the magnetic fields. Consider a circular accelerator. Equations (1.3)
and (2.18) imply that, for a given radius of curvature in a magnet, the particle energy
E is proportional to the magnetic field B. Inanironmagnet,thefieldcanbe
13 D. W. Kerst et al., Phys. Rev. 102, 590 (1956); G. K. O’Neill, Phys. Rev. 102, 1418 (1956).