1 Accelerators, Colliders and Their Application
13
within the negative, decelerating, phase of the sine wave and be left behind. Even if
one succeeded in achieving synchronism for the ideal, synchronous particle, others
of slightly different energy would not have the same velocity and take a different
time to circulate around the machine. Would not these particles gradually get out of
step until they were lost? After all, particles had to make many hundred thousand
turns before reaching full energy and while transverse focusing was understood
there was no apparent focusing available in the longitudinal direction. Fortunately
the comforting principle of phase stability, which prevents this happening, was
soon to be independently discovered by V. I. Veksler in Moscow in 1944 [14] and
McMillan in Berkeley in 1945 [15], opening the way to the construction of the first
synchrotrons. We shall return to this later.
When it came to the next generation of synchrotrons, interest focused on
colliding two opposing beams of particles. It had been known for some time that
the energy available in the centre of mass from a collision of particles, one in the
beam with energy E and the other of mass m 0 in a fixed target, only increased
with the square root of the accelerators energy,
√
m 0 E. Two particles of the same
mass and energy E colliding head on made available all their energy in the centre
of mass, 2E. The difficulty was making the two bunches of particles of sufficient
density to have a significant probability of collision or, in technical jargon a high
enough luminosity. Once this problem was solved a series of colliders: ISR, SppS,
LEP, Tevatron, HERA and finally LHC followed. Some of these (ISR, HERA and
LHC) were two separate rings which intersected to collide particles at several points
around the circumference. Others (SppS and LEP) collided protons with antiprotons
and electrons with their anti-particles: positrons. These exploited the fact that beams
of particles and antiparticles will circulate on identical trajectories, but in opposite
directions, in a single ring of bending and focusing magnets.
At present several studies are ongoing, to pave the way to even higher energies,
mainly increasing the size of the machine and using super conducting magnets with
higher critical field, to gain more bending and focusing fields in the lattice. One
example, the Future Circular Collider study, FCC, under the guidance of CERN, is
studying a 100 km proton storage ring to achieve centre of mass energies of up to
100 TeV. The R & D effort of accelerators of this dimension and complexity, in any
case, has to be done by a truly international, in other words worldwide effort.
References
1. J.D. Cockcroft, E.T.S. Walton: Proc. Roy. Soc. A 129 (1930) 477-489.
2. J.D. Cockcroft, E.T.S. Walton: Proc. Roy. Soc. A136 (1932) 619-630.
3. J.D. Cockcroft, E.T.S. Walton: Proc. Roy. Soc. A 137 (1932) 229-242.
4. R.J. Van der Graaf: Phys. Rev. 38 (1931) 1919.
5. R. Wideröe.: ETH Library, Zürich, Hs 903 (1923-28) 633-638.
6. D.W. Kerst, R. Serber: Phys. Rev. 60 (1941) 53-58.
7. G. Ising: Arkiv för matematik o. fysik 18 (1924) 1-4.
8. J.J. Livingood: Principles of cyclic particle accelerators, van Nostrand (1961).
13
within the negative, decelerating, phase of the sine wave and be left behind. Even if
one succeeded in achieving synchronism for the ideal, synchronous particle, others
of slightly different energy would not have the same velocity and take a different
time to circulate around the machine. Would not these particles gradually get out of
step until they were lost? After all, particles had to make many hundred thousand
turns before reaching full energy and while transverse focusing was understood
there was no apparent focusing available in the longitudinal direction. Fortunately
the comforting principle of phase stability, which prevents this happening, was
soon to be independently discovered by V. I. Veksler in Moscow in 1944 [14] and
McMillan in Berkeley in 1945 [15], opening the way to the construction of the first
synchrotrons. We shall return to this later.
When it came to the next generation of synchrotrons, interest focused on
colliding two opposing beams of particles. It had been known for some time that
the energy available in the centre of mass from a collision of particles, one in the
beam with energy E and the other of mass m 0 in a fixed target, only increased
with the square root of the accelerators energy,
√
m 0 E. Two particles of the same
mass and energy E colliding head on made available all their energy in the centre
of mass, 2E. The difficulty was making the two bunches of particles of sufficient
density to have a significant probability of collision or, in technical jargon a high
enough luminosity. Once this problem was solved a series of colliders: ISR, SppS,
LEP, Tevatron, HERA and finally LHC followed. Some of these (ISR, HERA and
LHC) were two separate rings which intersected to collide particles at several points
around the circumference. Others (SppS and LEP) collided protons with antiprotons
and electrons with their anti-particles: positrons. These exploited the fact that beams
of particles and antiparticles will circulate on identical trajectories, but in opposite
directions, in a single ring of bending and focusing magnets.
At present several studies are ongoing, to pave the way to even higher energies,
mainly increasing the size of the machine and using super conducting magnets with
higher critical field, to gain more bending and focusing fields in the lattice. One
example, the Future Circular Collider study, FCC, under the guidance of CERN, is
studying a 100 km proton storage ring to achieve centre of mass energies of up to
100 TeV. The R & D effort of accelerators of this dimension and complexity, in any
case, has to be done by a truly international, in other words worldwide effort.
References
1. J.D. Cockcroft, E.T.S. Walton: Proc. Roy. Soc. A 129 (1930) 477-489.
2. J.D. Cockcroft, E.T.S. Walton: Proc. Roy. Soc. A136 (1932) 619-630.
3. J.D. Cockcroft, E.T.S. Walton: Proc. Roy. Soc. A 137 (1932) 229-242.
4. R.J. Van der Graaf: Phys. Rev. 38 (1931) 1919.
5. R. Wideröe.: ETH Library, Zürich, Hs 903 (1923-28) 633-638.
6. D.W. Kerst, R. Serber: Phys. Rev. 60 (1941) 53-58.
7. G. Ising: Arkiv för matematik o. fysik 18 (1924) 1-4.
8. J.J. Livingood: Principles of cyclic particle accelerators, van Nostrand (1961).