LHC - Challenges in Accelerator Physics

In the LHC the energy available in the collisions between the constituents of the protons (the quarks and gluons) will reach the TeV range, that is about 10 times that of LEP and the Fermilab Tevatron. In order to maintain an equally effective physics programme at a higher energy E the luminosity of a collider (a quantity proportional to the number of collisions per second) should increase in proportion to E². This is because the De Broglie wavelength associated to a particle decreases like 1/E and hence the cross section of the particle decreases like 1/E². Whereas in past and present colliders the luminosity culminates around L = 10³²cm^-2 s ^-1, in the LHC it will reach L = 10³⁴cm^-2 s ^-1. This will be achieved by filling each of the two rings with 2835 bunches of 10¹¹ particles each. The resulting large beam current (I_b = 0.53 A) is a particular challenge in a machine made of delicate superconducting magnets operating at cryogenic temperatures.

When two bunches cross in the center of a physics detector only a tiny fraction of the particles collide head-on to produce the wanted events. All the others are deflected by the strong electromagnetic field of the opposing bunch. These deflections, which are stronger for denser bunches, accumulate turn after turn and may eventually lead to particle loss. This beam-beam effect was studied in previous colliders, where experience showed that one cannot increase the bunch density beyond a certain beam-beam limit to preserve a sufficiently long beam lifetime. In order to reach the desired luminosity the LHC has to operate as close as possible to this limit. Its injectors, the old PS and SPS, are being refurbished to provide exactly the required beam density.

While travelling down the 27 km long LHC beam pipe at a speed close to the speed of light, each of the 2835 proton bunches leaves behind an electromagnetic wake-field which perturbs the succeeding bunches. In this way any initial disturbance in the position or energy of a bunch is transmitted to its companions, and under certain phase conditions their oscillations can be amplified and lead to beam loss. These collective instabilities can be severe in the LHC because of the large beam current needed to provide high luminosity. Their effect is minimized by a careful control of the electromagnetic properties of the elements surrounding the beam. For instance the convolutions of the thousands of bellows which are used to allow the machine to contract during cooldown are shielded from the beam by thin fingers equipped with sliding contacts; the inner side of the stainless steel beam pipe is coated with pure copper to reduce its resistance to beam induced wall currents. However these precautions cannot suppress all instabilities, and sophisticated feedback systems as well as non linear lenses are being designed to damp the remaining ones.

The beams will be stored at high energy for about 10 hours. During this time the particles make four hundred million revolutions around the machine, a truly astronomical number. Meanwhile the amplitude of their natural oscillations around the central orbit should not increase significantly, because this would dilute the beams and degrade luminosity. This is difficult to achieve, since, in addition to the beam-beam interaction already mentioned, tiny spurious non linear components of the guiding and focusing magnetic-fields of the machine can render the motion slightly chaotic, so that after a large number of turns the particles may be lost. Studies concerning the onset of chaos have become very popular recently in many scientific domains: in particular astronomers now believe that planets in the solar system would show chaotic behaviour if observed for millions of years! The designers of particle colliders take part in this widespread effort, which has direct implications in their field. In the LHC the destabilizing effects of magnetic imperfections is more pronounced at injection energy, because the imperfections are larger owing to persistent current effects in the superconducting cables, and also because the beams occupy a larger fraction of the coil cross section. We must evaluate the Dynamic Aperture, the fraction of the coil cross section within which particles remain stable for the required time, and make sure that it exceeds the dimension of the injected beam with a sufficient safety margin. For the time being, no theory can predict with sufficient accuracy the long term behaviour of particles in non linear fields. Instead we use fast computers to track hundreds of particles step by step through the thousands LHC magnets for up to a million turns. Results are used to define tolerances for the quality of the magnets at the design stage and during production.

Despite all precautions the beam lifetime will not be infinite, in other words a fraction of the particles will diffuse towards the beam pipe wall and be lost. In this event the particle energy is converted into heat in the surrounding material and this can induce a quench of the superconducting magnets, thus interrupting operation for hours. To avoid this a collimation system will catch the unstable particles before they can reach the beam pipe wall, so as to confine losses in well shielded regions far from any superconducting element. The LHC combines for the first time a large beam current at very high energy with the most sophisticated superconducting technology. As a consequence it needs a much more efficient collimation system than previous machines.

A modern accelerator or collider is a huge investment which must remain a useful research tool for a long time, and therefore should be adaptable to emerging needs. For instance the CERN SPS accelerator was first upgraded into a proton antiproton collider, then a heavy ion accelerator, later a lepton injector for LEP and now a high density proton injector for LHC. The technical choices made in the LHC to deliver high performance while minimizing cost could drastically reduce the adaptability of the machine, since most of its elements are closely packed and embedded in a continuous cryostat. This is borne in mind by the designers, who make all efforts to include as much flexibility as possible in the lattice to allow further upgrades and cope with unpredictable demands.

In electron-positron colliders the particles loose every second through synchrotron radiation an amount of energy much larger than the beam stored energy. This loss must be continuously compensated by the RF system, and as a consequence this phenomenon limits the attainable energy while providing damping of particle oscillations. These effects are unimportant in the LHC because owing to the larger mass of the particles the energy radiated during the same time is only a tiny fraction of the beam energy. They will become significant in proton machines at much higher energies (around 100 TeV). However in the LHC the power emitted, about 3.7 kW, cannot be neglected as it has to be absorbed by the beam pipe at cryogenic temperature. This affects the installed power of the refrigeration system and is an important cost issue. In addition the synchrotron light impinges on the beam pipe walls as a large number of hard U.V. photons. These release absorbed gas molecules, which then increase the residual gas pressure, and liberate photo-electrons, which are accelerated accross the beam pipe by the strong positive electric field of the proton bunches. These photoelectrons add to the cryogenic load and may induce an instability of transeverse coupled bunch modes.

Last update: 14-JAN-99