Correction of the Long-Range Beam-Beam Effect in LHC using Electro-Magnetic Lenses

The beams in LHC collide head-on in at most four experimental points. Due to the small bunch spacing, the beams experience more than one hundred 'near-misses' on either side of the collision points. The transverse beam separation at these places, limited by the quadrupole aperture, is in the range of 7 to 13 sigma. The non-linear part of these 'long-range' interactions appears to be the dominant mechanism for beam blow-up or beam loss in simulation. A simple non-linear model of the long-range interactions can be devised. It shows that the latter may be locally corrected with good accuracy using wires as correcting lenses. The non-linearity measured by the tune footprint is reduced by one order of magnitude. Pulsing the correcting lenses cancels the so-called PACMAN effect

Beam-beam and compensation schemes: conclusions

This paper attempts at giving the important conclusions from this session

Investigations of the Parameter Space for the LHC Luminosity Upgrade

Increasing the LHC luminosity by a factor of ten is a major challenge, especially for the beam-beam long-range interactions and even more for the magnet technology and insertion layout. To help identifying consistent solutions in this multi-dimensional constrained space, a parametric model of an LHC insertion was prepared, based on the present LHC layout, i.e. ?quadrupole first? and small crossing angle. The model deals with the layout, beam optics, beam-beam effect, superconductor margin and peak heat deposition in the coils. The approach is simplified to obtain a large gain in the optimization time. This study puts in evidence, as critical for the luminosity upgrade, the following actions: enlarging significantly the quadrupole aperture, moving the insertion towards the interaction point, using the highest available critical field superconductors and complementing the insertion with an early separation scheme. The luminosity reach can then be extended to 2×1035 cm-2s-1 while 1×1035 can be obtained with significantly reduced requirements (lower beam currents, simpler RF system?)

The LHC dynamic aperture

In 1996, the expected field errors in the dipoles and quadrupoles yielded a long-term dynamic aperture of some 8sigma at injection. The target was set to 12sigma to account for the limitations of our model (imperfections and dynamics). From scaling laws and tracking, a specification for the field imperfections yielding the target dynamic aperture was deduced. The gap between specification and expected errors is being bridged by i) an improvement of the dipole field quality, ii) a balance between geometric and persistent current errors, iii) additional correction circuits (a3 ,b4 ). With the goal in view, the emphasis has now turned to the sensitivity of the dynamic aperture to the optical parameters.The distortion of the dynamics at the lower amplitudes effectively reached by the particles is minimized by optimizing the distribution of the betatron phase advance. At collision energy, the dynamic aperture is limited by the field imperfections of the low-beta triplets, enhanced by the crossing angle. With correction of the most important aberrations, the dynamic aperture reaches the target set to 10sigma

Strong focusing insertion solutions for the LHC luminosity upgrade

This paper shows that dealing appropriately with the geometrical loss factor opens the possibility of large luminosities with a lower beam current thanks to applying significantly stronger focusing. The peak luminosity potential is as large as 2×1035 cm-2s-1 for the full upgraded beam current, with scope for achieving a luminosity of about 1×1035 cm-2s-1 with reduced bunch current and/or increased bunch spacing. The required quadrupole aperture would need to be increased to about 125 mm

Decoupling of a strongly coupled lattice with an application to LHC

The systematic skew quadrupole field in the LHC superconducting dipole is estimated to be a2 = 0.310-4 at 1 cm. It causes systematic linear coupling resonances to be strongly excited (width up to 0.2 tune unit). With an exact antisymmetry of the optics, LHC is operated close to them. The theory of resonances predicts well the large focusing perturbations observed numerically and allows accurate decoupling with only two families of skew quadrupoles, some being paired. Robustness however favours a solution which does not rely on an accurate knowledge of the perturbation; it is obtained by relaxing the exact antisymmetry to operate the machine with matched tune splits of up to three units