A Statistical Approach to Analyse Effect of Misalignments and Correction Algorithms in High-Energy Linacs

This paper presents a new and general tracking method capable of analysing, in a statistical way, the dipole wakefield effects on a high-energy charged-particle beam

LHC Installation Scenarios and Dynamic Aperture

The nominal installation strategy of the LHC assumes that each of the 8 arcs of the ring will be equipped with dipoles coming from the same production line. One of the main arguments used to justify this option was the possibility to compensate most of the non-linearities induced by the dipole field errors via a single corrector circuit per arc and per multipole. Indeed, assuming small variations from magnet to magnet within a given production line, the multipolar components of the main dipoles appear as a systematic per arc in this scenario, which, de facto, guarantees their correctability even with a small number of corrector families. All the tracking studies done so far have used this installation scheme to model the field imperfections of the main LHC magnets. According to latest error tables, with the improvement of the dipole field quality, the uncertainty on the systematic field errors per production line has been strongly reduced and becomes quite comparable or even lower than the random multipolar components expected from dipole to dipole. It is then relevant to check if the present installation scenario is still justified and to compare it with other options less constraining from the installation point of view. Two other options will be studied in terms of dynamic aperture at injection: (1) the case where the dipoles are randomly installed in the LHC tunnel independently of their production line, (2) the case where the dipoles are installed end to end by batches of a small number of magnets (24 dipoles in our study) coming from the same production line. With the error table 9901, the LHC dynamic aperture at injection does not depend significantly on the installation strategy chosen for the main magnets

Determination of betatron tunes, Twiss parameters and sum and difference coupling coefficients with an AC dipole

The control of the mechanical and dynamic aperture of the LHC requires a tight control of linear optics parameters such as the tune, the beta-functions and the linear coupling resonance driving terms. This report presents a non-standard measurement method of these parameters based on a transverse excitation of the beam in "AC-dipole" mode, that is at one or several frequencies close to but outside the eigenfrequency spectrum of the beam. After having derived the general expression of the beam response in four dimensions, the measurement protocol and different possible hardware configurations will be described and simulation results obtained for the LHC will be presented

Chromatic Coupling Induced by Skew Sextupolar Field Errors in the LHC Main Dipoles and its Correction

In a recent study dealing with the chromatic behaviour of the LHC in the presence of multi-polar field errors, it has been clearly shown that the skew sextupolar systematic component of the arc dipoles was liable to generate a spectacular second order chromaticity, up to 50 times higher than its tolerance value estimated at Q" = 1000 at injection. This result was qualitatively explained by transverse coupling phenomena induced in the arcs (dispersive regions) and affecting the dynamics of off-momentum particles (linear coupling proportional to deltap=p or chromatic coupling). This paper presents an analytical approach of the problem based on the canonical perturbation theory and explaining perfectly the chromatic coupling phenomena induced in the LHC. This understanding is used to design a simple and powerful a3 compensation scheme which consists in replacing in each arc two pairs of lattice (normal) sextupoles by two pairs of skew sextupoles judiciously positioned. Tracking results performed on the LHC lattice version 6 illustrate the beneficial impact of the correction on the dynamic aperture of the ring

Determination of Chromaticity by the Measurement of Head-Tail Phase Shifts: Simulations, Results from the SPS and a Robustness Study for the LHC

The feasibility of chromaticity determination by measuring head-tail phase shifts has been shown both in the CERN-SPS and at HERA (DESY). These measurements, although verifying the technique, also raised some questions concerning its use for every day operation. This report includes the source of the missing constant factor that was found between theory and experiment, the consequences of the RF bucket deformation due to the acceleration in the SPS and detailed simulations and calculations on the LHC to estimate the accuracy of the head-tail chromaticity technique in the presence of other possible perturbations such as non-linear chromaticity, coupling and transverse impedance

A proposal to use microwave quadrupoles to shorten the beam delivery section of CLIC

The chromatic correction of the final focus, based on sextupoles and dipoles, requires for CLIC at 3 TeV a section which is long with respect to the main linac and the bare de-magnification telescope. The length needed is in conflict with the tight alignment of the beam delivery elements, necessary for the control of the collisions. This scheme also implies large peaks of betatron amplitudes which generate aberrations. To circumvent these problems, we explore the potential of microwave quadrupoles. They could be used for chromatic corrections since, in the presence of a correlation between momentum and position within the bunch, they play a role similar to that of sextupoles in the presence of dispersion. The correlation is done in the linac and no special optics is required, thus strongly reducing the space needed for the correction. Furthermore, the final doublet of the telescope could be only made of microwave quadrupoles, provided sufficiently high gradients be achievable, since a judicious choice of the RF phase render them achromatic. This would make the beam delivery at high energies even more compact and simple. We underline advantages and drawbacks of this proposal and list some items which need further study

Using microwave quadrupoles to shorten the CLIC beam delivery section

The chromatic correction of the final focus, based on sextupoles and dipoles, requires for CLIC at 3 TeV a section which is long with respect to the main linac and the bare de-magnification telescope. The length needed is in conflict with the tight alignment of the beam delivery elements, necessary for the control of the collisions. This scheme also implies large peaks of betatron amplitudes which generate aberrations. To circumvent these problems, we explore the potential of microwave quadrupoles. They could be used for chromatic corrections since, in the presence of a correlation z-delta between momentum and position along the bunch, they play a role similar to that of sextupoles in the presence of dispersion. The correlation is done in the linac and no special optics is required, thus strongly reducing the space needed for the correction. Furthermore, the final doublet of the telescope could be only made of microwave quadrupoles, provided sufficiently high gradients be achievable, since a judicious choice of the RF phase renders them achromatic. This would make the beam delivery at high energies even more compact and simple. We underline advantages and drawbacks of this proposal and list some items which need further study