Search Results (10 total)

We study the coil layouts of superconducting dipoles for particle accelerators based on the sector geometry. We show that a simple model based on a sector coil with a wedge allows us to derive an equation giving the short sample field as a function of the aperture, coil width, cable properties, and superconducting material. The equation agrees well with the actual results of several dipole coils that have been built in the past 30 years. The improvements due to the grading technique and the iron yoke are also studied. The proposed equation can be used as a benchmark to judge the efficiency of the coil design, and to carry out a global optimization of an accelerator layout.

A possible scenario for the luminosity upgrade of the Large Hadron Collider is based on large aperture quadrupoles to lower β^* in the interaction regions. Here we analyze the measurements relative to the field quality of the RHIC and LHC superconducting quadrupoles to find out the dependence of field errors on the size of the magnet aperture. Data are interpreted in the framework of a Monte Carlo analysis giving the reproducibility in the coil positioning reached in each production. We show that this precision is likely to be independent of the magnet aperture. Using this result, we can carry out an estimate of the impact of the field quality on the beam dynamics for the collision optics.

We study how the critical gradient depends on the coil layout in a superconducting quadrupole for particle accelerators. We show that the results relative to a simple sector coil are well representative of the coil layouts that have been used to build several quadrupoles in the past 30 years. Using a semianalytical approach, we derive a formula that gives the critical gradient as a function of the coil cross-sectional area, of the magnet aperture, and of the superconducting cable parameters. This formula is used to evaluate the efficiency of several types of coil layouts (shell, racetrack, block, open midplane).

Field quality in superconducting magnets strongly depends on the geometry of the coil. Fiberglass spacers (shims) placed between the coil and the collars have been used to optimize magnetic and mechanical performances of superconducting magnets in large accelerators. A change in the shim thickness affects both the geometry of the coil and its state of compression (prestress) under operational conditions. In this paper we develop a coupled magnetomechanical model of the main Large Hadron Collider dipole. This model allows us to evaluate the prestress dependence on the shim thickness and the map of deformations of the coil and the collars. Results of the model are compared to experimental measurements carried out in a dedicated experiment, where a magnet model has been reassembled 5 times with different shims. A good agreement is found between simulations and experimental data both on the mechanical behavior and on the field quality. We show that this approach allows us to improve this agreement with respect to models previously used in the literature. We finally evaluate the range of tunability that will be provided by shims during the production of the Large Hadron Collider main dipoles.

Estimates of random field-shape errors induced by cable mispositioning in superconducting magnets are presented and specific applications to the Large Hadron Collider (LHC) main dipoles and quadrupoles are extensively discussed. Numerical simulations obtained with Monte Carlo methods are compared to analytic estimates and are used to interpret the experimental data for the LHC dipole and quadrupole prototypes. The proposed approach can predict the effect of magnet tolerances on geometric components of random field-shape errors, and it is a useful tool to monitor the obtained tolerances during magnet production.

In hadron colliders, such as the Large Hadron Collider (LHC) to be built at CERN, the long-term stability of the single-particle motion is mostly determined by the field-shape quality of the superconducting magnets. The mechanism of particle loss may be largely enhanced by modulation of betatron tunes, induced either by synchrobetatron coupling (via the residual uncorrected chromaticity), or by unavoidable power supply ripple. This harmful effect is first investigated in a simple dynamical system model, the Hénon map with modulated linear frequencies. Then a realistic accelerator model describing the injection optics of the LHC lattice is analyzed. Orbital data obtained with long-term tracking simulations (10⁵–10⁷ turns) are post-processed to obtain the dynamic aperture. It turns out that the dynamic aperture can be interpolated using a simple empirical formula, as it decays proportionally to a power of the inverse logarithm of the number of turns. Furthermore, the extrapolation of tracking data at 10⁵ turns gives reliable estimates of the dynamic aperture for 10⁷ turns, which represent the expected duration of the LHC injection plateau.

The influence of linear coupling on nonlinear resonances in betatron motion is considered. A model of lattice with a single sextupole and a linearly coupled one-turn matrix is analyzed. The perturbative approach based on normal forms is considered, and the relation of the first resonant coefficient of the interpolating Hamiltonian with the island width or with the unstable separatrices is outlined. The dependence of the first resonant coefficient on the coupling angle is worked out for generic resonances. The analytical results are in very good agreement with the numerical simulations based on tracking and frequency analysis.

Symplectic mappings that model the four-dimensional betatron motion in a magnetic lattice are considered. We define the dynamic aperture in terms of the connected volume in the phase space of initial conditions that are bounded for a given number of iterations. Different methods for a fast estimate of this quantity are given; the analysis of the associated errors and the optimization of the integration steps are outlined. A comparison of the accuracy of these methods is given for both simple models and more realistic lattices.

The problem of defining effective sorting strategies for the random errors of a magnetic lattice is analyzed. The final goal is to define a way of sorting the magnets in order to maximize the dynamic aperture. The proposed method is made up of three steps. First, one defines quality factors based on the perturbative tools of nonlinear maps and normal forms. Second, the best quality factor for the model considered is chosen through tracking analysis. Third, among some permutations of the magnets one chooses the one whose quality factor is better. The effectiveness a posteriori of the sorting strategy is checked through tracking. An application to sort the sextupolar errors of a cell lattice of the Large Hadron Collider is given.

The geometry of the resonant orbits of symplectic four-dimensional mappings, in the neighborhood of an elliptic fixed point, is analyzed in the framework of a perturbative approach based on resonant normal forms. The analysis of the truncated interpolating Hamiltonian allows one to determine the classification, the location, and the stability of the integrable resonant structures in phase space.