Quench protection analysis in accelerator magnets, a review of the tools

As accelerator magnets see the increase of their magnetic field and stored energy, quench protection becomes a critical part of the magnet design. Due to the complexity of the quench phenomenon interweaving magnetic, electrical and thermal analysis, the use of numerical codes is a key component of the process. In that respect, we propose here a review of several tools commonly used in the magnet design community.Comment: 4 pages, Contribution to WAMSDO 2013: Workshop on Accelerator Magnet, Superconductor, Design and Optimization; 15 - 16 Jan 2013, CERN, Geneva, Switzerlan

Nb-Ti Symmetric Triplets for the LHC luminosity Upgrade

We study a Nb-Ti lay-out for the triplet in the low-beta interaction regions of the Large Hadron Collider, based on a stretched version of the present baseline. The triplet length is increased from the present value of 32 m up to about 60 m. The quadrupoles are based on a two layer coil made with the LHC main dipole cable. A parametric analysis of the dependence of the optics and magnet performances on the triplet length and aperture is carried out

Overview of Single-particle Nonlinear Dynamics

We give an overview of the single-particle non linear dynamics in circular accelerators. The main topics are: integration of equations of motion, fast symplectic tracking, dynamic aperture definition, long-term methods, quality factors and lattice optimization. Special emphasis is put on ideas and tools developed during the last decade

Scaling Laws for Dynamic Aperture due to Chromatic Sextupoles

Scaling laws for the dynamic aperture due to chromatic sextupoles are investigated. The problem is addressed in a simplified lattice model containing 4 N identical cells and one linear betatron phase shifter to break the overall cell-lattice symmetry. Two families of chromatic sextupoles are used to compensate the natural chromaticity. Analytical formulae for the dynamic apertur as a function of the number of cells and of the cell length are found and confirmed through computer tracking

Long term stability in hadron colliders in presence of synchrotron oscillations and tune ripple

The problem of long-term losses in hadron colliders such as the Large Hadron Collider (LHC) is considered. A previous formula that provides the reduction of dynamic aperture with the number of turns is generalized to include also the relevant cases of off-momentum and tune ripple. The dynamic aperture turns out to shrink with a power of the inverse logarithm of the number of turns. Long-term tracking data of the LHC are analysed in this framework. The formula proves to hold in all cases, and the possibility of using its extrapolation to predict long-term losses are explored

Normal Form Analysis of the LHC Dynamic Aperture

Normal form is a well developed tool to study the nonlinear dynamics of even the most complicated structures. This can become particularly useful in the design of large nonlinear hadron colliders like the LHC. In this study the correlation of various quality factors derived through normal forms with the dynamic aperture are used to investigate a machine that is dominated by octupolar errors

Dynamic aperture estimates and phase space distortions in nonlinear betatronic motion

Symplectic mappings which modelize the 4D betatronic motion in a magnetic lattice are considered. We define the dynamic aperture in terms of the connected volume in phase space of initial conditions which 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