Mathematical formulation to predict the harmonics of the superconducting Large Hadron Collider magnets : III. Precycle ramp rate effects and magnet characterization

The Large Hadron Collider (LHC) at CERN is equipped with a feed-forward control system known as the field description for the LHC (FiDeL) which is designed to predict the magnetic field and its multipoles, hence reducing the burden on beam based feedback. FiDeL consists of a physical and empirical parametric field model based on magnetic measurements at warm and in cryogenic conditions. It is particularly critical during beam injection when the field decays and at the beginning of acceleration when the field snaps back. It is known that the decay amplitude is largely affected by the powering history of the magnet, particularly by the precycle flattop current and duration and the preinjection preparation duration. Recently, we have collected data that quantify the dependence of the decay amplitude on the precycle ramp rate. This paper presents the results of the measurements performed to investigate this effect, and the method included in FiDeL to model the precycle dependence.With this complete picture of dynamic changes, we finally discuss the effect on the data taken at nominally constant field, along the magnet loadline. We show that a correction for dynamic changes is required for adequate magnet characterization.peer-reviewe

The LHC magnetic field model

The compensation of the field changes during the beam injection and acceleration in the LHC requires an accurate forecast and an active control of the magnetic field in the accelerator. The LHC Magnetic Field Model is the core of this magnetic prediction system. The model will provide the desired field components at a given time, magnet operating current, magnet ramp rate, magnet temperature and magnet powering history to the required precision. The model is based on the identification and physical decomposition of the effects that contribute to the total field in the magnet aperture of the LHC dipoles. Each effect is quantified using data obtained from series measurements, and modeled theoretically or empirically depending on the complexity of the physical phenomena involved. This paper presents the developments of the new finely tuned magnetic field model and evaluates its accuracy and predictive capabilities over a sector of the machine.peer-reviewe

Study of Coil Configuration and Local Optics Effects for the GaToroid Ion Gantry Design

GaToroid, a novel configuration for hadron therapy gantry, is based on superconducting coils that gen- erate a toroidal magnetic field to deliver the beam onto the patient. Designing the complex GaToroid coils requires careful consideration of the local beam optical effects. We present a Python-based tool for charged particle transport in complex electromagnetic fields. The code implements fast tracking in arbitrary three-dimensional field maps, and it is not limited to specific or regular reference trajectories, as is generally the case in accelerator physics. The tool was used to characterise the beam behaviour inside the GaToroid system. It automatically determines the reference trajectories in the symmetry plane and analyses three-dimensional beam dynamics around these trajectories. Beam optical parameters in the field region were compared for various magnetic configurations of GaToroid. This paper introduces the new tracker and shows the benchmarking results. Furthermore, first- order beam optics studies for different arrangements demonstrate the main code features and serve for the design optimisation

Mathematical formulation to predict the harmonics of the superconducting Large Hadron Collider magnets. II. Dynamic field changes and scaling laws

A superconducting particle accelerator like the LHC (Large Hadron Collider) at CERN, can only be controlled well if the effects of the magnetic field multipoles on the beam are compensated. The demands on a control system solely based on beam feedback may be too high for the requirements to be reached at the specified bandwidth and accuracy. Therefore, we designed a suitable field description for the LHC (FIDEL) as part of the machine control baseline to act as a feed-forward magnetic field prediction system. FIDEL consists of a physical and empirical parametric field model based on magnetic measurements at warm and in cryogenic conditions. The performance of FIDEL is particularly critical at injection when the field decays, and in the initial part of the acceleration when the field snaps back. These dynamic components are both current and time dependent and are not reproducible from cycle to cycle since they also depend on the magnet powering history. In this paper a qualitative and quantitative description of the dynamic field behavior substantiated by a set of scaling laws is presented.peer-reviewe

The field description model for the LHC quadrupole superconducting magnets

The LHC control system requires an accurate forecast of the magnetic field and the multipole field errors to reduce the burden on the beam-based feed-back. The Field Description for the LHC (FIDEL) is the core of this forecast system and is based on the identification and physical decomposition of the effects that contribute to the total field in the magnet apertures. The effects are quantified using the data obtained from series magnetic measurements at CERN and they are consequently modelled empirically or theoretically depending on the complexity of the physical phenomena. This paper presents a description of the methodology used to model the field of the LHC magnets particularly focusing on the results obtained for the LHC main quadrupoles (MQ) and insertion region wide aperture quadrupoles (MQY).peer-reviewe

The dependence of the field decay on the powering history of the LHC superconducting dipole magnets

The decay of the allowed multipoles in the Large Hadron Collider (LHC) dipoles is expected to perturb the beam stability during the particle injection. The decay amplitude is largely affected by the powering history of the magnet and is particularly dependent on the pre-cycle flat-top current and duration as well as the pre-injection preparation duration. With possible prospects of having different genres of cycles during the LHC operation, the powering history effect must be taken into account in the Field Description Model for the LHC and must hence be corrected during machine operation. This paper presents the results of the modelling of this phenomenon.peer-reviewe

Minimum Quench Energy and Early Quench Development in NbTi Superconducting Strands

The stability of superconducting wires is a crucial task in the design of safe and reliable superconducting magnets. These magnets are prone to premature quenches due to local releases of energy. In order to simulate these energy disturbances, various heater technologies have been developed, such as coated tips, graphite pastes, and inductive coils. The experiments studied in the present work have been performed using a single-mode diode laser with an optical fiber to illuminate the superconducting strand surface. Minimum quench energies and voltage traces at different magnetic flux densities and transport currents have been measured on an LHC-type, Cu/NbTi wire bathed in pool boiling helium I. This paper deals with the numerical analysis of the experimental data. In particular, a coupled electromagnetic and thermal model has been developed to study quench development and propagation, focusing on the influence of heat exchange with liquid helium

Protection estimates for the 13 kA bus bars interconnections at 3.5 - 4.5 TeV

This memorandum provides alternate estimates of the critical additional resistance Radd of the 13 kA superconducting bus bars interconnections (IC), both for the LHC main bending (MB) dipole and main quadrupole (MQ) magnets. The calculations are performed using the 1-D thermo-electrical model described in [1], based on the definition of transverse local heat transfer coefficient towards the cooling helium bath established from the analysis of short sample tests performed in 2009 and 2010. Details on the model and its validation are not discussed here. The most pessimistic (adiabatic), most optimistic (full cooling) and most likely (partial cooling) critical additional resistances are provided, depending on the bus-bar and cable RRR, dump time constant, and space distribution of the defect, for beam energy between 3.5 and 4.5 TeV

Measurement and modeling of magnetic hysteresis in the LHC superconducting correctors

The Large Hadron Collider, now under construction at CERN, relies heavily on superconducting magnets for its optics layout: besides the main magnets, almost all the correcting magnets are superconducting. Along with clear advantages, this brings about complications due to the effects of persistent currents in the superconducting filaments. Corrector magnets that trim key beam parameters or compensate field errors of the main magnets (among others those due to hysteresis), are in their turn hysteretic. In this paper we present the measured magnetic hysteresis and its possible influence on accelerator operation, with particular reference to realtime compensation of dynamic effects in the main magnets, and reproducibility issues between runs. The modeling strategy as a function of the required accuracy is discussed, and two examples are presented.peer-reviewe

Stability analysis of the Interconnection of the LHC Main Superconducting Bus Bars

The operation of the Large Hadron Collider calls for a thorough analysis of the thermo-electric behavior of the 13 kA superconducting bus-bars connecting its dipole and quadrupole main magnets. This presentation reports a synthesis of the work performed jointly by researchers and students at CERN and at the University of Bologna as a contribution to the understanding of the LHC incident occurred on September 19th 2008. This work is complementary to the analyses carried out at CERN by the MPE group. The aim of the work is to analyze the stability of the interconnections as far as the quality of manufacturing, operating conditions and protection system parameters are concerned. A first part of the work is devoted to the development of a numerical model suitable for the analysis of the faulty interconnections. The main type of defect analyzed is the lack of solder among the superconducting cable and the copper stabilizer components at the interface between bus bar and splice. The evaluation of the critical defect length limiting the maximum safe current for powering the magnets without risk of thermal runaway is provided, as a function of the RRR of cable and stabilizer, decay time constant of the LHC circuit, spatial distribution of the defect and cooling conditions. A second part of the work is related to the modeling of the heat transfer mechanism between the main superconducting bus bar and the surrounding helium bath. This study is aimed to analyze a set of experimental measurements on the heat transfer coefficient of the main bending dipole bus bars performed at CERN. The final part of the work consists in a preliminary analysis of the heat transfer mechanisms involved in the stability experiments of defective interconnections performed in the FRESCA facility