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

Abstract

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.

Field Quality Study of a 1-m-Long Single-Aperture 11-T <formula formulatype="inline"><tex Notation="TeX"> $\hbox{Nb}_{3}\hbox{Sn}$</tex></formula> Dipole Model for LHC Upgrades

“…Long-term dynamic effects in superconducting accelerator magnets are usually associated with the decay of the normal sextupole b 3 at injection, which is followed by a subsequent harmonics snapback during the acceleration ramp [10], [11]. Previous studies showed low level of these effects in Nb 3 Sn dipole and quadrupole models [12].…”

Active compensation of field errors within ±2ppm in superconducting magnets

“…Measurements with a maximum current of 11.8 kA have also been performed. The cycle parameters are selected in order to maximize the snapback amplitude [25]: I prep =0 A, t pre =0 s, dI/dt=10 A/s, t FT =1000 s, and t inj =1000 s. In In Fig. 7b, the current for the sextupole correction as a function of time, computed at the first iteration, is shown (the dipole current is also shown for clarity).…”

“…Superconductor magnetization and coupling currents are related to the rate of change of the magnetic field: the magnetization is induced at the periphery of superconducting filaments and the coupling currents depend on inter-strand cable resistance. The multipole content can be modeled [25] and corrected by means of a suitable compensation scheme, namely by placing additional corrector magnets on the main winding, designed to provide a field strength equal and opposite to the multipole errors [26]. Detailed measurements are mandatory to build accurately enough these models, in particular for the dynamic or ramp rate induced effects.…”

The Development of Superconducting Magnets for Use in Particle Accelerators: From the Tevatron to the LHC

“…A significant result linking the snapback amplitude and its decay constant in the case of an exponential fit was found during the first years of the LHC dipole production; this scaling law has been proven both for the LHC and Tevatron dipoles [64]. A major effort was carried out to build a LHC field model [66,67] using all the relevant information and permitting the programming of the circuit magnets before day 1 of commissioning.…”