Quadrupole magnet

Summary

Quadrupole magnets, abbreviated as Q-magnets, consist of groups of four magnets laid out so that in the planar multipole expansion of the field, the dipole terms cancel and where the lowest significant terms in the field equations are quadrupole. Quadrupole magnets are useful as they create a magnetic field whose magnitude grows rapidly with the radial distance from its longitudinal axis. This is used in particle beam focusing. The simplest magnetic quadrupole is two identical bar magnets parallel to each other such that the north pole of one is next to the south of the other and vice versa. Such a configuration will have no dipole moment, and its field will decrease at large distances faster than that of a dipole. A stronger version with very little external field involves using a k=3 Halbach cylinder. In some designs of quadrupoles using electromagnets, there are four steel pole tips: two opposing magnetic north poles and two opposing magnetic south poles. The steel is magnetized

Official source

https://en.wikipedia.org/wiki/Quadrupole_magnet

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Optics design and performance of an ultra-low emittance damping ring for the compact linear collider

A high-energy (0.5-3.0 TeV centre of mass) electron-positron Compact Linear Collider (CLIC) is being studied at CERN as a new physics facility. The design study has been optimized for 3 TeV centre-of-mass energy. Intense bunches injected into the main linac must have unprecedentedly small emittances to achieve the design luminosity 1035cm-2s-1 required for the physics experiments. The positron and electron bunch trains will be provided by the CLIC injection complex. This thesis describes an optics design and performance of a positron damping ring developed for producing such ultra-low emittance beam. The linear optics of the CLIC damping ring is optimized by taking into account the combined action of radiation damping, quantum excitation and intrabeam scattering. The required beam emittance is obtained by using a TME (Theoretical Minimum Emittance) lattice with compact arcs and short period wiggler magnets located in dispersion-free regions. The damping ring beam energy is chosen as 2.42 GeV. The lattice features small values of the optical functions, a large number of compact TME cells, and a large number of wiggler magnets. Strong sextupole magnets are needed for the chromatic correction which introduces significant nonlinearities, decreasing the dynamic aperture. The nonlinear optimization of the lattice is described. An appropriate scheme of chromaticity correction is determined that gives reasonable dynamic aperture and zero chromaticity. The nonlinearities induced by the short period wiggler magnets and their influence on the beam dynamics are also studied. In addition, approaches for absorption of synchrotron radiation power produced by the wigglers are discussed. Realistic misalignments of magnets and monitors increase the equilibrium emittance. The sensitivity of the CLIC damping ring to various kinds of alignment errors is studied. Without any correction, fairly small vertical misalignments of the quadrupoles and, in particular, the sextupoles, introduce unacceptable distortions of the closed orbit as well as intolerable spurious vertical dispersion and coupling due to the strong focusing optics of the damping ring. A sophisticated beam-based correction scheme has been developed in order to bring the design target emittances and the dynamic aperture back to the ideal value. The correction using dipolar correctors and several skew quadrupole correctors allows a minimization of the closed-orbit distortion, the cross-talk between vertical and horizontal closed orbits, the residual vertical dispersion and the betatron tune coupling. The small emittance, short bunch length, and high current in the CLIC damping ring could give rise to collective effects which degrade the quality of the extracted beam. A number of possible instabilities and an estimate of their impact on the ring performance are briefly surveyed. The effects considered include fast beam-ion instability, coherent synchrotron radiation, Touschek scattering, intrabeam scattering, resistive-wall wake fields, and electron cloud.

EPFL2006

The interconnections between Large Hadron Collider (LHC) main dipole and quadrupole magnets are made of soldered joints of two superconducting cables stabilized by a copper bus bar. The 2008 incident revealed the possible presence of defects in the interconnections of the 13 kA circuits that could lead to unprotected resistive transitions. Since then thorough experimental and numerical investigations were undertaken to determine the safe operating conditions for the LHC. This paper reports the analysis of experimental tests reproducing defective interconnections between main quadrupole magnets. A thermo-electromagnetic model was developed taking into account the complicated sample geometry. Close attention was paid to the physical description of the heat transfer towards helium, one of the main unknown parameters. The simulation results are reported in comparison with the measurements in case of static He I cooling bath. The outcome of this study constitutes a useful input to improve the stability assessment of the 13 kA bus bars interconnections.

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Thermo-electric analysis of the interconnection of the LHC main superconducting bus bars

Luca Bottura, Pier Paolo Granieri

Spurred by the question of the maximum allowable energy for the operation of the Large Hadron Collider (LHC), we have progressed in the understanding of the thermo-electric behavior of the 13 kA superconducting bus bars interconnecting its main magnets. A deep insight of the underlying mechanisms is required to ensure the protection of the accelerator against undesired effects of resistive transitions. This is especially important in case of defective interconnections which can jeopardize the operation of the whole LHC. In this paper we present a numerical model of the interconnections between the main dipole and quadrupole magnets, validated against experimental tests of an interconnection sample with a purposely built-in defect. We consider defective interconnections featuring a lack of bonding among the superconducting cables and the copper stabilizer components, such as those that could be present in the machine. We evaluate the critical defect length limiting the maximum allowable current for powering the magnets. We determine the dependence of the critical defect length on different parameters as the heat transfer towards the cooling helium bath, the quality of manufacturing, the operating conditions and the protection system parameters, and discuss the relevant mechanisms.

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Optics design and performance of an ultra-low emittance damping ring for the compact linear collider

EPFL2006