Multipole Errors Research Articles

Long term stability studies in the presence of crab cavities and high order multipoles in the CERN super proton synchrotron and high luminosity large hadron collider

In 2018 the world’s first Crab Cavity (CC) experiments with protons were successfully performed, aiming to study the CC effect on a proton beam and evaluate the engineering challenges. Before the commencement of these experiments, the impact of the CCs and their multipoles on the long term particle stability of the SPS was studied using dynamic aperture simulations. Furthermore, in order to ensure the long term stability and luminosity performance of the LHC upgrade, the High Luminosity LHC (HL-LHC), the limits of stable motion were also examined in the presence of CC multipole errors, CC voltage errors and additional non-linearities such as the beam–beam effects. This paper presents the comprehensive dynamic aperture results for the SPS and HL-LHC for different CC, accelerator and beam configurations in view of guiding the engineering specifications of the tolerances of the crab cavity multipole errors.

Concept Design of a Superconducting Magnet for a Compact Heavy-Ion Synchrotron

A compact synchrotron is now under development at the National Institutes for Quantum Science and Technology (QST), with the goal of downsizing the heavy-ion therapy system with superconducting magnets conduction-cooled by GM cryocoolers. The synchrotron is required to accelerate several kinds of heavy-ion beams from 4 MeV/u to 430 MeV/u. A superconducting magnet with both dipole and quadrupole coils is adopted to generate a dipole field from 0.3 to 3.5 T and a quadrupole field from 0.1 to 1.5 T/m with a ramp rate of 0.6 T/s. A coil winding pattern and iron yoke are optimized to achieve field homogeneity in the required area. For the small-scale synchrotron, the coil ends are optimized with a novel parameter combining the beta function and multipole errors considering the beam dynamics.

Quantum Chemical Calculations with Machine Learning for Multipolar Electrostatics Prediction in RNA: An Application to Pentose.

To develop a realistic electrostatic model that allows for the anisotropy of the atomic electron density, high-rank atomic multipole moments computed by quantum chemical calculations have been studied extensively. However, it is hard to process huge RNA systems only relying on quantum chemical calculations due to its highly computational cost. In this study, we employ five machine learning methods of Gaussian process regression with automatic relevance determination (ARDGPR), Kriging, radial basis function neural networks, Bagging, and generalized regression neural network to predict atomic multipole moments. Atom-atom electrostatic interaction energies are subsequently computed using the predicted atomic multipole moments in the pilot system pentose of RNA. Here, the performance of the five methods is compared in terms of both the multipole moment prediction errors and the electrostatic energy prediction errors. For the predicted high-rank multipole moments of the four elements (O, C, N, and H) in capped pentose, ARDGPR and Kriging consistently outperform the other three methods. Therefore, the multipole moments predicted by the two best methods of ARDGPR and Kriging are then used to predict electrostatic interaction energy of each pentose. Finally, the absolute average energy errors of ARDGPR and Kriging are 1.83 and 4.33 kJ mol-1, respectively. Compared to Kriging, the ARDGPR method achieves a 58% decrease in the absolute average energy error. These satisfactory results demonstrated that the ARDGPR method with the strong feature extraction ability can predict the electrostatic interaction energy of pentose in RNA correctly and reliably.

Design and field measurement of dipole magnets for a 300-MeV proton and heavy ion synchrotron in SESRI

Space Environment Simulation and Research Infrastructure (SESRI) is a new national research infrastructure under construction at Harbin Institute of Technology (HIT) in China. Its 300-MeV proton and heavy ion accelerator is a major radiation source, and a compact synchrotron has been designed with a circumference of less than 44 m. The synchrotron dipoles are essential components of the accelerator, and they have been designed and tested carefully to meet the stringent physical requirements. The measured transverse field homogeneity is less than 2 × 10-4 from 0.2 T to 1.4 T and roughly agrees with the simulated results. With a modified linear programming algorithm, the integral magnetic field uniformity within 0.2–1.1 T is optimised from 6 × 10-4 to 1.5 × 10-4, and the corresponding multi-pole field-component errors are greatly reduced. By shortening the pole ends, the reproducibility of integral field among six magnets at 0.2 T is less than 3 × 10-4. In addition, the transient effect of the magnetic field is also evaluated and tested. Through analysis of the transient effect and structural strength, low-carbon steel and stainless steel are selected for the side plates and end plates, respectively. According to the transient measurement results, the feedforward compensation can be implemented to produce a more accurate current waveform. On 1 January 2022, the beam was successfully accumulated with the preset current waveform, and the beam intensity met the design requirements.

Frequency analysis and dynamic aperture studies in a low energy antiproton ring with realistic 3D magnetic fields

We briefly present recent progress with our algorithm and its implementation called SIMPA described in a previous paper. The algorithm has a new and unique approach to long-term 4D tracking of charged particles in arbitrary static electromagnetic fields. Using the improvements described in this paper, we made frequency analysis and dynamic aperture studies in ELENA. The effect of the end fields and the perturbation introduced by the magnetic system of the electron cooler on dynamic aperture is shown. A special feature of this study is that we have not introduced any multipole errors into the model. The dynamic aperture calculated in this paper is the direct consequence of the geometry of the magnetic elements. Based on the results, we make a few suggestions to reduce the losses during the deceleration of the beam.

A Rotating-Coil Scanner for the Precise Magnetic Characterization of Superconducting Accelerator Magnets at Ambient Temperature

This article presents a versatile scanning system for the magnetic measurements of the accelerator magnets. This system, based on a rotating-coil magnetometer, has been developed to meet the accuracy requirements imposed by the inner-triplet quadrupoles for the High Luminosity Large Hadron Collider (HL-LHC) project at CERN. The main field strength of the magnet must be measured with an accuracy of 100 ppm, and the required accuracy for the angle and the axis are 0.1 mrad and 0.1 mm, respectively. All these parameters must be measured both locally and integrated over the entire magnet length at various stages of production. In this way, it is possible to intercept the manufacturing errors at an early stage of production. Moreover, these measurements are used for the alignment of the magnet assembly in its cryostat. The measurements are performed at an ambient temperature, with low excitation currents. The presented system provides a full set of data for the characterization of the magnet in a single measurement run, including the field quality (multipole field errors) and the magnetic axis location at several longitudinal positions in the magnet bore. The system is able to achieve the required accuracy by using induction coils based on the printed circuit board (PCB) technology, a high-resolution encoder, and retro-reflectors for the laser tracker positioned directly on the PCB. The system is also equipped with a motor unit that allows a high degree of automation in the measurements.

Magnetic Measurements of the First Short Models of Twin Aperture Magnets for FCC-ee

We report on the results of magnetic measurements of the first short models of twin aperture magnets for the FCC-ee arcs. To date, we have built and tested three 1-m long bending magnets, using different materials for the ferromagnetic yoke and a 1-turn vs. a multi-turn excitation. Besides the interest in checking the unusual I-layout, the focus is also on the behavior at low field, down to about 15 mT in the gap, and its impact on field quality (in particular, on the gradient term). In parallel, we have also built a 1-m long quadrupole model, to test the peculiar twin configuration and assess the multipole field errors as a function of the excitation current, checking especially the dipole and sextupole terms. The results presented can be the basis of further developments for this kind of magnets.

Development of a rotating-coil scanner for superconducting accelerator magnets

Abstract. The High-Luminosity upgrade project for the Large Hadron Collider (HL-LHC) at CERN (Conseil Européen pour la Recherche Nucléaire) will require new superconducting magnets for the insertion regions. Among these magnets, the new triplet quadrupoles, based on Nb3Sn technology, require magnetic-field measurements of a high precision in the field angle and multipole field errors. In this paper, we present a scanning system based on a rotating-coil magnetometer and its transport system, including the design of the mechanical structure and the induction coils based on printed-circuit-board (PCB) technology. The system and its components are cross-calibrated with other field transducers, such as stretched-wire systems, and their measurement precision is established in a measurement campaign of 2 m long reference quadrupoles.

Challenges in extracting pseudo-multipoles from magnetic measurements

Extracting the coefficients of Fourier–Bessel series, known as pseudo-multipoles or generalized gradients, from magnetic measurements of accelerator magnets involves technical and mathematical challenges. First, a novel design of a short, rotating-coil magnetometer is required that does not intercept any axial field component of the magnet. Moreover, displacing short magnetometers, step-by-step along the magnet axis, yields a convolution of the local multipole field errors and the sensitivity (test function) of the induction coil. The deconvolution must then contend with the limited signal-to-noise ratio of the measured quantities, which are integrated voltages corresponding to spatial flux distributions. Finally, the compensation schemes, as implemented on long coils and based on scaling laws derived for the integrated field harmonics, cannot be applied to short magnetometers intercepting only a local field distribution. All this requires careful design of experiment to derive the optimal length of the induction coil, the step-size of the scan, and the highest order of pseudo-multipoles in the field reconstruction. This paper presents the theory of the measurement method, the data acquisition and deconvolution, and the design and production of a saddle-shaped, rotating-coil magnetometer.

Quantitative analysis of multipole errors induced by mechanical deformations of an undulator

To minimize unwanted beam dynamics effects in a storage ring, multipole errors in an undulator are normally reduced by sorting and shimming methods. Nonetheless, an investigation of the error source is worth pursuing and interesting. Our work focuses on multipole errors introduced by mechanical deformations of an APPLE-II type undulator, which undergoes complicated forces during operation. Our results give guidelines for mechanical specifications derived from quantitative analyses.

Reduction of dynamic multipole content in insertion devices using flat wires

Multipole errors of an insertion device are generally corrected based on measurements and analysis of the magnetic field integrals. Multipole components in a strong and narrow nonuniform field of an insertion device appear as dynamic multipoles. Flat wires were installed and commissioned to determine if the dynamic multipoles can be eliminated in an APPLE-II type undulator. In this work, we will discuss and compare the reduction of the dynamic multipole content and its beam dynamics effects with the flat wire through an analysis of field calculations and beam-based measurements in the storage ring.

Simulation of beam–beam interaction with crab cavities for LHC upgrade

The crab cavities are a critical component in the high luminosity LHC upgrade project to compensate the luminosity loss from large crossing angle collision. However, these crab cavities will not be perfect in the real accelerator. In this paper, we studied the effects of crab cavity imperfections on colliding beam luminosity lifetime degradation for the LHC upgrade through detailed numerical simulations. Our simulation results suggest that the white noise jitter in the crab cavity RF phase and voltage rms amplitudes should be kept below a few 10−5 for a good luminosity lifetime, while with frequency-dependent jitter, the amplitudes should be kept below a few 10−4 for a good lifetime. The RF multipole errors in the current crab cavity designs are small enough and would not cause extra luminosity degradation.

Correcting for background fields and multipole field errors in the localization of the magnetic axis in quadrupole magnets

The fiducial marker localization with respect to the magnetic axis of the magnet elements is a crucial step in the qualification of the magnets for particle accelerators. Background fields, such as the Earth’s magnetic field and fringe fields from electrical sources may degrade the accuracy of this axis localization. In this paper, we discuss stretched-wire measurements, in static and vibrating operation modes, for the correction of stray fields in the quadrupole axis localization to an accuracy of 0.3 μm. Moreover, we present an analytical model to correct the magnetic axis position error due to higher-order multipole field errors in the magnet. This correction is particularly important for the static stretched-wire measurement because the wire movement must be large enough to obtain a sufficient signal-to-noise ratio.

Design of Prototype Magnets for HUST Proton Therapy Beamline

A proton therapy facility with two 360° gantry treatment rooms and one fixed beamline is under development at the Huazhong University of Science and Technology (HUST), which is based on an isochronous superconducting cyclotron. The energy is modulated in the range of 70–240 MeV with an energy selection system. In this paper, we report the main design specifications of the beamline in the HUST-PTF project, in which the main features are the intensity suppression scheme beamline. Two prototype magnets (one quadrupole and one dipole) used in the beamline are also studied and presented. Two-dimensional contour optimization and pole-end chamfer iteration are used to minimize the harmonic errors of the integral field. Finally, both the field homogeneity and multipole errors achieve the precision requirement over the operating field range.

Constructing a Permanent Magnet Phase Shifter

A permanent-magnet (PM) phase shifter has been constructed for tandem elliptically polarizing undulators at the Taiwan photon source. To increase the magnetic field reproducibility and to allow installation in a limited space, a robust mechanical structure is desired. To decrease multipole errors and optimize the magnetic field, algorithms for magnet sorting were used and magnetic field shimming was done. The start-to-end construction of a PM phase shifter will be discussed and explained in detail.

GENERALIZED MATHEMATICAL MODEL OF THE CALIBRATION PROCESSAND THE DIRECT MEASUREMENT OF THE PARAMETERS MULTIPOLE

The quality of measuring systems of the microwave range, including vector network analyzers, largely depends on the reliability of calibration procedures and direct measurements, which allow to take into account information about the reproducible errors of measuring systems for subsequent correction. The aim of the paper is mathematical modeling of the errors of the measuring system for the generalized case for 2-n pole device.The problems of increasing the accuracy of measuring microwave systems due to compensation of systematic errors determined during calibration are considered. Calibration of measuring systems and correction of the results of direct measurements based on calibration results require the use of appropriate mathematical models of errors. Mathematical models of errors are represented in the form of multipolar errors, included between the object of measurement and the measuring system, which is assumed to be ideal, free of errors. The article proposes a generalized mathematical model of errors, described by a network of errors containing n ports connected to the n-port measuring system, and n ports connected to the n port of the measurement object. To obtain in general form the calibration equation for the 2n-port model of the error multipolar network, its transmission wave matrix [T], recorded in a cellular form, was used, and then a relationship was found between the measurement result in a matrix form with the cellular wave matrix T. A solution for finding the error matrix of matrix equation that connects the matrices known from the results of the corresponding attestation for the standards with the results of measurements during calibration in the matrix form. When solving this equation, a matrix product of «sandwich» type appears due to the cellular wave matrix [T]. The solution is possible when using the Kronecker product of two matrix, the matrix translation operator, the RS operator of the matrix, and the Gaussian elimination method. An equation is obtained for reconstructing the actual values of the scattering matrix of the measurement object, starting from the results of direct measurements in the matrix form and the error matrix. When solving the reconstruction equation, it is advisable to use a matrix inverse to the transmission matrix [T].The developed generalized mathematical model can be used, for example, when it is necessary to measure the parameters of complex microwave devices made on boards (wafer), with probe transitions to measuring ports, where it is important to consider the presence of additional microwave power leaks between ports.

Design of an rf quadrupole for Landau damping

The recently proposed superconducting quadrupole resonator for Landau damping in accelerators is subjected to a detailed design study. The optimization process of two different cavity types is presented following the requirements of the High Luminosity Large Hadron Collider (HL-LHC) with the main focus on quadrupolar strength, surface peak fields, and impedance. The lower order and higher order mode (LOM and HOM) spectrum of the optimized cavities is investigated and different approaches for their damping are proposed. On the basis of an example the first two higher order multipole errors are calculated. Likewise on this example the required rf power and optimal external quality factor for the input coupler is derived.

Post-Processing Magnetic Measurement Data of Accelerator Magnets by the Boundary Element Method

This paper deals with the application of the boundary element method to the post-processing of magnetic measurement data in accelerator magnets. In this way, field mapping can be limited to the domain boundary and the quantities of interest, e.g., the magnetic flux density along a trajectory or multipole field errors, can be computed from the boundary data.

Probing halfβy*optics in the Accelerator Test Facility 2

A nanometer beam size at the interaction point (IP) is required for future linear colliders to achieve the desired rate of particle collisions. KEK Accelerator Test Facility 2 (ATF2), a scaled down implementation of the linear collider beam delivery system, serves for demonstrating the feasibility of the final focus system (FFS). An unprecedented low vertical beam size at the IP of about 40 nm has been already measured in ATF2 using the optics with a nominal ${\ensuremath{\beta}}_{y}^{*}$. In our study we decrease the ${\ensuremath{\beta}}_{y}^{*}$ value in order to investigate the performance of more chromatic optics and to study the limits of beam focusing at the IP. Stronger beam focusing amplifies the aberrations from the final focus imperfections which cause an increase of the beam size at the IP. Simulations show that the multipolar errors and final doublet fringe fields spoil the IP beam sizes for ultralow ${\ensuremath{\beta}}_{y}^{*}$ optics but can be mitigated either by increasing the value of the horizontal ${\ensuremath{\beta}}^{*}$ or installing a pair of octupole magnets. We report on our first experimental steps towards the ultralow ${\ensuremath{\beta}}_{y}^{*}$ in ATF2. New methods for the beam diagnostics at the IP were developed in order to precisely set the desired optics. ${\ensuremath{\beta}}_{y}^{*}$ value was half the nominal value. The beam tuning was performed and the measured beam size is compared with the simulation results.

Active and passive compensation of APPLE II-introduced multipole errors through beam-based measurement

The effect of an APPLE II-type elliptically polarized undulator (EPU) on the beam dynamics were investigated using active and passive methods. To reduce the tune shift and improve the injection efficiency, dynamic multipole errors were compensated using L-shaped iron shims, which resulted in stable top-up operation for a minimum gap. The skew quadrupole error was compensated using a multipole corrector, which was located downstream of the EPU for minimizing betatron coupling, and it ensured the enhancement of the synchrotron radiation brightness. The investigation methods, a numerical simulation algorithm, a multipole error correction method, and the beam-based measurement results are discussed.