Rotating-Coil Measurement System for Small-Bore-Diameter Magnet Characterization.

Rotating-coil measurement systems are widely used to measure the multipolar fields of particle accelerator magnets. This paper presents a rotating-coil measurement system that aims at providing a complete data set for the characterization of quadrupole magnets with small bore diameters (26 mm). The PCB magnetometer design represents a challenging goal for this type of transducer. It is characterized by an aspect ratio 30% higher than the state of the art, imposed by the reduced dimension of the external radius of the rotating shaft and the necessity of covering the entire magnet effective length (500 mm or higher). The system design required a novel design for the mechanical asset, also considering the innovation represented by the commercial carbon fiber tube, housing the PCB magnetometer. Moreover, the measurement system is based primarily on standard and commercially available components, with simplified control and post-processing software applications. The system and its components are cross-calibrated using a stretched-wire system and another rotating-coil system. The measurement precision is established in a measurement campaign performed on a quadrupole magnet characterized by an inner bore diameter of 45 mm.

Hysteresis Modeling in Iron-Dominated Magnets Based on a Multi-Layered NARX Neural Network Approach.

A full-fledged neural network modeling, based on a Multi-layered Nonlinear Autoregressive Exogenous Neural Network (NARX) architecture, is proposed for quasi-static and dynamic hysteresis loops, one of the most challenging topics for computational magnetism. This modeling approach overcomes drawbacks in attaining better than percent-level accuracy of classical and recent approaches for accelerator magnets, that combine hybridization of standard hysteretic models and neural network architectures. By means of an incremental procedure, different Deep Neural Network Architectures are selected, fine-tuned and tested in order to predict magnetic hysteresis in the context of electromagnets. Tests and results show that the proposed NARX architecture best fits the measured magnetic field behavior of a reference quadrupole at CERN. In particular, the proposed modeling framework leads to a percent error below 0.02% for the magnetic field prediction, thus outperforming state of the art approaches and paving a very promising way for future real time applications.

Drift-Free Integration in Inductive Magnetic Field Measurements Achieved by Kalman Filtering.

Sensing coils are inductive sensors commonly used to measure magnetic fields, such as those generated by electromagnets used in many kinds of industrial and scientific applications. Inductive sensors rely on integrating the output voltage at the coil's terminals in order to obtain flux linkage, which may suffer from the magnification of low-frequency noise resulting in a drifting integrated signal. This article presents a method for the cancellation of integrator drift. The method is based on a first-order linear Kalman filter combining the data from the coil and a second sensor. Two case studies are presented. In the first one, the second sensor is a Hall probe, which senses the magnetic field directly. In a second case study, the magnet's excitation current was used instead to provide a first-order approximation of the field. Experimental tests show that both approaches can reduce the measured field drift by three orders of magnitude. The Hall probe option guarantees, in addition, one order of magnitude better absolute accuracy than by using the excitation current.

Electron paramagnetic resonance magnetic field sensors for particle accelerators.

We report on four electron paramagnetic resonance sensors for dynamic magnetic field measurements at 36 mT, 100 mT, 360 mT, and 710 mT. The sensors are based on grounded co-planar microwave resonators operating at about 1 GHz and 3 GHz, realized using printed circuit board technology, and on single-chip integrated microwave oscillators operating at about 10 GHz and 20 GHz, realized using complementary metal-oxide-semiconductor technology. The sensors are designed to mark precisely the moment when a time-dependent magnetic field attains a specific value. The trigger from the sensor can be used to preset the output of real-time magnetic field measurement systems, called "B-trains," which are in operation at several large synchrotron installations, including five of the CERN's particle accelerators. We discuss in detail the performance achieved, in particular, the magnetic field resolution that is in the range of 0.1 nT/Hz1/2-6 nT/Hz1/2. The effects of material anisotropy and temperature are also discussed. Finally, we present a detailed characterization of the sensors with field ramps as fast as 5 T/s and field gradients as strong as 12 T/m.

Dynamic Ferromagnetic Hysteresis Modelling Using a Preisach-Recurrent Neural Network Model.

In this work, a Preisach-recurrent neural network model is proposed to predict the dynamic hysteresis in ARMCO pure iron, an important soft magnetic material in particle accelerator magnets. A recurrent neural network coupled with Preisach play operators is proposed, along with a novel validation method for the identification of the model's parameters. The proposed model is found to predict the magnetic flux density of ARMCO pure iron with a Normalised Root Mean Square Error (NRMSE) better than 0.7%, when trained with just six different hysteresis loops. The model is evaluated using ramp-rates not used in the training procedure, which shows the ability of the model to predict data which has not been measured. The results demonstrate that the Preisach model based on a recurrent neural network can accurately describe ferromagnetic dynamic hysteresis when trained with a limited amount of data, showing the model's potential in the field of materials science.

Integrator Drift Compensation of Magnetic Flux Transducers by Feed-Forward Correction.

Integrator drift is a problem strongly felt in different measurement fields, often detrimental even for short-term applications. An analytical method for modelling and feed-forward correcting drift in magnetic flux measurements was developed analytically and tested experimentally. A case study is reported on the proof of principle as a novel kind of quasi-DC field marker of the 5-ppm Nuclear Magnetic Resonance (NMR) transducer Metrolab PT2026, applied to the Extra Low ENergy Antiproton (ELENA) ring and the Proton Synchrotron Booster (PSB) at CERN. In some particle accelerators, such as in ELENA, the resulting feed-forward correction guarantees 1 µ T field stability over 120-s long magnetic cycle on a plateau of 50 mT, reducing by three orders of magnitude the field error caused by the integrator drift with respect to the state of the art.

Ferrimagnetic resonance field sensors for particle accelerators.

We report on two ferrimagnetic resonance (FMR) sensors for absolute dynamic magnetic field measurements at 36 and 100 mT. The sensors are designed to mark precisely and reproducibly the moment when a time-transient magnetic field attains a specific value. The trigger from the sensor can then be used for real-time magnetic field measurement systems, called "B-trains," which are in operation at several large synchrotron installations including five of CERN's particle accelerators. We discuss in detail the design, the operation, and the performance of the FMR sensors based on two different types of printed circuit board (PCB) resonator structures.

A software framework for developing measurement applications under variable requirements.

A framework for easily developing software for measurement and test applications under highly and fast-varying requirements is proposed. The framework allows the software quality, in terms of flexibility, usability, and maintainability, to be maximized. Furthermore, the development effort is reduced and finalized, by relieving the test engineer of development details. The framework can be configured for satisfying a large set of measurement applications in a generic field for an industrial test division, a test laboratory, or a research center. As an experimental case study, the design, the implementation, and the assessment inside the application to a measurement scenario of magnet testing at the European Organization for Nuclear Research is reported.

A polyvalent harmonic coil testing method for small-aperture magnets.

A method to characterize permanent and fast-pulsed iron-dominated magnets with small apertures is presented. The harmonic coil measurement technique is enhanced specifically for small-aperture magnets by (1) in situ calibration, for facing search-coil production inaccuracy, (2) rotating the magnet around its axis, for correcting systematic effects, and (3) measuring magnetic fluxes by stationary coils at different angular positions for measuring fast pulsed magnets. This method allows a quadrupole magnet for particle accelerators to be characterized completely, by assessing multipole field components, magnetic axis position, and field direction. In this paper, initially the metrological problems arising from testing small-aperture magnets are highlighted. Then, the basic ideas of the proposed method and the architecture of the corresponding measurement system are illustrated. Finally, experimental validation results are shown for small-aperture permanent and fast-ramped quadrupole magnets for the new linear accelerator Linac4 at CERN (European Organization for Nuclear Research).