Abstract - Stephan Russenschuck

High-quality magnetic measurements are crucial at different phases of an accelerator project; to validate numerical models and the design of the normal and superconducting magnets, magnet-to-magnet reproducibility during series production, and feedback to the machine operation. Unfortunately, no universal method exists for these measurements and the numbers of magnets are usually small; not only prototypes but not an industrial series either. Moreover, the uncertainty must remain below 10-4 for the absolute and 10-6 for the relative measured quantities.

While the GUM (Guide to the Expression of Uncertainty in Measurement) covers extensively random and systematic errors, the more complex magnetic measurements suffer from intrinsic errors (due to the necessary model-order reduction in the physical modelling), ignorance (due to the non-availability of predictive models of 3D effects, hysteresis, and multi-physics effects such as magnetostriction) and gross-errors (due to operational errors such as mix-up of calibration data). While gross-errors can be avoided by a proper quality assurance structure and database management system, ignorance can be identified by imposing the regularity conditions of magnetic field (field avatars) or supplementing numerical models by digital twins derived from measured quantities.

Time-varying fields in accelerators are difficult to compute in the range of the accuracy required for magnet operation. This is due to the complexity of the dynamic phenomena such as hysteresis and 3D eddy currents, and the required model-order reduction in the numerical model. On the other hand, magnetic measurements that intercept all these physical phenomena are often limited to a set of excitation conditions and restricted spatial domains (due to obstacles such as fixations and vacuum vessels, or in strongly curved magnets). The measurement results are therefore difficult to extrapolate without a validated physical model of the device.

A new line of research therefore aims at measurement-data driven field simulation with model updating to characterize dynamic effects in accelerator magnets, to create field maps and derive integrated quantities for machine operation. The core idea is to construct a state estimator, employing a reduced-order model of the device, that can be updated by magnetic measurements. This hybrid twin can then be used to predict the integrated bending strength and the current state of the magnet after arbitrary pre-cycling.

Recent developments at the TM section have paved the way for this research. In the magnetostatic case, the inhomogeneous fields of spectrometer and detector magnets are represented as 3D boundary data and measured recursively to reduce measurement duration. Moreover, an approach of model-order reduction was developed, correcting the predicted dynamic state of a pulsed electromagnet in the presence of eddy currents. Both cases rely on statistical Bayesian inference, frequently referred to as Kálmán filtering, to update a numerical model. This reflects the recent change in paradigm. Instead of veloping more and more complex microscopic models, they build on macroscopic datadriven models, focusing on extrapolation and predictability.

Stephan Russenschuck studied Electrical Engineering at the Technical University Darmstadt (TUD), Germany. He received the Dipl.-Ing degree in 1986 and the Dr.-Ing. degree in 1990 both from the Technical University Darmstadt. In 2000 he was recognized as a University Lecturer (Habilitation) for Theory of Electromagnetic Fields at the University of Vienna, Austria.

S. Russenschuck is a senior staff member in the Accelerator Technology (TE) Department of the European Organization for Nuclear Research, CERN, Geneva, Switzerland. He is the leader of the test and magnetic measurement section in the TE department.

For over 10 years he was the chairman of the technical and doctoral student committee (TSC). During the construction period of the LHC he was responsible for the electromagnetic design of the LHC main dipole magnets and later for the magnet polarities and the electrical quality assurance of the LHC machine.

His research interests are mathematical optimization and numerical field computation techniques in support of magnet design, magnetic measurements, and machine operation. S. Russenschuck is the author of the numerical field computation program ROXIE and the author of the book “Field computation for accelerator magnets” published at Wiley-VCH.