Advanced Diagnostics of Rutherford Cable Performance in Accelerator Magnets | Current redistribution & Quench development
Ruben Keijzer is a PhD student in the department Energy, Materials and Systems. (Co)Promotors are prof.dr.ir. H.H.J. ten Kate and dr. M.M.J. Dhalle from the faculty Science & Technology (TNW) University of Twente and dr. G. Willering from CERN Institute Geneva Switzerland.
To increase its discovery potential, the Large Hadron Collider at CERN is currently being upgraded to achieve a higher luminosity, which will increase the number of collision events in the particle detectors. To achieve this, some of the superconducting magnets that employ Nb-Ti as its superconductor are being replaced with magnets that use Nb3Sn instead, which allows for attaining higher magnetic fields. Nb3Sn magnet technology does however pose additional engineering challenges: as opposed to Nb-Ti, which is ductile, Nb3Sn is a brittle material. Its brittle nature makes the superconductor more susceptible to damage during manufacturing and magnet operation. During the testing and prototyping phase of the new Nb3Sn magnets for the High Luminosity Large Hadron Collider, several magnets underperformed and could not reach their target magnetic field. The underperforming magnets also showed anomalous readings on several diagnostic tools. In this thesis work, we aimed to better understand these non-trivial signals and to learn how they might be used to diagnose the type of conductor damage that is present in the underperforming magnets. To this end, a new numerical model which can predict both the thermal and electrodynamic behaviour of the superconducting cables under defect conditions was developed. In addition, a dedicated experiment was performed on a heavily instrumented model coil, where artificial damage was introduced in a controlled way to study how it affects the magnet’s performance and behaviour.
Rutherford cables
For use in accelerator magnets, the superconducting wires, which consist of twisted Nb-Ti or Nb3Sn filaments embedded in a copper matrix, are first assembled into a Rutherford-type of cable. A Rutherford cable is characterized by a bundle of twisted wires two-axes rolled into a high-aspect-ratio trapezoidal shape with two layers, which makes it suitable for the winding of cosθ-type of magnets. The cable strands have a certain amount of mutual thermal and electro-magnetic coupling. This inter-strand coupling, which depends on the contact area and surface conditions of the strands, strongly influences the transient electric and thermal-electric behavior of the Rutherford cable.
Numerical tools
The two numerical simulation codes used in this thesis work are THEA and RuNe. THEA is an existing code for the thermal, hydraulic and electric analysis of superconducting cables and is used to study current redistribution effects over long length - and time scales. For localized transient effects, a higher spatial and temporal resolution is required, rendering THEA computationally less efficient. Therefore, in the framework of this thesis RuNe (Rutherford Network) was developed, a new 3D thermal-electric PEEC-FEM model that efficiently simulates quench dynamics, but is also still able to study current redistribution effects on a larger scale.
Experimental
This thesis aims to extract more information from the two main diagnostic tools used in accelerator magnets under test: voltage taps and quench antennas. By combining voltage taps with differential measurement schemes, the sub-microvolt precision that is needed to reliably detect the small voltages caused by conductor damage was achieved, even for 5.5 m long magnets developing sizeable inductive voltages during ramping or picking up significant environmental EM noise. Quench antennas consisting of arrays of pick-up coils that provide detailed additional insight into the current redistribution effects especially during the initial development phase of a quench, but also during its steady-state propagation. Systematic comparison between model predictions and test results showed the quench antenna signals to carry information regarding the detailed location of the initial hot spot; the presence and importance of possible damage-related non-uniformity of the current distribution; and thermal/electrical inter-strand resistances. Moreover, a dedicated experiment was performed on a Short Model Coil (SMC), a two-layer racetrack magnet. Intentional damage was introduced in gradual stages, by locally interrupting an increasing number of strands over a series of tests. Strategically placed voltage taps were introduced to monitor the current redistribution process around the defect in detail. This controlled experiment provided a varied range of reference data confirming the model predictions and validating its accuracy.
Current redistribution
In a Rutherford cable with a local defect involving one or a few broken or degraded strands, current will bypass the defect through the other strands. Current redistributes mainly through strands adjacent to the defect rather than through crossing strands, because the former have a higher mutual inductance and lower electrical contact resistance with the affected strand(s). When the current in an adjacent strand is then driven to its critical value, that strand becomes saturated and the excess current redistributes through the next-neighboring strand. This effect proceeds in a cascading sequence of saturating strands. Such current redistribution can be seen as a diffusion process governed by the values of the self - and mutual inductances of the strands and their electrical inter-strand contact resistances. The length over which current redistributes increases with time. This means that the current bypasses the defect through an increasing number of parallel resistances, since the non-affected strands themselves have zero resistance. The main physics of this process can be captured with a 1D analytical diffusion model, the predictions of which were reproduced with THEA, which allows to relate it to cable-specific parameters. In actual magnet tests, this type of local damage-induced current redistribution manifests itself as a resistive voltage recorded during a plateau in the current ramp, which decays gradually with time. This type of decaying voltage was measured on several HL-LHC model – and prototype magnets with performance limitations and is thus indeed a clear indicator of local conductor damage in the cable. The decaying voltage can appear on current plateaus several kA below a magnet’s quench limit and is therefore a useful predictor of magnet performance. With the current redistribution process around the intentionally introduced defect in the SMC magnet monitored with the extra voltage taps, RuNe’s model predictions could be confirmed in more detail. The local inter-strand contact parameters of the Rutherford cable in the coil were successfully estimated from comparison between model and experiment. Somewhat surprisingly, it was observed that the SMC magnet can reliably reach its operating current with as many as four strands adjacent to a defect fully saturated. This illustrates the importance of testing magnets all the way to the short-sample limit in quality assurance and acceptance tests.
Quench development and normal zone propagation
The evolution of a normal zone in a Rutherford cable is divided in two phases: the development phase and the propagation phase. During the development phase, the normal zone is still growing transversely in the cable until eventually all strands in the cable lateral cross-section have turned normal, at which point the propagation phase starts. These two phases can be distinguished in the experimental voltage data recorded during a quench by an accelerating voltage during the development phase, followed by a kink and then a linear voltage rise during the propagation phase. When electro-thermal coupling between strands is stronger the development phase is shorter. Using harmonic quench antenna data in combination with RuNe simulations, quench origins can be reconstructed for both conductor-limited quenches as well as training quenches, but this is a computationally intensive analysis. A faster and easier method using the time integral of the magnetic dipole moment was therefore also developed for finding the quench start location in the cable cross-section of conductor-limited quenches directly from the quench antenna data.
Different normal zone propagation modes were studied using the model RuNe. Previously poorly understood anomalous measurements from an 11 T dipole magnet could be likely identified as due to a defect-dominated propagation mode, whereby the normal zone front propagates along overloaded strands due to the presence of a local defect. This propagation mode was later also observed in the
SMC experiment, further validating the model and illustrating how the information contained in the diagnostic data can help identify the detailed root cause of magnet issues. In summary, the unique combination of the model RuNe and the advanced diagnostic tools allowed to describe the earliest stages of a quench in Rutherford cable based accelerator magnets in much more detail than possible before.
