Strand Trajectories Research Articles

Extensive Analyses of Superconducting Cables 3D Geometry With Advanced Tomographic Examinations

In the framework of activities embedding magnet design and associated R&D activities and relying on Cable in Conduit Conductors (CICC) technology, the singularity of the concept can rise some challenges versus their modelling in operation. Indeed, CICC includes thousands of superconducting strands, twisted together under a multi-staged scheme that also includes deformation by cabling and compaction during manufacture. This causes the accurate predictability of strands position in CICC extremely difficult, while it can be a key element for modelling their performances in operation. As a matter of fact the coupling losses rely on the CICC capability to establish inter-strand shielding currents, driven by the inter-strand contacts mapping which are only accessible in prediction via accurate 3D strand trajectories geometry. Same applies for prediction of CICC mechanical properties (deformation of Nb3Sn strands) and hydraulic properties (helium coolant force-flowed between the strands), making those investigations of high added-value. In this context, INFLPR installed a new set-up dedicated to micro-tomography to examine CICCs with high resolution, and get an overall overall 3D overview regarding picture of the strands location. CEA and INFLPR further developed a post-processing method to reconstruct the strands trajectories with high accuracy. The measurement and data analysis workflow was applied to two CEA middle-size CICCs with variable void fraction from which contact statistics were issued. The obtained database was exploited to reconstruct equivalent 3D resistive network. Above applications using CICC topology database are discussed, compared to experimental AC losses database issued by CEA and interpreted considering the CEA model COLISEUM. The outcomes are discussed and subsequent guidelines for future work presented.

Numerical Investigation on Induced Current Distribution and AC Losses in a Prototype Cable for the European DEMO TF Coils

A new geometrical model has been implemented in the THELMA code, aiming at permitting the study of multistage, forced-flow cable-in-conduit conductors with rectangular cross-section, like that proposed for the toroidal field (TF) magnets of the future fusion reactor DEMO. This model gives verisimilar strand trajectories which should enable the adoption of a more detailed interstrand electrical contact model. This paper shows the results of the first application of these new code features to a set of contact resistance and ac loss experiments carried out by Twente University on a DEMO TF prototype conductor. The results of this analysis present some unforeseen aspects that need further work to be fully understood, to improve and validate the model.

Theoretical analysis of braiding strand trajectories and simulation of three-dimensional parametric geometrical models for multilayer interlock three-dimensional tubular braided preforms

Multilayer interlock three-dimensional (3D) tubular braided composites have been widely used in propeller blades, high pressure pipelines, rocket nose cones and engine nozzles owing to prominent interlaminar shear properties, reliable damage tolerance and outstanding torsion performance. The prediction of the mechanical properties and the design of the fabric structures for the 3D braided composites are dependent on the trajectory distribution of strands and the geometrical model of the braided structure. This paper aims to build theoretical models for the braiding strand trajectories and presents a creative method to establish the parametric geometrical models for the multilayer interlock 3D tubular braided structures. Firstly, mathematical models of braiding strand trajectories are derived based on the analysis for the characteristics of carrier paths, the interlacing and interlocking of braided structures and the motion of braiding strands. The mathematical models are then developed to establish parametric expressions for multilayer interlock 3D tubular braided structures by the advanced development of UG NX®. In addition, the models of corresponding braiding strand trajectories and braiding structures can be obtained automatically in the simulation environment with the modification of design parameters. Finally, the established models are compared with the carbon fiber braided specimen. The results show that the innovative parametric geometric models of the multilayer interlock 3D tubular braided structures accurately describe the key characteristics of the preform.

Multi-scale 3D modelling of a DEMO prototype cable from strand to full-size conductor based on X-ray tomography and image analysis

The design of a superconducting magnet system of a fusion reactor candidate is usually based on the Cable in Conduit Conductor (CICC) concept. CICC consist of complex structures with several hundreds of highly packed, multistage twisted superconductor and copper strands, cooling structures – all wrapped in thin steel foils and jacketed in relatively thick stainless-steel pipes. As recently demonstrated, such complex morphology can be captured by fully 3D X-ray tomography. One of the three alternative winding pack (WP) options for the toroidal field coils of the European DEMO superconducting magnet system as proposed by the Italian ENEA, features a layer-wound WP design adopting a wind-and-react conductor with high aspect ratio rectangular cross section. A multi-physics modelling requiring high accuracy from the strand to the full-size conductor scale was tested on two X-ray tomography systems. For the microstructural integrity analysis of the internal tin one mm diameter Nb3Sn strand, manufactured by Western Superconducting Technologies, a microtomograph with ˜1 μm feature recognition was used. For the full-size conductor (66 x 25 mm2 internal dimensions) a high energy (> 300 kVp) microtomograph with voxel resolution of ˜20 μm was employed. Voids and/or geometrical imperfections were detected, accurately pin-pointed and locally investigated at high resolution before and after heat treatment. Dimensional measurements on the 3D internal structure of the strand showed the small dimensional changes of the strand after the heat treatment. A significant result was the determination of the twist-pitch factor in a purely non-invasive way. The 3D reconstructions of the CICC cables were used to verify the cabling and compaction processes as well as the structural integrity of the strands, wrapping foils and spiral cooling structures. Also, 3D reconstruction of strand trajectories provided a strong input for a multiphysical modelling/interpretation of mechanical–electrical properties of CICC in cryogenic–electromagnetic environments.

Development of a New Generic Analytical Modeling of AC Coupling Losses in Cable-in-Conduit Conductors

Coupling losses induced in cable-in-conduit conductors (CICC) when subject to a time-varying magnetic field are a major issue commonly encountered in large fusion tokamaks (e.g., JT-60SA, ITER, DEMO). The knowledge of these losses is crucial to determine the stability of CICC but is yet difficult to achieve analytically (thus in a short computation time) given the specific and complex architecture of these conductors although numerical solutions such as THELMA and JACKPOT already exist. In an attempt to ease the resolution of this problem, we have previously presented a theoretical generic study of a group of elements twisted together (representing a cabling stage of a CICC) and derived the analytical expression of its coupling losses. We have now extended this study to a two cabling stage conductor by establishing an analytical model to calculate its coupling losses as function of its effective features. In a second part, we compare our results to these of THELMA and JACKPOT on geometries representing ITER CS and JT-60SA TF conductors. Finally, we have set up a specific algorithm to reconstruct strand trajectories from X-ray images and have extracted the effective geometrical parameters of a JT-60SA TF conductor. Our next objective is then to extract its effective electrical parameters from interstrand resistivity measurements to be able to compare the coupling losses predicted by our analytical model with those measured within the SULTAN facility.

Accurate 3D modeling of Cable in Conduit Conductor type superconductors by X-ray microtomography

Operation and data acquisition of an X-ray microtomography developed at INFLPR are optimized to produce stacks of 2-D high-resolution tomographic sections of Cable in Conduit Conductor (CICC) type superconductors demanded in major fusion projects. High-resolution images for CCIC samples (486 NbTi&Cu strands of 0.81mm diameter, jacketed in rectangular stainless steel pipes of 22×26mm2) are obtained by a combination of high energy/intensity and small focus spot X-ray source and high resolution/efficiency detector array. The stack of reconstructed slices is then used for quantitative analysis consisting of accurate strand positioning, determination of the local and global void fraction and 3D strand trajectory assignment for relevant fragments of cable (∼300mm). The strand positioning algorithm is based on the application of Gabor Annular filtering followed by local maxima detection. The local void fraction is extensively mapped by employing local segmentation methods at a space resolution of about 50 sub-cells sized to be relevant to the triplet of triplet twisting pattern.For the strand trajectory assignment part we developed a global algorithm of the linear programing type which provides the vast majority of correct strand trajectories for most practical applications. For carefully manufactured benchmark CCIC samples over 99% of the trajectories are correctly assigned. For production samples the efficiency of the algorithm is around 90%. Trajectory assignment of a high proportion of the strands is a crucial factor for the derivation of statistical properties of the cable such as twisting pattern, cos(θ) or void fraction.

Optimization of Interstrand Coupling Loss and Transverse Load Degradation in ITER $\hbox{Nb}_{3}\hbox{Sn}$ CICCs

For the ITER Central Solenoid (CS), with Nb3Sn CICCs that operate under fast ramping conditions, the selection of the twist pitch lengths can have a significant impact on the performance. The critical current and temperature margin are influenced by the thermal contraction of the composite materials, the transverse electromagnetic forces, and coupling currents. The numerical cable model JackPot-ACDC is developed to calculate the interstrand coupling loss for any time-dependent current and magnet field for all strand trajectories in a CICC. It was a priori predicted that the amount of coupling loss and critical current degradation is subject to interference due to different subcable twist pitches. Here test results are discussed of the ITER CS conductor sample, manufactured according to the proposed design, optimizing the transverse load degradation, the temperature margin, and the coupling loss.

Prostate brachytherapy postimplant dosimetry: Seed orientation and the impact of dosimetric anisotropy in stranded implants

In postimplant dosimetry for prostate brachytherapy, dose is commonly calculated using the TG-43 1D formalism, because seed orientations are difficult to determine from CT images, the current standard for the procedure. However, the orientation of stranded seeds soon after implantation is predictable, as these seeds tend to maintain their relative spacing, and orient themselves along the implant trajectory. The aim of this study was to develop a method for determining seed orientations from reconstructed strand trajectories, and to use this information to investigate the dosimetric impact of applying the TG-43 2D formalism to clinical postimplant analysis. Using in-house software, the preplan to postimplant seed correspondence was determined for a cohort of 30 patients during routine day-0 CT-based postimplant dosimetry. All patients were implanted with stranded-seed trains. Spline curves were fit to each set of seeds composing a strand, with the requirement that the distance along the spline between seeds be equal to the seed spacing within the strand. The orientations of the seeds were estimated by the tangents to the spline at each seed centroid. Dose distributions were then determined using the 1D and 2D TG-43 formalisms. These were compared using the TG-137 recommended dose metrics for the prostate, prostatic urethra, and rectum. Seven hundred and sixty one strands were analyzed in total. Defining the z-axis to be cranial-positive and the x-axis to be left-lateral positive in the CT coordinate system, the average seed had an inclination of 21° ± 10° and an azimuth of -81° ± 57°. These values correspond to the average strand rising anteriorly from apex to base, approximately parallel to the midsagittal plane. Clinically minor but statistically significant differences in dose metrics were noted. Compared to the 2D calculation, the 1D calculation underestimated prostate V100 by 1.1% and D90 by 2.3 Gy, while overestimating V150 and V200 by 1.6% and 1.3%, respectively. Urethral and rectal dose quantifiers tended to be underestimated by the 1D calculation. The most pronounced differences were in the urethral D30 and rectal D2cc, which rose by 3.8 and 1.9 Gy, respectively, using the 2D calculation. The total volume of the 100% isodose region as a percentage of the prostate volume was found to increase by 0.4%. Stranded seeds in the supine patient are not oriented in a uniformly random manner, nor are they aligned along the axis of the CT scanner. Instead, this study identified a consistent anterior pitch that is likely attributable to differences in patient pose between implant and CT imaging. The angle of the ultrasound probe with respect to the patient during implant may have also been a contributing factor. The dose metrics derived using the 1D formalism were found to be within 2%, on average, of those derived using the 2D formalism. For greater accuracy, 2D dosimetry can be pursued using the strand-fitting method described in this work. If a 1D representation is used, integrating over the empirically determined seed orientation density reported here may be more appropriate than assuming that seed inclinations are distributed uniformly.

Mechanical-Electrical Modeling of Stretching Experiment on 45 ${\rm Nb}_{3}{\rm Sn}$ Strands CICCs

Cable-In-Conduit Conductors made with Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn strands will be used in ITER magnets. The current carrying capability of these Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn strands is known to be highly dependant on the strain state resulting from mechanical loading. The intricate cabling pattern of CICC, added to the thermal differential shrinkage between conductor jacket and Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn filaments induce complex strand trajectories and a highly inhomogeneous strain state. This “cable strain map” also evolves with operating loads (Lorentz force/hoop stress). The SAMAN experiment, conducted in the FBI facility at Karlsruhe Institute of Technology, aimed to stretch subsize, ITER-like conductors, in order to observe the evolution of the critical current associated with these loadings. The application of the Multifil finite element code, developed at Ecole Centrale de Paris, has helped quantifying the local strains along every individual strand, and their evolutions during cooldown (from heat treatment), energizing and stretching phenomena. Using Multifil output mechanical data as input in the CEA electrical code CARMEN has allowed computing the critical current in every strand, thus leading to an understanding of the critical current degradation of such subsize conductors. This paper shows, for two SAMAN samples, what is the impact of bending strain concentration on a CICC current transport capability.

Investigation of a Mechanism Forming Irregular Loops in Large CIC Conductor

Coupling loss with long time constants has been found a troublesome phenomenon for large size magnet application of superconductor because it would not be simply estimated from AC loss measurement of short sample conductor. In order to investigate the mechanism of the loss, we measured trajectories of strands of sample CIC (3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> = 81) conductor. The measured length is 1 m along the conductor axis. By analyzing those trajectories, two important facts are cleared. One is that contact periods between two strands are calculated by the function of twisting pitches, not always by the Least Common Multiplier of twisting pitches. The other is that contact probabilities of two strands at each contactable point of sub cables depend on the difference of rotation angles of sub cables. To confirm the validity of this method, we calculated lengths of coupling current loops within 1 m in length by using experimentally obtained contact probabilities. The results are in very good agreement with lengths obtained from experimental results of strand trajectories. Then we computed the loop length in the long conductor (<100 m), it was obtained that the average loop length would reached about 3 m.

Investigation of Irregular Strand Positions Causing Additional AC Losses in CIC Conductor

AC losses with long time constants can not be simply estimated from a short sample conductor because there are many irregular loops formed by strands strongly displaced from their original positions. In our previous work, we measured trajectories of 81 strands of NbTi conductor and it was proved that strongly displaced strands produced many line contacts with other strands, and thereby caused low contact resistance and long time constants. Long loops due to the displacement of strands should also produce large AC loss because the time constant of the loss is proportional to the inductance, i.e., the length of coupling current loops. In order to investigate the long loops in practical conductors, we developed a method to estimate the strand positions over the entire length. In this method, only one cross section of the conductor is required to calculate gravities of each sub-cable. The strand trajectories are obtained in a manner that the same order sub-cables rotate around the gravity to form one order higher sub-cable. The estimated trajectories are in good agreement with the measured ones, with errors of 1 mm.