Interstrand Coupling Currents Research Articles

AC loss and contact resistance of different CICC cable patterns: Experiments and numerical modeling

• The AC loss and interstrand contact resistance measured on three prototype Nb 3 Sn Cable-In-Conduit Conductors with significantly different cabling twist pitch patterns. • Simulations, done by using the JackPot model are in fair agreement, confirming the consistency of data and allowing reliable predictions with the JackPot model. • For CICC cables, a design petal wrap coverage of 70 % should be maintained for CS cables to reduce the AC loss. A critical threshold value of void fraction exists, which makes the presence of petal wraps ineffective in reducing coupling loss. • The JackPot simulations with derived corrections for inter-petal contact resistance representing 70 % petal wrap coverage show that the Twente cable design has the lowest coupling loss. • So far, the Twente cable design seems a suitable candidate for CFETR or DEMO conductors, made of strain-sensitive strands such as Nb 3 Sn or other materials, for minimization of coupling loss and strand indentation. For upcoming nuclear fusion energy reactors, like the China Fusion Engineering Test Reactor (CFETR) and EU-DEMO, the superconducting Cable-In-Conduit Conductors (CICC) are in the design phase, and the operating conditions like electromagnetic forces can be higher than in previous devices like ITER. The prototype conductors for the Central Solenoid (CS) coils in the CFETR, for example, are designed to produce a peak field of 19.9 T and are expected to be made of high current density Nb 3 Sn strands. Investigations are also ongoing on the application of bismuth strontium calcium copper oxide (BSCCO) and MgB 2 strands for CICCs in fusion reactors. The latter material, MgB 2, could be applied for superconductors subjected to lower magnetic fields, such as Poloidal Field coils, Correction Coils, and Feeders. The performance of all these strands is sensitive to strain, and the mechanical strength of the brittle filaments is relatively weak. This requires a thorough analysis of the cable pattern in terms of the mechanical support of the strands along their length in combination with the minimization of the interstrand coupling currents and strand indentation. As an initial step to finding the most appropriate cable pattern for CICCs, three prototype CICCs made of ITER type Nb 3 Sn strands with significantly different cable twist patterns are tested experimentally for AC coupling loss, interstrand contact resistance, and strand indentation. The three cabling patterns referred to as the Twente, CWS (copper wound superconducting strand), and CFETR-CSMC (CFETR Central Solenoid Model Coil) design. The numerical code JackPot ACDC developed at the University of Twente is used to analyze the interstrand coupling loss and contact resistance. The new ASIPP (Institute of Plasma Physics, Chinese Academy of Sciences) triplet modified CWS design is aimed at reducing strand pinching during cabling, which causes degradation of transport properties during compaction and cyclic loading. The Twente design has the same objective but also aims at reducing the coupling loss while maximizing the mechanical lateral support for the strands by making the twist pitch ratio of the sequential cabling stages close to one. The CFETR-CSMC, taken as a reference for comparison, has cable a pattern mostly similar to the ITER CS cable design.

Anisotropic monoblock model for computing AC loss in partially coupled Roebel cables

When exposed to time-dependent magnetic fields, REBCO Roebel cables generate AC loss resulting from both magnetic hysteresis and induced inter-strand coupling currents. Until now, the AC loss has been computed in a two-dimensional approximation assuming fully coupled or decoupled strands, and a finite inter-strand resistance could be simulated only with three-dimensional models. In this work, we propose a homogenization procedure that reduces the three-dimensional geometry of the Roebel cable to two dimensions, without ignoring connections between the strands. The homogenized cable consists of two parallel ‘monoblocks’ with an anisotropic resistivity. The proposed model enables computation of AC coupling loss without the need for complex three-dimensional simulations. For experimental validation, a Roebel cable with soldered strands was prepared. The inter-strand resistance was determined by applying a transverse current and measuring the voltage profile. Additionally, the AC magnetization loss of the cable was measured in fields of 1 to 50 mT with frequencies of 1 to 2048 Hz using a calibration-free technique. With the measured inter-strand resistance as input parameter, the monoblock model gives a good estimate for the AC loss, even for conditions in which the coupling loss is dominant.

Calculation of interstrand coupling losses in superconducting Rutherford cables with a continuum model

Rutherford cables for particle accelerator magnets are subjected to time dependent magnetic fields during the typical accelerator operating cycle, which in turn induce coupling currents flowing in the loops formed at the contacts between different strands. An analysis of the magnitude and losses associated with these coupling currents is relevant to the design of field quality and cryogenic heat loads.The models reported in the literature exhibit some limits related to computational burden when applied to the analysis of interstrand coupling currents for real cable geometries, and conceptual limits when trying to couple different physical simulations. To solve this problem, a continuum model of Rutherford cables was improved to account for the non-uniform contact conductances between the strands along the cable length, also developing a novel strategy for the computation of the induced voltages. Thanks to these features we attain the required level of detail in the description of the short-range interstrand currents, which could not be properly computed with earlier versions of the continuum model. The model was validated by comparison with analytical results available in the literature for simplified case studies with uniform magnetic field applied orthogonal to the cable. Examples of current and loss distributions are presented in the paper, to prove the potential of the model to analyze Rutherford cables of any configuration. A study regarding the proper choice of the boundary conditions of the problem is presented, which suggests the need for experimental investigation on the actual distribution of currents and losses in the long cable lengths used in accelerator magnets.

Analysis of Field Errors for LARP Nb$_3$ Sn HQ03 Quadrupole Magnet

Author(s): Wang, X; Ambrosio, G; Chlachidze, G; DiMarco, J; Ghosh, AK; Holik, EF; Prestemon, SO; Sabbi, G; Stoynev, SE | Abstract: The U.S. large hadron collider (LHC) Accelerator Research Program, in close collaboration with The European Organization for Nuclear Research (CERN), has developed three generations of high-gradient quadrupole (HQ) Nb3Sn model magnets, to support the development of the 150 mm aperture Nb3Sn quadrupole magnets for the high-luminosity LHC. The latest generation, HQ03, featured coils with better uniformity of coil dimensions and properties than the earlier generations. The HQ03 magnet was tested at fermi national accelerator laboratory (FNAL), including the field quality study. The profiles of low-order harmonics along the magnet aperture observed at 15 kA, 1.9 K can be traced back to the assembled coil pack before the magnet assembly. Based on the measured harmonics in the magnet center region, the coil block positioning tolerance was analyzed and compared with earlier HQ01 and HQ02 magnets to correlate with coil and magnet fabrication. To study the capability of correcting the low-order nonallowed field errors, magnetic shims were installed in HQ03. The expected shim contribution agreed well with the calculation. For the persistent-current effect, the measured a4 can be related to 4% higher in the strand magnetization of one coil with respect to the other three coils. Finally, we compare the field errors due to the interstrand coupling currents between HQ03 and HQ02.

Lumped-Element Dynamic Electro-Thermal model of a superconducting magnet

Modeling accurately electro-thermal transients occurring in a superconducting magnet is challenging. The behavior of the magnet is the result of complex phenomena occurring in distinct physical domains (electrical, magnetic and thermal) at very different spatial and time scales. Combined multi-domain effects significantly affect the dynamic behavior of the system and are to be taken into account in a coherent and consistent model.A new methodology for developing a Lumped-Element Dynamic Electro-Thermal (LEDET) model of a superconducting magnet is presented. This model includes non-linear dynamic effects such as the dependence of the magnet’s differential self-inductance on the presence of inter-filament and inter-strand coupling currents in the conductor. These effects are usually not taken into account because superconducting magnets are primarily operated in stationary conditions. However, they often have significant impact on magnet performance, particularly when the magnet is subject to high ramp rates.Following the LEDET method, the complex interdependence between the electro-magnetic and thermal domains can be modeled with three sub-networks of lumped-elements, reproducing the electrical transient in the main magnet circuit, the thermal transient in the coil cross-section, and the electro-magnetic transient of the inter-filament and inter-strand coupling currents in the superconductor. The same simulation environment can simultaneously model macroscopic electrical transients and phenomena at the level of superconducting strands.The model developed is a very useful tool for reproducing and predicting the performance of conventional quench protection systems based on energy extraction and quench heaters, and of the innovative CLIQ protection system as well.

Multipoles Induced by Inter-Strand Coupling Currents in LARP <formula formulatype="inline"> <tex Notation="TeX">$\hbox{Nb}_{3}\hbox{Sn}$</tex></formula> Quadrupoles

The U.S. LHC Accelerator Research Program has been developing Nb3Sn quadrupole magnets of progressively increasing performance and complexity for the High-Luminosity LHC project. The magnets are wound with Rutherford cables following the wind-and-react process. The resulting inter-strand coupling can generate strong field distortions during current ramp. The latest series of 120 mm aperture magnets (HQ) are designed and built for high field quality, offering an opportunity for detailed studies of these effects. Magnetic measurements of first-generation HQ magnets showed strong ramp-rate dependence. A stainless-steel core was introduced for the second generation of magnet coils to control the inter-strand coupling currents and the resulting dynamic multipoles. We report the observed dynamic effects and compare with calculations taking into account the coil geometry and cross-contact resistance in the Rutherford cable. In particular, the dependence of field quality on width and position of the stainless steel core is discussed.

Coupling Loss, Interstrand Contact Resistance, and Magnetization of Nb$_{3}$Sn Rutherford Cables With Cores of MgO Tape and S-Glass Ribbon

Multistrand cables may exhibit two classes of parasitic magnetization both of which can distort the bore-field of an accelerator magnet: (1) a static magnetization (“hysteretic”) resulting from intrastrand persistent currents, and (2) a dynamic magnetization produced by interstrand coupling currents generated during field ramping. The latter, which are moderated by the interstrand contact resistances (ICR), can be controlled by the presence of an insulating core inserted between the layers of the cable. Stainless steel ribbon (with its associated native oxide coating) is a frequently used core. Recently, however, MgO-paper tapes and woven s-glass ribbons have been suggested by LBNL (Lawrence Berkeley National Laboratory) as alternative core materials in the interests of improved flexibility and compatibility with the cabling process. This paper reports on the results of calorimetric AC loss (hence ICR) measurements on a set of four such cables and presents the results within the context of previously measured cored and uncored Nb3Sn cables. Also considered is a typical ramp-rate-induced coupling magnetization and its relationship to persistent-current magnetizations over the operating range of an accelerator magnet.

Coupling- and Persistent-Current Magnetizations of $\hbox{Nb}_{3}{\hbox{Sn}}$ Rutherford Cables

Multistrand cables may exhibit two classes of parasitic magnetization both of which can distort the bore-field of the host magnet. They are: (1) a dynamic magnetization that is produced by interstrand coupling currents generated by time-varying magnet excitation and moderated by the interstrand contact resistances (ICR), (2) a static magnetization (¿hysteretic¿) resulting from the intrastrand persistent currents. This paper (i) compares the ICRs of two sets of cables with and without stainless steel cores and subjected to three levels of compaction during cabling, (ii) presents the results within the context the previously measured ICRs of a series of similar cables with cores of various widths, and (iii) concludes by comparing the LHC-ramp-rate induced coupling magnetization of a typical Rutherford cable with its transport-current-moderated persistent-current magnetizations at low and high fields.

Calculation of Field Quality in Fast-Ramping Superconducting Magnets

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Fast-ramping superconducting (SC) accelerator magnets are the subject of R&amp;D efforts at various laboratories. The simulation of field quality in fast-ramping magnets requires modifications of magnet design tools such as the CERN field computation program ROXIE. In this paper we present the efforts towards dynamic 2-D simulations of fast-ramping SC magnets. Models for persistent currents, inter-strand coupling currents, inter-filament coupling currents, and for eddy-currents in conducting coil-wedges are described and validated. </para>

Interstrand resistances in cored Rutherford-type superconducting cables

The network model of interstrand contact resistances (ICRs) is often used to describe the flow of interstrand coupling currents in Rutherford cables, and to predict the contribution of these currents to the ac losses of such cables. Recent evidence indicates that in cored Rutherford cables, the interstrand resistances are significantly lower in the cable edge region than they are in the flat area of the cable. To investigate these non-uniformities, the VI method was used to determine voltage profiles for cored cables of varying length. The results of the measurements have implications for both the measurement of ICRs via the VI method, and the calculation of ac losses.

Coupling losses in cable-in-conduit conductors for LHD poloidal coils

Coupling losses in Large Helical Device (LHD) poloidal coils have been measured during operations with three different waveforms. The superconductors of the poloidal coils are cable-in-conduit conductors (CICC) cooled by supercritical helium. In the experiments, the operating currents were simultaneously changed with a given waveform, and the enthalpy increase due to the losses was observed at the inlet and outlet of the helium coolant. Inter-strand coupling currents through resistive contact points mainly caused the losses. Time constants of the coupling currents are estimated by using analytical expressions with a circuit model. The results indicate a broad distribution of the time constants from the order of 10–1000 s.

General 2D equation for coupling currents in a flat superconducting cable subjected to a time-dependent magnetic field in the face-on orientation

An equation for inter-strand coupling currents induced in a finite piece of flat superconducting cable by the time-dependent magnetic field directed perpendicular to the cable wide surface is derived. Analytical solution of this equation demonstrates longitudinal periodic oscillations in the stationary inter-strand currents. Oscillations are absent only if the sample length coincides with an integer number of cable twist pitches. Due to the boundary influence, stationary strand currents at any sample length are never exactly the same as specified by the uniform solution. Numerical calculations for the harmonically oscillating external magnetic field have been performed and the dependence of the loss per cycle per twist pitch on frequency was obtained. Relation between the loss and the sample length is discussed.

Static and dynamic parasitic magnetizations and their control in superconducting accelerator dipoles

Long dipole magnets guide the particle beams in synchrotron-type high energy accelerators. In principal Cu-wound DC-excited dipoles could be designed to deliver a very uniform transverse bore field, i.e. with small or negligible harmonic (multipolar) distortion. But if the Cu is replaced by (a) superconducting strand that is (b) wound into a Rutherford cable carrying a time-varying transport current, extra magnetizations present within the windings cause distortions of the otherwise uniform field. The static (persistent-current) strand magnetization can be reduced by reducing the filament diameter, and the residue compensated or corrected by strategically placed active or passive components. The cable’s interstrand coupling currents can be controlled by increasing the interstrand contact resistance by: adjusting the level of native oxidation of the strand, coating it, or by inserting a ribbon-like core into the cable itself. Methods of locally compensating the magnetization of NbTi and Nb 3Sn strand and cable are discussed, progress in coupling-current suppression through the use of coatings and cores is reviewed, and a method of simultaneously reducing both the static and dynamic magnetizations of a NbTi cable by means of a thin Ni core is suggested.

Experimental verification of `supercurrents' in superconducting cables exposed to AC-fields

Supercurrents were recently identified as a source of reduced magnet stability which can explain the measured ramp rate limitation in large superconducting magnets. They also explain an unexpected periodic field modulation along the axes of superconducting accelerator dipoles. Supercurrents are extra coupling currents between the strands of a cable which are induced by a variable field sweep rate Ḃ( x) along the length of the cable. They flow over the whole cable length and have time constants many orders of magnitudes larger than `normal' interstrand coupling currents. In an experiment using a two-strand model cable, supercurrents were induced by an external field variation, or by ramping of a transport current. Their time dependence was measured using a Hall probe. The experimental results demonstrate the appearance of coupling currents much larger than the normal ac-coupling currents flowing around half twist pitch loops. Their time constant was τ=65 s for a cable length of L=4.7 m. A stepwise reduction of the cable length revealed the expected τ ∝ L 2 dependence. A model calculation with a theoretical model proposed previously for a two-strand cable shows a very good agreement with the experimental results.

Influence of supercurrents on the stability of superconducting magnets

Supercurrents were recently identified as a source of reduced magnet stability which can explain the measured ramp rate limitation in large superconducting magnets. They also explain an unexpected periodic field modulation along the axes of superconducting accelerator dipoles. Supercurrents are extra coupling currents between the strands of a cable which are induced by a variable field sweep rate Ḃ( x) along the length of the cable. They flow over the whole cable length and have time constants many orders of magnitudes larger than `normal' interstrand coupling currents. Supercurrents may lead to a highly inhomogeneous current distribution and to additional coupling losses (`supercurrent losses'), even in magnet sections with Ḃ=0. Both effects can drastically reduce the magnet stability during fast ramping up. The complete solution of the space and time dependence is given for a two-strand model cable. The theory of supercurrents can explain typical results of ramp rate limitation in large magnets.

AC losses dependence on a CuNi layer location in NbTi CICC

In the frame of the ITER fusion program, large Cable In Conduit Cables (CICC) made with NbTi superconductors are foreseen for the poloidal field system. These coils are pulsed and so subjected to fast variations in magnetic field. Superconductors have then to be designed in order to reduce AC losses to an acceptable level. A solution could be to insert a copper nickel resistive barrier in the copper stabilizer surrounding the filamentary area of the composite. The purpose of this barrier is to reduce interstrand coupling currents. In order to predict the effect of this barrier on AC losses, a modeling of a 36 strands CICC has been realized. According to this code, the ability of the resistive barrier to reduce coupling currents is dependent on its location. For this study, three CICC with three barrier locations, from the inner to the outer diameter of the copper crown stabilizer, have been produced. AC losses have been measured and compared to our numerical model.

A model for calculating a.c. losses in multistage superconducting cables

Superconducting magnets in tokamaks for fusion experiments are subjected to fast variations in magnetic field. As the high current conductors used in these magnets are made of multistage cables, these variations induce interstrand coupling currents that create losses. These losses are usually characterized by the so-called time constant of the conductor. A model is given to calculate this time constant. Working formulas are also proposed to calculate the current induced in the different cabling stages. This model takes into account the strand characteristics and the detailed cabling pattern. Using it, a method is also given to deduce the time constant from resistive measurements. The influence of the resistive barrier (chrome plating, CuNi shell, outer bronze matrix) is pointed out. Finally, this model is applied to a conductor that is foreseen for the toroidal coils of the International Thermonuclear Experimental Reactor (ITER).

Ramp rate induced quenches in the one-metre dipole model magnets for the CERN LHC

During the investigation of 1 m model dipoles for the Large Hadron Collider (LHC) a considerable number of quenches are performed at high ramp rate. In this paper the results are presented of these quenches which are made both at 1.7-2.1 K and at 4.3 K for ramp rates varying between 10 As/sup -1/ and 300 As/sup -1/. The quench current is strongly affected by the inter-strand coupling currents and the heat due to these currents. Furthermore, the influence of a current precycle is considered which can result in a significant increase of the quench current (at the same ramp rate). It is shown that this increase can be attributed to the presence of so called "super coupling currents" which strongly influence the current distribution among the strands, exhibiting characteristic time in the order of a few hundred to a few thousand seconds. Generally, the origin of the ramp rate induced quenches is close to the midplane of the inner coil of the magnet, where the field perpendicular to the wide side of the cable is maximum.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Hall effect on coupling losses in aluminum-stabilized superconductors

An aluminum-stabilized superconductor with a high current capacity is often used under the coexistence of the transverse and the parallel magnetic fields. A changing transverse field produces a path of inter-strand coupling currents in cross sections of the aluminum region. The magnetic interaction between the current and the parallel field causes what is called the Hall effect, so that the coupling loss feature is different from that of the ordinary conductor. The aluminum-stabilized conductor must generally be designed so as to avoid the increment in the resistivity of the aluminum due to the Hall effect at quench, but the low loss point of view should also simultaneously be taken into account in such a conductor design. >

An experiment on interstrand coupling currents in soldered cables

The effective frequency-dependent transverse resistivity experienced by coupling currents in superconducting cables was studied experimentally. The results extend the theory regarding the effective transverse resistivity of soldered strands to the whole AC domain. An accompanying magnetic effect due to the twist of the filaments has been measured and qualitatively explained by a simple model of the filament layer in the strands. It is seen that the coupling current experiences maximum resistivity if the strands are almost untwisted. >