IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 20, NO. 3, JUNE 2010 1387 Coupling- and Persistent-Current Magnetizations of Nb Sn Rutherford Cables Edward W. Collings, Michael D. Sumption, MichaelA. Susner, Emanuela Barzi, Daniel Turrioni, R. Yamada, Alexander V. Zlobin, and Arend Nijhuis Abstract—Multistrand cables may exhibit two classes of para- sitic magnetization both of which can distort the bore-field of the host magnet. They are: (1) a dynamic magnetization that is pro- duced by interstrand coupling currents generated by time-varying magnet excitation and moderated by the interstrand contact re- sistances (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-cur- rent-moderated persistent-current magnetizations at low and high fields. Index Terms—Coupling magnetization, interstrand contact re- sistance, persistent-current magnetization, Rutherford cable. I. INTRODUCTION A TIME-VARYING field applied to a Rutherford cable induces interstrand coupling currents (ISCCs) that loop around a half-pitch of the cable and through the crossover and adjacent-strand ICRs, and respectively. The former is de- fined as the resistance per crossover and is the edge-to-edge resistance between a pair of adjacent strands. Field ramping also generates “supercurrents” [1] or boundary-induced cou- pling currents (BICCs) [2]–[4] that flow over the whole cable length and induce field errors that conform to the period of the twist pitch. In order to achieve tight control of the particle beam during injection, acceleration, and storage it is necessary to minimize field distortions caused by ISCCs and BICCs [5]. Both of these are suppressed by increasing ICR. But since too high a value reduces cable stability [6] a compromise is sought. For LHC cables upon which many studies have been based, and Manuscript received October 18, 2009. First published March 18, 2010; cur- rent version published May 28, 2010. The U.S. Department of Energy, Office of High Energy Physics, funded the research at FNAL and CSMM, in the latter case under DE-FG02-95ER40900. E. W. Collings, M. D. Sumption, and M. A. Susner are with the Center for Superconducting and Magnetic Materials (CSMM), MSE Dept., The Ohio State University, Columbus, OH 43210 USA (e-mail: collings@matsceng.ohio-state. edu). E. Barzi, D. Turrioni, R. Yamada, and A. V. Zlobin are with the Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510 USA (e-mail: barzi@fnal.gov; zlobin@fnal.gov). A. Nijhuis is with the Low Temperature Division, Faculty of Applied Physics, University of Twente, Enschede, NL (e-mail: a.nijhuis@tnw.utwente.nl). Color versions of one or more of the figures in this paper are available online at http://lieeexplore.ieee.org. Digital Object Identifier 10.1109/TASC.2010.2041202 hence for accelerator cables in general e.g. [7] it is agreed (i) that should be in the range [5] or [7] and (ii) that , although relatively small, should be not less than 0.2 [2] as explained below. The coupling-generated field errors that were first encoun- tered in NbTi main dipoles and quadrupoles will again appear in their counterparts unless suitable precautions are taken. For this reason we have studied various ways to control in based cables [8]–[10]; below we continue this work fo- cusing on variable core width and cable pressure studies. Under LHC operating conditions field errors will be acceptably low provided the cables meet the above-quoted and spec- ifications. These resistances can be extracted from the results of AC-loss measurements purposely carried out, as described below, at relatively high applied-field ramp-rates or frequen- cies. As explained in [8] the coupling losses per cycle per of a cable (width, , thickness, , strand count, , transposition pitch, ) exposed to fields linearly ramping at a rate to amplitude applied perpendicular (face-on, FO, leading to and parallel (edge-on, EO, ) to the cable’s broad face are given by: (1a) (1b) or the “frequency-dependent” variant of (1a) (see [8]): (2) Then recognizing that , (1) and (2) can be re-written explicitly in terms of the coupling magneti- zation, . Eqns. (1a) and (2) express the FO-measured loss or magnetization in terms of a pair of parallel resistors and enabling an “equivalent” or “effective” to be defined as . It is clear that al- though itself is not part of the resistive-network model of the cable, regarded just as a number emerging from the loss experiment it is a useful index of magnetization. Thus it is this that should conform to the ICR prescription. Embodied in the above definition of is the requirement that if is to be 20 then should be not less than 0.2 for the following reason: Picture a 28-strand cable with “stan- dard” ICRs of 20 and 0.2 . The parallel-resistor 1051-8223/$26.00 © 2010 IEEE