Coupling losses in superconducting transposed conductors located in changing magnetic fields

Magnetic measurement of interstrand contact resistance and persistent-current magnetization of Nb3Sn Rutherford cables with cores of MgO tape and woven S-glass ribbon

“…Coupling Magnetization in General: As explained in [2] (see also [3]) ]) the coupling losses per cycle per m 3 of a Rutherford cable (width, w, thickness, t, strand count, N, transposition pitch, 2L p ) exposed to fields linearly ramping at a rate dB/dt to amplitude B m applied perpendicular (face-on, FO) and parallel (edge-on, EO) to the cable's broad face are given by: (1) which, to describe coupling loss in a relatively low frequency sinusoidal oscillating applied field, given that dB/dt = (π 2 /2)B m f [2], becomes…”

“…In such cases at sufficiently high frequencies Q coup (f) departs from linearity and eventually passes through a maximum at a critical frequency (2) and hence a total loss of the form: (4) in which, according to Verweij [6], R eff = 2π(DE)f c where E is a function of (w/t) and the number of cables in the stack and D is a function of the individual-cable properties, N and L p . To summarize, values of R eff are obtainable by way of: (i) the slope of the linear Q t (f) versus f line, (ii) the "raw" initial slope of a nonlinear Q t (f), (iii) the initial slope of a nonlinear Q t (f) after fitting the data to equation (3), (iv) f c itself, either directly observed or obtained by data fitting to equation (3). The raw magnetic data are displayed in FIGURE 1, and the analyzed results are presented in TABLE 2 and FIGURE 2.…”

“…Over the years numerous techniques have been employed to suppress these effects and improve field quality over the entire operating range of the accelerator. To establish a bench-mark we summarize the coupling-and persistent-current magnetizations of NbTi-wound LHCinner cable recognizing that both will be stronger in Nb 3 Sn cables.…”

CUDI: A model for calculation of electrodynamic and thermal behaviour of superconducting Rutherford cables

“…At each time step a matrix with dimensions N B (5N S -3) by N B (5N S -3)+1 is set up, containing all the relations of eqs. (4)- (6). Many matrix components contain the resistance R s , which is a function of the current I s , the critical current I crit (B, T), and hence also of the strand temperature T s .…”

“…The same type of network model is applied in 1980 to calculate the ISCCs for the ISABELLE cable [5]. Since 1988 other network models have been developed [6,7,8,9,10,11,12], that could also handle saturated strands, adjacent contact resistances R a and field changes parallel to the large cable face. Later a full electrodynamic network model was developed, including as well the self-field, self-and mutual inductances, longitudinal fields, and possibilities for spatial variations in field, field sweep rate, contact resistances, and critical current [13].…”