Parameterization of the critical surface of REBCO conductors from Bruker M. Danial and J. van Nugteren July 20, 2017 Contents 1 Introduction 2 1.1 Bruker HTS................................ 2 2 Critical surface Fit 2 2.1 Preliminary Fits.............................. 2 2.2 Temperature Dependence of the critical current density........ 3 2.3 Magnetic field dependence of the critical current density....... 5 2.4 Anisotropy shape of of the critical current density........... 7 2.5 Surface Fit of of the critical current density.............. 7 2.6 Discussions................................ 8 2.7 Results of the Fit Against Data Set................... 8 1
1 Introduction 1.1 Bruker HTS The Bruker high temperature superconductor cable is produced by the industrial production company Bruker HTS GmbH (Germany). A second generation REBa 2 Cu 3 O 7 x or REBCO coated conductors, it is a possible candidate as the material used for high fields accelerator magnets. The varying methods of production of such rare Earth coated conductors make it challenging to determine the performance of such devices. The parametization of the critical surface of REBCO manufactured by Bruker could thus be used to model the performances of such devices from other industrial manufacturers. 2 Critical surface Fit 2.1 Preliminary Fits Based on the parametization work done for Fujikura[1] the fit for the critical surface of Bruker REBCO whose data was collected by Geneva University (Carmine Senatore) was presumed to follow the similar function of field to intensity(b), temperature (T) and field orientation (θ) given by [2]: J c (B, T, θ) = J c,c (B, T ) + J c,ab(b, T ) J c,c (B, T ) 1 + ( ) ν θ π/2 g(b,t ) J c,c (B, T ) = α c B bqc c (1 b c ) qc (1 t n ) γc J c,ab (B, T ) = α ab B bp ab ab (1 b ab) q ab [(1 t n1 ) n2 + a(1 t n )] γ ab B i,ab = B i0,ab [(1 t n1 ) n2 + a(1 t n )] B i,c = B i0,c (1 t n ) The function, however did not provide a satisfactory fit to the data. 2
2.2 Temperature Dependence of the critical current density A closer look at the temperature dependence of the critical current density showed an inverse exponential relationship between the change in temperature and the critical current density. Such observations were consistent with the works of Carmine Senatore[3] which says that temperature dependence of Jc can be described over a broad range of temperatures and magnetic fields by the equation J c (T, B) = J c (T = 0, B)e y T/T Figure 1 Temperature dependence of Jc in the perpendicular plane between 4.2 3
K and 77 K for the tape from Bruker HTS. Measurements are points and lines are fits. Figure 2 Temperature dependence of Jc in the parallel plane between 4.2 K and 77 K for the tape from Bruker HTS. Measurements are points and the lines are fits. This can be explained by the thermal activation processes associated to the pinning centers. The presence of defects generating weak isotropic pinning and T* is the characteristic pinning energy at these defects [4,5] particular explains the exponential decay of Jc. T* value determines the rate of decrease of Jc as T varies. This value varies not only from different manufacturers but from each tape produced as the addition of of 4
artificial precipitates during fabrication affects the manner in which vortex spinning occurs on each tape. 2.3 Magnetic field dependence of the critical current density It is assumed that dual pinning of vortex still occurs in the c and ab directions. Using the equation below a fit was obtained for the magnetic field dependence of the critical current density in the c direction, perpendicular data measurements were used: where J c0,c, B c, T c J c,c (B, T ) = J c0,c(10 5 )exp( (T/T c ) n 1 )exp( (B/B c ) m 1 ), m 1 and n 1 are constants. 5
Figure 3 Magnetic field dependence of Jc in the perpendicular plane between 4.2 K and 77 K for the tape from Bruker HTS. Measurements are points and the red lines are fits. Using the equation below a fit was obtained for the magnetic field dependence of the critical current density in the b direction, parallel data measurements were used: J c,ab (B, T ) = J c0,ab(10 5 )exp( (T/T ab) n 2 )((B/B ab) + c) h(t/t ab2 )+p where Tab, J c 0,ab, c, h, n 2, Tab, B ab and p are constants. Figure 4 Magnetic field dependence of Jc in the parallel between 4.2 K and 77 K for the tape from Bruker HTS. Measurements are points and the red lines are fits. 6
2.4 Anisotropy shape of of the critical current density The anisotropy shape of Jc was assumed to present a symmetry with respect to both parallel and perpendicular planes as such the anisotropy factor (g) is given by: where g 0, g 1, g 2 and g 3 are constants. g(b, T ) = g o + g 1 exp( B[g 2 exp(t g 3 )]) 2.5 Surface Fit of of the critical current density Using the function of field to intensity(b), temperature (T) and field orientation (θ): Jc(B, T, θ) = min(j c,c, J c,ab ) + max(0, (J c,ab J c,c ) (1 + θ π 2 ) g v a surface fit is obtained for the Critical current density. Figure 5 Surface Fit of Critical current density as a function of Magnetic field from 0 to 19 T, Temperature of 4.2 K and 77 K and the field orientation from 0 to 7
90 for the tape from Bruker HTS. Yellow points are measurements are points and the surfaces are fits. 2.6 Discussions The fits are satisfactory to the current data set used. Greater measurements of the dependence of temperature to Jc for fixed magnetic field values and field orientation can be done to determine the quality of the fits. More measurements can also be made for different angles of field orientation to better determine the validity of the fits. Using the current fit, further analysis will be made to determine if the YBCO tapes manufactured by manufacturers such as SuNAM Co. Ltd. (Korea), SuperOx ZAO (Russia)and SuperPower Inc. (US). 2.7 Results of the Fit Against Data Set g o g 1 g 2 g 3 [-] [-] [-] [-] 0.03 0.25 0.06 0.058 J c0,c Tc Bc m 1 n 1 A [ ] [K] [T] [-] [-] mm 2 5.055 30.18 1.494 3.76 0.4633 J c0,ab Tab Bab c n 2 h p Bab Tab2 A [ ] [K] [T] [-] [-] [-] [-] [T] [K] mm 2 4.401 43.27 1 0.7698 2.207-0.01107-0.177 1 1 References [1] J. Fleiter and A. Ballarino, Parameterization of the critical surface of REBCO conductors from Fujikura, September 2014 Internal Note 2014-24 EDMS Nr: 1426239,. [2] J. Fleiter and A. Ballarino, Parameterization of the critical surface of REBCO conductors from Fujikura, September 2014 Internal Note 2014-24 EDMS Nr: 1426239, 8
[3] C. Senatore, C. Barth, M. Bonura, M. Kulich, G. Mondonico, Field and temperature scaling of the critical current density in commercial REBCO coated conductors, EuCARD-2 Journal Publications, December 2015 [4] Puig T, Gutierrez J, Pomar A, Llordes A, Gazquez J, Ricart S, Sandiumenge F and Obradors X Vortex pinning in chemical solution nanostructured YBCO films Superconductor Science and Technology 21 034008, 2008 [5] Gutierrez J, Puig T and Obradors X Anisotropy and strength of vortex pinning centers in YBa2Cu3O7-x coated conductors Applied Physics Letters 90 162514, 2007 9