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Numerical Ginzburg-Landau studies of J c in 2D and 3D polycrystalline superconductors G.J.Carty and D P Hampshire Superconductivity Group, Department of.

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Presentation on theme: "Numerical Ginzburg-Landau studies of J c in 2D and 3D polycrystalline superconductors G.J.Carty and D P Hampshire Superconductivity Group, Department of."— Presentation transcript:

1 Numerical Ginzburg-Landau studies of J c in 2D and 3D polycrystalline superconductors G.J.Carty and D P Hampshire Superconductivity Group, Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK Calculated critical current density values are presented for simulated 2D and 3D polycrystalline superconductors. In high applied magnetic fields J c in 2D is similar in functional form and magnitude to that predicted by the Kramer model, while a second mechanism operates in low fields, consistent with the experimental data originally review by Kramer. In 3D superconductors J c follows the Kramer- like b –½ (1 – b) 2 reduced-field dependence throughout the entire field range, as is observed in state-of-the-art materials. We acknowledge the support of Duncan Rand, Lydia Heck, Thomas Winiecki and the Durham University Scholarship Fund 1.Calculation Method  A semi-implicit numerical TDGL algorithm is used, with the normal metal components simulated with a Usadel-derived model[1].  The 3D polycrystalline superconductor is simulated as a packing of truncated octahedra, thus giving identical grains separated by constant-width boundaries, but without any continuous planar grain boundaries running through the material.  The edges of the superconductor are diffused over a width of 10 ξ to lower the overall surface barrier.  The grain boundaries consist of a non-superconducting region that is wider than the inner region where ρ is increased by electron scattering, consistent with the strong strain dependence of T c [2] and avoiding H c 3 effects. [1] G. Carty, M. Machida, and D. P. Hampshire, Phys. Rev. B 71, 144507 (2005). [2] J. W. Ekin, Cryogenics 20, 611 (1980) [3] E. K. Kramer, J. Elec. Mat. 4, 839 (1975) 5. Conclusions 3. 3D results  The simulated 3D superconductor is made up of truncated octahedral grains, as shown in Fig. 4 (the diffused edges are as shown in Fig. 1)  Simple ρ N = ρ S grain boundaries are used, due to 3D computational limitations.  Figure 5 shows that in both high and low E -fields, J c in 3D is about 20% of its value for the equivalent 2D system.  In Fig. 6 we see that fluxons within the grains of the superconductor are almost completely straight – all significant bending is on entering and leaving grain boundaries.  As in the 2D system, dissipation in the 3D system results from flux flow along grain boundaries. Figure 6: | ψ | 2 in slices of simulated 3D superconductor at H = 0.151 H c 2 Figure 5: Kramer plot comparing J c in 2D and 3D superconductors at high and low E -fields Figure 4: 3D packing of truncated octahedra 2. 2D results Normal Fully superconducting Main material (constant ρ ) Grain boundary (increased ρ ) Edges matched by periodic boundary conditions Figure 1: Diagram of the simulated 2D superconductor system  2D calculations use a slice through the 3D structure, as shown in Fig. 1.  When plotted on a Kramer plot, J c for the 2D system has a ‘knee’ at H ~ 0.8 H c 2, suggesting that J c results from two different mechanisms.  The inner grain boundary resistivity does not affect J c – this can be seen in Fig. 2.  Changing kappa, or the grain size may move the position of the knee, but not the high-field reduced-field dependence.  Fluxons within the grain boundaries, visible in the enlarged inset of Fig. 3, move for J > J c  these grain boundary fluxons thus determine the critical state. Figure 2: Kramer plot for 2D κ = 10 superconductor with 30 ξ grains, demonstrating two mechanisms and ρ N / ρ S -independence of J c Figure 3: Plots of a) | ψ | 2 and b) magnitude of normal current at H = 0.43 H c 2  Magnetization J c measurements in both 2D and 3D polycrystalline superconductors have been simulated using time-dependent Ginzburg- Landau theory. In both cases, J c is determined by flux flow along grain boundaries.  In 2D, there are two mechanisms determining J c, related to the state of ordering of fluxons within the grains. The low-field mechanism is dependent on grain size, while the high-field mechanism is not.  In 3D, the J c for high B -fields is about 20% of the value for the equivalent 2D system. J c and the pinning force F p have the correct experimental dependences - low E -field F p is given by: 4. Comparison with Experimental Data  Two distinct mechanisms determining J c, crossing over at a specific reduced field b, as seen in our 2D computational results, are also observed experimentally, such as in the Nb 3 Sn data in Fig. 7.  Consistent with our 2D computational results, only the low-field mechanism is microstructure-dependent. Figure 7: Kramer plot for Nb 3 Sn samples with various metallic and gaseous dopants[3]. An average B c 2 value = 20.5 T is assumed


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