Magnetic Characterization and FEM Computation of MgB2 Bulk Spheres

We have investigated magnetization cycles of a MgB₂ sphere, 4 mm size, at temperatures of 25, 30, and 35 K up to an applied magnetic field μ₀H strength of 3 T. Further to magnetization cycles, we also studied the shift of the magnetization peak position as a function of the maximum applied field for field values between the first penetration field and the full penetration field. In this way, we found a shift of the magnetization peak field position toward a saturation value of the applied field, above which no further shift is observed. The shift of the magnetization peak field position has been observed in YBCO thin films, and ascribed to the magnetization trapped in the granular borders of the material. The same mechanisms may be supposed acting in the MgB₂ sphere, provided that the saturated peak of the magnetization curve lies in the μ₀H <; 0 region due to the effect of local field B on the critical current J_c(B) in the spherical geometry. This will show up the shift effect in the H <; 0 region. A FEM model with H-formulation has also been implemented, in which the magnetization cycle is taken into account by the power-law E(J) characteristic for the electric field. Our experimental and numerical findings can provide a simple understanding of the observed magnetization cycle in this spherical geometry in saturated and nonsaturated conditions.