Low-field critical current density in porous MgB2 powders

Porous MgB2 powders are comprised of an ensemble of irregularly shaped constituents. In this work we introduce a model for the critical current density in such powders in the presence of a low external field H (H < 4 T) and in the high-porosity limit, where effects of vortex-lattice elasticity can be neglected and vortex pinning takes place within the powder-constituents. The ensuing critical current-density expression is a product of three decoupled factors: The first sets the scale for the critical current-density magnitude, while the second and third factors contain the field and powder-constituent size-parameters dependencies, respectively. The field dependent factor is of the form H−n and 0.5⩽n⩽1.0, where the limiting exponents n = 0.5 and n = 1.0 correspond to vortex configurations within a powder-constituent of a linear array and a two-dimensional lattice, respectively. For the calculations, we assume for the powder constituent shape a cylinder of arbitrary height and radius, where an external field and a single pinned vortex are aligned in parallel to the cylinder's axis. The exact fields of this configuration are derived. The size-parameters dependence implies enhanced critical current density for a cigar-like shape powder-constituent aligned with the field, and of radius smaller than about three times the penetration depth. These conclusions are consistent with pertaining data.