Vortex plastic flow, local flux density, magnetization hysteresis loops, and critical current, deep in the Bose-glass and Mott-insulator regimes

We present simulations of flux-gradient-driven superconducting vortices interacting with strong columnar pinning defects as an external field $H\left(t\right)\mathrm{}$ is quasistatically swept from zero through a matching field $B_{\phi }$. We analyze several measurable quantities, including the local flux density $B(x, y, H(t\left)\right)$, magnetization $M\left(H\right(t\left)\right)$, critical current $J_c\mathrm{}\left(B\right(t\left)\right)$, and the individual vortex flow paths. We find a significant change in the behavior of these quantities as the local flux density crosses $B_{\phi }$, and quantify it for many microscopic pinning parameters. Further, we find that for a given pin density $J_c\mathrm{}\left(B\right)\mathrm{}$ can be enhanced by maximizing the distance between the pins for $B<\mathrm{}{B}_{\phi }$.