Temperature Dependence of a Width of $\Delta$H = $\Delta$B Region in 5 wt.\% (Fe, Ti) Paticle-Doped MgB$_2$ Superconductor

A temperature dependence of a width of $\Delta$H = $\Delta$B region has been studied for 5 wt.\% (Fe, Ti) particle-doped MgB$_2$ superconductor. The result revealed that widths of the region are linear along temperature. Here we show the meaning of the result and details of the calculation. In previous report, we represented a theory that a width of $\Delta$H = $\Delta$B region is related with upper critical field of the superconductor, which is that pinned fluxes at volume defect are picked out and move in $\Delta$H = $\Delta$B region when a distance between them is the same as that of upper critical field. Thus, we inspected the relationship between a width of the region and upper critical field along temperature. The theory would gain another justification if temperature dependence of a width of the region is proportional to that of upper critical field. We discussed several topics for $\Delta$H = $\Delta$B region of 5 wt.\% (Fe, Ti) particle-doped MgB$_2$ superconductor, which are Fe of (Fe, Ti) particle, Bean model, volume dependence of the region, etc..