Heating due to AC losses in high-temperature superconductors

Because of low thermal conductivity of high-temperature superconducting materials, AC losses can lead to pronounced heating of the interior parts of a bulk sample. For samples cooled from their surface, it results in the strong nonuniform distribution of temperature over the thickness. The influence of this phenomenon on the AC loss value is analyzed using the approach based on the Bean critical state model complemented by the temperature dependence of the critical current density and by the heat equation. It is shown analytically and by numerical calculations that the heating increases the losses in the magnetic fields below the complete penetration field and reduces in fields above the complete penetration field. When the losses are calculated without considering the heating, the error in the loss value can achieve a few hundreds percents, even in relatively low magnetic fields of industrial frequency.