Maximum performance of an active magnetic regenerator

Magnetocaloric materials change their temperature when a magnetic field is applied or removed, which allows building a magnetic cooling device. We derive an analytical expression for the maximum heat that such a material can transfer in one cooling cycle by investigating the operation of a simplified active magnetic regenerator (AMR). The model largely only depends on the adiabatic temperature change, the specific entropy change, and the temperature span between the hot and cold reservoirs. While this expression overestimates the performance of a real AMR due to its simplification, it can predict an upper limit of any AMRs' performance independent of the implementation details. Based on this, we calculate the upper limit of the cooling power of magnetic cooling devices at any temperature span, frequency, mass, and material. This upper limit is used to predict how the thermal span is scaling with the applied magnetic field, and it can be utilized for the optimization of the magnetic field source. Additionally, we confirm that the product of isothermal entropy and adiabatic temperature change, already used in the literature, is a suitable figure of merit for magnetocaloric materials.