Two ways to model voltage-current curves of adiabatic MgB2 wires

Usually overheating of the sample destroys attempts to measure voltage-current curves of conduction cooled high critical current MgB2 wires at low temperatures. Typically, when a quench occurs a wire burns out due to massive heat generation and negligible cooling. It has also been suggested that high n values measured with MgB2 wires and coils are not an intrinsic property of the material but arise due to heating during the voltage-current measurement. In addition, quite recently low n values for MgB2 wires have been reported. In order to find out the real properties of MgB2 an efficient computational model is required to simulate the voltage-current measurement. In this paper we go back to basics and consider two models to couple electromagnetic and thermal phenomena. In the first model the magnetization losses are computed according to the critical state model and the flux creep losses are considered separately. In the second model the superconductor resistivity is described by the widely used power law. Then the coupled current diffusion and heat conduction equations are solved with the finite element method. In order to compare the models, example runs are carried out with an adiabatic slab. Both models produce a similar significant temperature rise near the critical current which leads to fictitiously high n values