Relation Between Transverse and Longitudinal Normal Zone Propagation Velocities in Impregnated ${\rm MgB}_{2}$ Windings

Abstract

The transverse normal zone propagation velocity, v t, in impregnated magnets controls the 3D normal zone expansion during a quench. It is dominated by the thermal conductivities of the conductor insulation and the impregnation material. The longitudinal propagation velocity v l is mainly determined by the heat generation, critical surface of the superconductor and thermal conduction along the conductor. It has been generally assumed that the ratio v t/v l is proportional to the square root of the ratios of the corresponding effective heat conductivities. In this paper we study computationally the validity of this approach for an MgB2 wire surrounded by an epoxy layer. We take into account the finite n-value of the composite conductor in our finite element method (FEM) models. We computed v l with Whetstone-Roos formula and 1D and 2D FEM models. The 2D model was also used to compute v t. In addition to this, minimum quench energies given by the 1D and 2D FEM models were compared.