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

The transverse normal zone propagation velocity, $v_{\rm t}$, 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 $v_{\rm l}$ 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 $v_{\rm t}/v_{\rm l}$ 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 ${\rm MgB}_{2}$ 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 $v_{\rm l}$ with Whetstone-Roos formula and 1D and 2D FEM models. The 2D model was also used to compute $v_{\rm t}$. In addition to this, minimum quench energies given by the 1D and 2D FEM models were compared.