Magneto-thermal phenomena in bulk high temperature superconductors subjected to applied AC magnetic fields

In the present work we study, both theoretically and experimentally, the temperature increase in
a bulk high temperature superconductor subjected to applied AC magnetic fields of large
amplitude. We calculate analytically the equilibrium temperatures of the bulk sample as a
function of the experimental parameters using a simple critical state model for an infinitely long
type-II superconducting slab or cylinder. The results show the existence of a limit heat transfer
coefficient (AUlim) separating two thermal regimes with different characteristics. The
theoretical analysis predicts a ‘forbidden’ temperature window within which the temperature of
the superconductor can never stabilize when the heat transfer coefficient is small. In addition,
we determine analytical expressions for two threshold fields Htr1 and Htr2 characterizing the
importance of magneto-thermal effects and show that a thermal runaway always occurs when
the field amplitude is larger than Htr2. The theoretical predictions of the temperature evolution
of the bulk sample during a self-heating process agree well with the experimental data. The
simple analytical study presented in this paper enables order of magnitude thermal effects to be
estimated for simple superconductor geometries under applied AC magnetic fields and can be
used to predict the influence of experimental parameters on the self-heating characteristics of
bulk type-II superconductors.