On the evolution of thermo-electromagnetic state of a superconductor with a heat-coupled Ginzburg-Landau model

Creative Commons License

Coşkun E.

PHYSICA A: STATISTICAL MECHANICS AND ITS APPLICATIONS, sa.703, ss.1-14, 2026 (SCI-Expanded, Scopus)

Özet

The isothermal time-dependent Ginzburg–Landau model studied in our earlier works was
coupled with an appropriately formulated heat equation that takes into account temperature
dependence of specific heat, thermal conductivity and Ginzburg–Landau parameter with a
source term representing Joule heating due to normal current. The parameters are chosen
from niobium. The resulting Heat-Coupled Model(HTDGL) was numerically integrated with
what we call ‘method of planes’ using high-order integration schemes of ODESUITE. Numerical
experiments shed light on temporal evolution of thermo-electromagnetic state of superconduc-
tor. In particular, it was shown that both zero-field(ZF) and field-cooled(FC) procedures lead
to stationary configuration of vortices having hexagonal pattern, as observed experimentally,
with almost the same Abrikosov constant. Furthermore, it was observed that magnetic field
penetration in FC procedure induces normal current around the boundary of sample, which in
turn leads to rise of temperature near the edges in early stages of temporal evolution. Oscillatory
applied field versus average temperature hysteresis loop shows that vortex motion leads to local
increase of temperatures for both pure and impure superconductors with pinning sites and that
interaction with pinning sites plays the greater role in thermal fluctuations due to induced local
Joule heat. Fluctuations in the number of vortices were also observed under oscillatory field.