Self-Field Effects in a Josephson Junction Model for ${J_\text{c}}$ in REBCO Tapes

We have modeled the effects of self-field on the critical current density
$\boldsymbol{J_\text{c}}$
in high temperature superconducting REBCO tapes, by considering them as a collection of Josephson junctions (JJs) in parallel. We have used a 2D JJ framework for each junction and included their component self-field effects using the well known expression for the magnetic field produced by a thin strip. We provide computational and analytic expressions for the spatial distribution of
$\boldsymbol{J_\text{c}}$
, enabling us to calculate the critical current of coated conductors over the whole field range. We find that
$\boldsymbol{J_\text{c}}$
in self field for thin tapes is broadly independent of the width but strongly dependent on the thickness of the tape. For example, if a tape thickness is doubled, even if
$\boldsymbol{J_\text{c}}$
is unchanged in high field, we expect the self-field
$\boldsymbol{J_\text{c}}$
to drop by
$\sim \!20 \,\%$
because of the larger self-field produced. Our results are compared to experimental results for technological coated conductors from the literature and good agreement is found.