Magnetic field distribution in large two-dimensional Josephson junctions

Asymptotic approach to the theory of large (
a \ll \lambda_{J}
) two-dimensional Josephson junction is developed. As a result, the usual dc sine-Gordon equation for the rapidly changing Josephson phase difference φ is reduced to the much more simple hydrodynamic-type equations
div\{A(k)\rightarrow{k}\} = 0
, curl
\rightarrow{k} = 0
, for the slowly changing wave vector
\rightarrow{k}
(A is a simple function of
k
). The reduced equations are applied for analysis of a square-shaped Josephson junction and are solved using the rigorous boundary conditions. The obtained dependence of the junction critical current on the applied magnetic field is discussed and compared with the recent experimental data.