  We investigate the in-field critical current density Jc(B) of SNS Josephson
Junctions (JJs) and polycrystalline superconductors with grain boundaries
modelled as Josephson type planar defects, both analytically and through
computational time-dependent Ginzburg-Landau (TDGL) simulations in 2D and 3D.
For very narrow SNS JJs, we derive analytic expressions for Jc(B) that to our
knowledge are the first high field solutions for Jc(B) for JJs across the
entire field range up to the effective upper critical field. They generalise
the well-known (low-field) exponential junction thickness dependence for Jc
from de Gennes, often used in the Josephson relation. We extend the new
analytic expressions to describe wider junctions and confirm their validity
using TDGL optimised for high field applications. They provide an explanation
for the B^{-0.6} field dependence found for Jc(B) in high temperature
superconductors, and the Kramer dependence and inverse power-law grain size
widely found in many low temperature superconductors.
