A zigzag boundary between a $d_{x^2 - y^2}$ and an s-wave superconductor is believed to behave like a long Josephson junction with alternating sections of 0 and π symmetry. We calculate the field-dependent critical current of such a junction, using a simple model. The calculation involves discretizing the partial differential equation for the phase difference across a long 0-π junction. In this form, the equations describe a hybrid ladder of inductively coupled small 0 and π resistively and capacitively shunted Josephson junctions (RCSJ's). The calculated critical critical current density Jc(Ha) is maximum at non-zero applied magnetic field Ha, and depends strongly on the ratio of Josephson penetration depth λJ to facet length Lf. If λJ/Lf ≫1 and the number of facets is large, there is a broad range of Ha where Jc(Ha) is less than 2% of the maximum critical current density of a long 0 junction. All of these features are in qualitative agreement with recent experiments. In the limit λJ/Lf →∞, our model reduces to a previously-obtained analytical superposition result for Jc(Ha). In the same limit, we also obtain an analytical expression for the effective field-dependent quality factor QJ(Ha), finding that \(Q_J(H_a) \propto \sqrt{J_c(H_a)}\). We suggest that measuring the field-dependence of QJ(Ha) would provide further evidence that this RCSJ model applies to a long 0-π junction between a d-wave and an s-wave superconductor.