  We report a theoretical study of multiterminal Josephson junctions under the
influence of a magnetic field $B$. We consider a ballistic rectangular
two-dimensional metal $N_0$ connected by the edges to the left, right, top and
bottom superconductors $S_L$, $S_R$, $S_T$ and $S_B$, respectively. We
numerically calculate in the large-gap approximation the critical current $I_c$
versus $B$ between the left and right $S_L$ and $S_R$ for various aspect
ratios, with the top and bottom $S_T$ and $S_B$ playing the role of
superconducting mirrors. We find the critical current $I_c$ to be enhanced by
orders of magnitude, especially at long distance, due to the phase rigidity
provided by the mirrors. We obtain superconducting quantum interference
device-like magnetic oscillations. With symmetric couplings, the
self-consistent superconducting phase variables of the top and bottom mirrors
take the values $0$ or $\pi$, as for emerging Ising degrees of freedom. We
propose a simple effective Josephson junction circuit model that is compatible
with these microscopic numerical calculations. From the $I_c(B)$ patterns we
infer where the supercurrent flows in various device geometries. In particular
in the elongated geometry, we show that the supercurrent flows between all
pairs of contacts, which allows exploring the full phase space of the relevant
phase differences.
