Superconducting dc SQUID interferometer in magnetic field

The theory of a superconducting quantum interferometer placed in an external magnetic field H _e, which takes into account the finite geometrical dimensions of the system (the width of tunnel junctions) L₁ and L₂, and the inner surface of the interferometer's ring σ is presented. The exact equations describing the behaviour of a finite dimensions interferometer are formulated. In the limit of a strong external field ( H_e ≫ 1), the analytical solution of the problem is given. The dependences of the critical stationary current I_max, which passes through the interferometer are expressed as a function of the external field H_e for different values of L₁, L₂, σ. The dependence of the internal magnetic field inside the interferometer H₀ as a function of H_e and transport current I is found. In the limiting case of point contacts ( L₁ = L₂ ≪ 1) a comparison of the results obtained in the present paper and of previous results on this subject is made.