The maximum current that can be carried by a long unbiased superconducting tunnel junction as a function of applied magnetic field has been calculated. A symmetric junction geometry was assumed for which the boundary conditions relate the space derivatives of the phase difference φ at the two ends. In addition, we graph the current density distribution within the junction when the total current is maximum, and we show the shape of the current vortices in the large-field case and the details of the self-limiting of the tunnel current as a function of junction length in zero applied field.
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Owen et al. (1967) studied this question.
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