A model of the multijunction ac Josephson effect in a superconductor

We present a model of the multijunction ac Josephson effect in a superconductor. Josephson predicted that at a finite applied voltage (V_o) an alternating supercurrent of frequency \omega_J =2eV_o/\hslash flows between 2 superconductors separated by an insulating layer, called the ac Josephson effect. Adding 2 or more Josephson junctions (so-called multijunction) with an applied voltage, we have shown that the resultant current (which is equivalent to the vector sum of the currents in each junction) has the same frequency as the single Josephson junction. The amplitude of the resultant current for the multijunction is increased with the increasing number of junctions. For maximum current, the phase and frequency follow the relation \omega_J t+\delta_{0N} =\left( {4n+1} \right)\pi /2. Furthermore, we have shown that in the absence of applied voltage this multijunction theory is similar to the dc SQUID theory for 2 junctions and satisfied all conditions for identical and nonidentical Josephson junctions.