A simple theory is given for various effects of surface acoustic waves (SAW) on the characteristics of the Josephson effect in tunnel junctions which are narrow with respect to the Josephson penetration depth. We consider the case where a SAW is propagated on the substrate on which the tunnel junction is fabricated. It is shown that new types of steps in the dc-current-voltage curves of the junction biased with a current source can occur when (1) the phase velocity of the Josephson current density wave matches the velocity of SAW and (2) the phase velocity of the Josephson current density wave modified by SAW matches the phase velocity of tire electromagnetic fields. Possible applications of the new phenomena to (1) a tunable SAW transducers and (2) a tunable generator of submillimeter wave pulses are briefly discussed.
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