Peculiarities of the stacks with finite number of intrinsic Josephson junctions

We study the breakpoint region on the outermost branch of current-voltage characteristics of the stacks with different number of intrinsic Josephson junctions. We show that at periodic boundary conditions the breakpoint region is absent for stacks with even number of junctions. For stacks with odd number of junctions and for stacks with nonperiodic boundary conditions the breakpoint current is increased with number of junctions and saturated at the value corresponding to the periodic boundary conditions. The region of saturation and the saturated value depend on the coupling between junctions. We explain the results by the parametric resonance at the breakpoint and excitation of the longitudinal plasma wave by the Josephson oscillations. A way for the diagnostics of the junctions in the stack is proposed.