  Modulation of the critical current across layers, Ic(H), of stacked Josephson
junctions (SJJs) as a function of an applied magnetic field parallel to the
junction planes is studied theoretically and experimentally for different
junction lengths and coupling parameters. It is shown that the Ic(H) patterns
of long SJJs are very complicated without periodicity in H. This is due to
interaction between junctions in the stack. This, in turn, gives rise to the
existence of multiple quasi-equilibrium Josephson fluxon modes and submodes
which are different with respect to the symmetry of the phase and the fluxon
sequence in SJJs. The critical current of long SJJs is multiple valued and is
governed by switching between energetically close fluxon modes/submodes. Due to
this, the probability distribution of the critical current may become wide and
may consist of multiple maxima each representing a particular mode/submode.
Experimentally, multiple branched Ic(H) patterns and multiple maxima in the Ic
probability distribution were observed for Bi2Sr2CaCu2O8+x intrinsic SJJs,
which are in a good agreement with numerical simulations and support the idea
of having different quasi-equilibrium fluxon modes/submodes in intrinsic SJJs.
