Linear and nonlinear excitations in two stacks of parallel arrays of long Josephson junctions

Abstract

We investigate a structure consisting of two parallel arrays of long Josephson junctions sharing a common electrode that allows inductive coupling between the arrays. A model for this structure is derived starting from the description of its continuous limit. The excitation of linear cavity modes known from continuous and discrete systems as well as the excitation of a new state exhibiting synchronization in two dimensions are inferred from the mathematical model of the system. The stable nonlinear solution of the coupled sine-Gordon equations describing the system is found to consist of a fluxon-antifluxon string. This is a two-dimensional phase-locked solitonic mode. Both linear and nonlinear excitations are numerically investigated and experimentally demonstrated in two stacks of five-junction arrays.

Fluxons and their interactions in a system of three stacked Josephson junctions

“…On the other hand due to coupling between junctions the fluxons and the antifluxon attract each other. 11,13,21,22 As a result of the competition between driving and interaction of junction coupling the fluxons and the antifluxon are separated by the distance, d. For ␥Ͼ0 the antifluxon is behind the fluxons and the distance between them, d, increases with the driving force. Thus in the framework of the PWLA one should distinguish the following three intervals as shown in Fig.…”

“…The repulsion or the bunching effect will be determined by checking the relative distance between the center portion of the solitons. 11,13,22 This magnitude is defined as Y ϭ(X 1 ϪX 2 )/l. Using symmetry arguments to calculate the involved integrals, the equation of motion for the distance, Y, is calculated in the same manner as Choosing the mode ͑f-a-f͒ the potential of Eq.…”

“…This interaction was first studied in the case of two junctions by Mineev et al 10 and later it was widely investigated. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] The symmetry between the two equations in the case of two junctions may hide some important aspects of the fluxon motion. In order to investigate the general properties of a system of an arbitrary number of junctions we study the case of three junctions.…”