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5
Coupled Structures of Long Josephson
Junctions
G. Carapella
G. Costabile
ABSTRACT
Long Josephson junctions are very attractive non-linear systems where soli-
tonic dynamics [14] is fully developed and directly related to experimentally
observable quantities. In this system the soliton occurs as a solution of the
sine-Gordon equation describing the long junction; physically, it represents
a fluxon, a current vortex enclosing a flux quantum. Coherent motion of
fluxons is an intriguing subject, also because of its possible practical appli-
cations. In fact, microwave and far infrared fluxon oscillators [15] greatly
enhance their performances if such a motion is established. Here we will con-
sider three different coupled structures of long Josephson junctions where
coherent fluxon motion is experimentally demonstrated.
1 Stacks of two long Josephson junctions
In this system, the coupling between junctions originates from the screen-
ing currents in mon electrode when its thickness is about equal or
smaller than the London ration depth λL. This “ic” coupling,
which has been formalized in a model [16] for the multilayered structures,
accounts for many dynamical phenomena in long stacked junctions, includ-
ing synchronization of fluxon motion.
The physical system and its model
If we refer voltage and current polarities to the intermediate electrode in the
stack with “double overlap” geometry shown in Fig. 1, the model equations
are [16], [9]
ϕxx −ϕtt = sin(ϕ)+αϕt + εψxx −γA,
ψxx −ψtt = sin(ψ)+αψt + εϕxx + γB,
()
ϕx (0) = ϕx (l)=η(1 + ε) ,
ψx (0) = ψx (l)=η(1 + ε) ,
. Christiansen, . Sørensen, and . Scott (Eds.): LNP 542, pp. 103−119, 2000.
Springer-Verlag Berlin Heidelberg 2000
104G. Carapella, G. Costabile
ϕ, H
z
x
A 2
W A
0 B d
y
3 B ψ,
FIGURE 1. Stack with “double
overlap” geometry.
where ε, −1 <ε<0, is the ic coupling constant, defined as a
fun