Scattering of quasi-one-dimensional solitons on impurities in large Josephson junctions

Abstract

Fluxon transmission through impurities of different shape in a quasi-onedimensional long Josephson junction is investigated. The junction width is significantly less than its length but, at the same time, is of the order of the Josephson penetration length λ J or exceeds it. The retrapping current on the impurities of the point, line and rectangular shape is computed as a function of the junction width both numerically and analytically. Good agreement between the analytic formulae and the numerical simulation results for the intermediate (several λ J ) junction width is observed.

Leapfrogging of electrical solitons in coupled nonlinear transmission lines: effect of an imperfect varactor

“…The effects of a localized impurity on soliton signals in NLTLs have been investigated in several previous works; it is there well established that a localized impurity will always accelerate a soliton approaching the impurity when it is a structural default in the defective electrical component [25,26]. This response of KdV soliton to the presence of a localized impurity in the NLTL is actually universal; indeed, similar behaviours are predicted in many other distinct physical systems such as Josephson junction transmission lines [44,45], Frenkel-Kontorova systems [46,47] and double-well systems [48].…”

“…(46) to (48) into Eqs. (44) and (45) and integrating once with respect to z, we obtain the following equations to the order 0( 3 ):…”

Radiation emission due to fluxon scattering on an inhomogeneity in a large two-dimensional Josephson junction

“…Thus, with the pair of equations (17) and (18) one has the complete formula for the energy calculation. From this point it is possible to proceed to the emitted radiation studies for the particular shapes of Ω.…”

“…At this point we can substitute the actual expressions ( 23) and ( 24) that corresponds to the rectangular impurity into Eqs. (17) and (18). Then the radiation function (18) in the moving frame is obtained after the consecutive integration over the y, τ , and ξ variables:…”

“…Moreover, fluxon dynamics in the large area JJ is an interesting and important problem in its own right. It has been studied in different contexts such as dynamical properties 16,17 , pinning on impurities 18 and applications 19,20 . However, up to now the radiation emission due to the 2D fluxon scattering on the impurity has been studied in detail only for the special case of the point-like impurity described by the Dirac δ-function 21 .…”