Magnetic-flux propagation on a Josephson transmission line

Abstract

Effects of peening on magneticflux density in a metallic glassThe propagation of magnetic flux pulses along the insulating barrier of a long Josephson junction is investigated both theoretically and experimentally. The theoretical study includes applications of both (i) the recently developed "inverse-scattering-transform method" (ISTM) to the corresponding sine-Gordon equation in characteristic (light cone) coordinates and (ii) Whitham's method (WM) of averaged Lagrangian analysis to the sine-Gordon equation in laboratory coordinates. As the number of solitons (flux quanta) in the pulse becomes large, the ISTM becomes numerically unwieldy while WM becomes more accurate; thus these two analytical tools are complementary. WM has the advantage of being readily modified to account for small dissipative effects. Our experimental observations of magnetic-flux propagation were entirely restricted to the "large-amplitude limit" in which the average of the ac Josephson current is effectively zero. In this limit, WM indicates pulse propagation with linear dissipation. This result has been confirmed on a Josephson transmission line for which it was possible to predict pulse propagation from parameters which were measured independently on small crossed strip junctions. PACS numbers: 74.35.+x, 84.20.Pc, 85.4D.Ek the terms a¢t and {3¢ut; and in the limit a = 0 and {3= 0, Eq. (1.1) reduces to the sine-Gordon equation ¢xx -¢tt =sin¢.

Long Josephson tunnel junctions with doubly connected electrodes

“…We will analyze the general cases when all A. Boundary conditions Figure 3 shows one elementary cell of the equivalent circuit for a static Josephson junction transmission line. Classically, the two inductances have been merged in their parallel combination 23,24 so that the role played by each supercurrent separately was lost; however, for our purposes it is mandatory to keep the distinction, since, in general, L b = L t . In the absence of an external in-plane field, H app = 0, the magnetic flux j linked to the cell is…”

“…(22) reduces tô Figure 5 displays the numerically computed zero-field energŷ H sG versus ι 2 for symmetric in-line junctions having different normalized lengths ; for > 2π , the numerical findings are very well approximated by Eq. (23). As the expansion in the right-hand side of Eq.…”

Future Directions of Nonlinear Dynamics in Physical and Biological Systems

“…Comparison of exact solution (23) (25) After substitution (21) into (25) and taking into account that factor a tends to 1 for sufficiently large amplitude, we find that fa coincides with exact solution (23).…”

“…The first succeeded measurement of a many-fluxon waveform was made in 1976 by Scott and his collaborators [25]. While the experimental detection of a single fluxon was performed in 1982 by Matsuda and Uehara [26].…”

Josephson fluxon pump: Theoretical aspects and experimental implementation of elementary flux quanta generator with BSCCO

“…Because of the useful properties, the Josephson systems have been under intensive attention of the scientific community [1][2][3][4]. A current-driven flux flow generator demonstrated in [2] and flux flow oscillator (FFO) has been experimentally realized [3,4].…”