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¢.
~l he two-dimensional steady-state distribution of lower hybrid waves is governed by the complex modified Korteweg-deVries equation, v + vttt * (lw| 2 z/)t = 0. where v is proportional to the electric field and £ and r are two spatial coordinates. The equation is studied numerically. Two types of solitary waves can arise. One is a constant phase pulse, whereas the other is an envelope solitary wave. These solitary waves are not solitons. The occurrence of the constant phase pulses points to the possibility of internal reflections due to scattering off ponderomotive density fluctuations. This necessitates solving the equation as a boundary value problem. With typical fields for lower hybrid heating of a tokamak, it is found that large reflections can occur close to the edge of the plasma.
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