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The flux-flow dynamics in a long Josephson junction is studied bothanalytically and numerically. A realistic model of the junction is consideredby taking into account a nonuniform current distribution, surface losses andself-pumping effects. An approximate analytical solution of the modifiedsine-Gordon equation is derived in the form of a unidirectional dense fluxontrain accompanied by two oppositely directed plasma waves. Next, somemacroscopic time-averaged quantities are calculated making possible to evaluatethe current-voltage characteristic of the junction. The results obtained by thepresent method are compared with direct numerical simulations both for thecurrent-voltage characteristics and for the loss factor modulated spatially dueto the self-pumping. The comparison shows very good agreement for typicaljunction parameters but indicates also some limitations of the method.

Surface losses and self-pumping effects in a long Josephson junction - a semi-analytical approach