We consider a fractional Josephson vortex in a long 0-kappa Josephson junction. A uniformly applied bias current exerts a Lorentz force on the vortex. If the bias current exceeds the critical current, an integer fluxon is torn off the kappa-vortex and the junction switches to the voltage state. In the presence of thermal fluctuations the escape process takes place with finite probability already at subcritical values of the bias current. We experimentally investigate the thermally induced escape of a fractional vortex by high resolution measurements of the critical current as a function of the topological charge kappa of the vortex and compare the results to numerical simulations for finite junction lengths and to theoretical predictions for infinite junction lengths. To study the effect caused by the junction geometry we compare the vortex escape in annular and linear junctions.
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