the curve e ), permit to sustain our explanation of the deviation of the experimental data from theoretical prediction presented in Fig.7. 

## VII. CONCLUSIONS 

We have developed a theoretical and experimental study of the Fiske step resonances in low-dissipative Josephson junctions with randomly distributed misaligned Abrikosov vor- tices. This analysis is an extension of the approach elaborated in Ref. [27] to inhomogeneous Josephson junctions. The local inhomogeneous magnetic field of misaligned Abrikosov vor- tices leads to an additional contribution to the Josephson phase difference. The influence of randomly distributed misaligned Abrikosov vortices was described in terms of the correlation area σ (see, Eq. (6)) which depends both on the Abrikosov vortex density n$_{A}$ and on the misalignment length of vortices δ . We obtained a peculiar regime as σ ≥ σ ∗ = S ( λ 2 $_{J}$γω 0 c 2 0 ) 2 characterized by a weak non-monotonic dependence of the maximum Fiske step amplitude on n$_{A}$ . In this regime the amplitude of excited electromagnetic waves in the junction a$_{n}$ ≥ 1. 

This behaviour is in a sharp contrast with a strong decrease of the maximum critical current I$_{c}$ with n$_{A}$ . The critical parameter σ ∗ depends on the dissipation γ in the junction. For low-dissipative junctions the parameter σ ∗ << S . 

We carried out the experiments on small low-dissipative Nb based Josephson tunnel junction with artificially introduced Abrikosov vortices. We measured both the critical current I$_{c}$ and the Fiske resonant steps in the I − V curves. We observed that the critical current I$_{c}$ strongly decreases with the density of Abrikosov vortices in a complete agreement with a theory, Eq. (8). 

In the absence of trapped Abrikosov vortices the experimental dependence of the ampli- tude of first Fiske resonance on B$_{‖}$ is in a good agreement with the theoretical description by Eqs. (4) and (5), where the term J$_{1}$ is taken into account. As the misaligned Abrikosov vortices were introduced in the junction, Fiske resonances were observed even in the absence of B$_{‖}$ . However, an application of a small magnetic field B$_{‖}$ allowed to increase the ampli- tude of Fiske resonances. The voltage position of the first Fiske resonance determined by a geometry of the junction, did not vary in the presence of Abrikosov vortices. The measured dependence of the maximum amplitude of first Fiske step I (1) ,max F on n$_{A}$ showed the qual- itative agreement with our theoretical analysis (Eq. (11)) i.e. with a weak non-monotonic 

