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Lately a specific kind of blazars drew the attention of the gamma-ray astronomy community: the extreme TeV BL Lacs, blazars that present an extremely energetic and hard emission at very high-energy. Explaining their features is still an open challenge, in fact the most used phenomenological models have difficulties to satisfactorily reproduce their SED. Based on a scenario we have recently proposed, we suppose that the non-thermal particles are firstly accelerated by a jet recollimation shock, which induces turbulence in the rest of the jet. Non-thermal particles are further accelerated by the turbulence, which hardens the particle spectra and accordingly the radiative emission. Given the physical properties of the plasma, as inferred by emission models, we expect a strong impact of the accelerating particles on the turbulence. Assuming isotropy and homogeneity, the interaction between non-thermal particles and turbulence and their spectra is modeled solving a system of two non-linear, coupled Fokker-Planck equations, while the radiative emission is calculated through the Synchrotron Self Compton model. The emission predicted by our model is then compared with the prototype extreme TeV BL Lac object 1ES 0229+200 and the parameters obtained to reproduce its SED are in line with the expectations.