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Fast magnetic reconnection may occur in different astrophysical sources,producing flare-like emission and particle acceleration. Currently, thisprocess is being studied as an efficient mechanism to accelerate particles viaa first-order Fermi process. In this work we analyse the acceleration rate andthe energy distribution of test particles injected in three-dimensionalmagnetohydrodynamical (MHD) domains with large-scale current sheets wherereconnection is made fast by the presence of turbulence. We study thedependence of the particle acceleration time with the relevant parameters ofthe embedded turbulence, i.e., the Alfv\'en speed $V_{\rm A}$, the injectionpower $P_{\rm inj}$ and scale $k_{\rm inj}$ ($k_{\rm inj} = 1/l_{\rm inj}$). Wefind that the acceleration time follows a power-law dependence with theparticle kinetic energy: $t_{acc} \propto E^{\alpha}$, with $0.2 < \alpha <0.6$ for a vast range of values of $c / V_{\rm A} \sim 20 - 1000$. Theacceleration time decreases with the Alfv\'en speed (and therefore with thereconnection velocity) as expected, having an approximate dependence $t_{acc}\propto (V_{\rm A} / c)^{-\kappa}$, with $\kappa \sim 2.1- 2.4$ for particlesreaching kinetic energies between $1 - 100 \, m_p c^2$, respectively.Furthermore, we find that the acceleration time is only weakly dependent on the$P_{\rm inj}$ and $l_{\rm inj}$ parameters of the turbulence. The particlespectrum develops a high-energy tail which can be fitted by a hard power-lawalready in the early times of the acceleration, in consistency with the resultsof kinetic studies of particle acceleration by magnetic reconnection incollisionless plasmas.

Properties of the First-order Fermi acceleration in fast magnetic reconnection driven by turbulence in collisional MHD flows