Fast magnetic reconnection may occur in different astrophysical sources , producing flare-like emission and particle acceleration .
Currently , this process is being studied as an efficient mechanism to accelerate particles via a first-order Fermi process .
In this work we analyse the acceleration rate and the energy distribution of test particles injected in three-dimensional magnetohydrodynamical ( MHD ) domains with large-scale current sheets where reconnection is made fast by the presence of turbulence .
We study the dependence of the particle acceleration time with the relevant parameters of the embedded turbulence , i.e. , the Alfvén speed V _ { A } , the injection power P _ { inj } and scale k _ { inj } ( k _ { inj } = 1 / l _ { inj } ) .
We find that the acceleration time follows a power-law dependence with the particle kinetic energy : t _ { acc } \propto E ^ { \alpha } , with 0.2 < \alpha < 0.6 for a vast range of values of c / V _ { A } \sim 20 - 1000 .
The acceleration time decreases with the Alfvén speed ( and therefore with the reconnection velocity ) as expected , having an approximate dependence t _ { acc } \propto ( V _ { A } / c ) ^ { - \kappa } , with \kappa \sim 2.1 - 2.4 for particles reaching kinetic energies between 1 - 100 m _ { p } c ^ { 2 } , respectively .
Furthermore , we find that the acceleration time is only weakly dependent on the P _ { inj } and l _ { inj } parameters of the turbulence .
The particle spectrum develops a high-energy tail which can be fitted by a hard power-law already in the early times of the acceleration , in consistency with the results of kinetic studies of particle acceleration by magnetic reconnection in collisionless plasmas .