We present a parameter study of the magnetohydrodynamical dynamo driven by cosmic rays in the interstellar medium (ISM) focusing on the efficiency of magnetic field amplification and the issue of energy equipartition between magnetic, kinetic and cosmic ray (CR) energies. We perform numerical CR-MHD simulations of the ISM using the extended version of ZEUS-3D code in the shearing box approximation and taking into account the presence of Ohmic resistivity, tidal forces and vertical disk gravity. CRs are supplied in randomly distributed supernova (SN) remnants and are described by the diffusion-advection equation, which incorporates an anisotropic diffusion tensor. The azimuthal magnetic flux and total magnetic energy are amplified depending on a particular choice of model parameters. We find that the most favorable conditions for magnetic field amplification correspond to magnetic diffusivity of the order of $3times 10^{25} cm^2s^{-1}$, SN rates close to those observed in the Milky Way, periodic SN activity corresponding to spiral arms, and highly anisotropic and field-aligned CR diffusion. The rate of magnetic field amplification is relatively insensitive to the magnitude of SN rates in a rage of spanning 10% up to 100% of realistic values. The timescale of magnetic field amplification in the most favorable conditions is 150 Myr, at galactocentric radius equal to 5 kpc. The final magnetic field energies fluctuate near equipartition with the gas kinetic energy. In all models CR energy exceeds the equipartition values by a least an order of magnitude, in contrary to the expected equipartition. We suggest that the excess of cosmic rays can be attributed to the fact that the shearing-box does not permit cosmic rays to leave the system along the horizontal magnetic field.
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