Large-scale coherent magnetic fields observed in the nearby galaxies are thought to originate by a mean-field dynamo. This is governed via the turbulent electromotive force (EMF, $overline{mathcal{E}} $) generated by the helical turbulence driven by supernova (SN) explosions in the differentially rotating interstellar medium (ISM). In this paper we aim to investigate the possibility of dynamo action by the virtue of buoyancy due to a cosmic ray (CR) component injected through the SN explosions. We do this by analysing the magnetohydrodynamic simulations of local shearing box of ISM, in which the turbulence is driven via random SN explosions and the energy of the explosion is distributed in the CR and/or thermal energy components. We use the magnetic field aligned diffusion prescription for the propagation of CR. We compare the evolution of magnetic fields in the models with the CR component to our previous models that did not involve the CR. We demonstrate that the inclusion of CR component enhances the growth of dynamo slightly. We further compute the underlying dynamo coefficients using the test-fields method, and argue that the entire evolution of the large scale mean magnetic field can be reproduced with an $alpha-Omega$ dynamo model. We also show that the inclusion of CR component leads to an unbalanced turbulent pumping between magnetic field components and additional dynamo action by the Radler effect.
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