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We conduct global galactic–scale magnetohydrodynamical (MHD) simulations of the cosmic–ray driven dynamo. We assume that exploding stars deposit small–scale, randomly oriented, dipolar magnetic fields into the differentially rotating ISM, together with a portion of cosmic rays, accelerated in supernova shocks. Our simulations are performed with the aid of a new parallel MHD code PIERNIK. We demonstrate that dipolar magnetic fields supplied on small SN–remnant scales, can be amplified exponentially by the CR–driven dynamo to the present equipartition values, and transformed simultaneously to large galactic–scales by an inverse cascade promoted by resistive processes.
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