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A numerical model of isotropic homogeneous turbulence with helical forcing isinvestigated. The resulting flow, which is essentially the prototype of thealpha^2 dynamo of mean-field dynamo theory, produces strong dynamo action withan additional large scale field on the scale of the box (at wavenumber k=1;forcing is at k=5). This large scale field is nearly force-free and exceeds theequipartition value. As the magnetic Reynolds number R_m increases, thesaturation field strength and the growth rate of the dynamo increase. However,the time it takes to built up the large scale field from equipartition to itsfinal super-equipartition value increases with magnetic Reynolds number. Thelarge scale field generation can be identified as being due to nonlocalinteractions originating from the forcing scale, which is characteristic of thealpha-effect. Both alpha and turbulent magnetic diffusivity eta_t aredetermined simultaneously using numerical experiments where the mean-field ismodified artificially. Both quantities are quenched in a R_m-dependent fashion.The evolution of the energy of the mean field matches that predicted by analpha^2 dynamo model with similar alpha and eta_t quenchings. For this model ananalytic solution is given which matches the results of the simulations. Thesimulations are numerically robust in that the shape of the spectrum at largescales is unchanged when changing the resolution from 30^3 to 120^3 meshpoints,or when increasing the magnetic Prandtl number (viscosity/magnetic diffusivity)from 1 to 100. Increasing the forcing wavenumber to 30 (i.e. increasing thescale separation) makes the inverse cascade effect more pronounced, although itremains otherwise qualitatively unchanged.Comment: 21 pages, 26 figures, ApJ (accepted

The Inverse Cascade and Nonlinear Alpha‐Effect in Simulations of Isotropic Helical Hydromagnetic Turbulence