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A study of large scale dynamo growth rates from numerical simulations and implications for mean field theories

Understanding large scale magnetic field growth in turbulent plasmas in the magnetohydrodynamic limit is a goal of magnetic dynamo theory. In particular, assessing how well large scale helical field growth and saturation in simulations matches that predicted by existing theories is important for progress. Using numerical simulations of isotropically forced turbulence without large scale shear with the implications, we focus on several aspects of this comparison that have not been previously tested: (1) Leading mean field dynamo theories which break the field into large and small scales predict that large scale helical field growth rates are determined by the difference between kinetic helicity and current helicity with no dependence on the non-helical energy in small scale magnetic fields. Our simulations show that the growth rate of the large scale field from fully helical forcing is indeed unaffected by the presence or absence of small scale magnetic fields amplified in a precursor non-helical dynamo. However, because the precursor non helical dynamo in our simulations produced fields that were strongly sub-equipartition with respect to the kinetic energy, we cannot yet rule out the potential influence of stronger non- helical small scale fields. (2) We have identified two features in our simulations which cannot be explained by the most minimalist versions of two-scale mean field theory: (i) fully helical small scale forcing produces significant non-helical large scale magnetic energy and (ii) the saturation of the large scale field growth is time-delayed with respect to what minimalist theory predicts. We comment on desirable generalizations to the theory in this context and future desired work.