Conservation of Magnetic Helicity and Its Constraint on $α$-Effect of Dynamo Theory

Details Conservation of Magnetic Helicity and Its Constraint on $α$-Effect of Dynamo Theory Conservation of Magnetic Helicity and Its Constraint on $α$-Effect of Dynamo Theory

2000-11-29

arxiv.org/abs/astro-ph/0011548v2

Astronomy and Astrophysics

Astrophysics

31 pages, 5 figures, submitted to ApJ

Scientific paper

Dynamical studies of MHD turbulence on the one hand, and arguments based upon magnetic helicity on the other, have yielded seemingly contradictory estimates for the $\alpha$ parameter in turbulent dynamo theory. Here we show, with direct numerical simulation of three-dimensional magnetohydrodynamic turbulence with a mean magnetic field, $\OB$, that the constraint on the dynamo $\alpha$-effect set by the magnetic helicity is time-dependent. A time-scale $t_c$ is introduced such that for $t - < \b \cdot \nabla \times \b >)$; for $t>t_c$, the classical result of the $\alpha$-coefficient given by the Mean-Field Electrodynamics is reduced by a factor of $1/({R_m |\OB|^2/v_{rms}^2})$, as argued by Gruzinov & Diamond, Seehafer and Cattaneo & Hughes. Here, $R_m$ is the magnetic Reynolds number, $v_{rms}$ the rms velocity of the turbulence, $\tau_{cor}$ the correlation time of the turbulence, and $\overline B$ is in velocity unit. The applicability of and connection between different models of dynamo theory are also discussed.

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