Magnetic helicity evolution in a periodic domain with imposed field

Abstract

In helical hydromagnetic turbulence with an imposed magnetic field (which is constant in space and time) the magnetic helicity of the field within a periodic domain is no longer an invariant of the ideal equations. Alternatively, there is a generalized magnetic helicity that is an invariant of the ideal equations. It is shown that this quantity is not gauge invariant and that it can therefore not be used in practice. Instead, the evolution equation of the magnetic helicity of the field describing the deviation from the imposed field is shown to be a useful tool. It is demonstrated that this tool can determine steady state quenching of the alpha-effect. A simple three-scale model is derived to describe the evolution of the magnetic helicity and to predict its sign as a function of the imposed field strength. The results of the model agree favorably with simulations.

8 pages, 4 figures, Phys. Rev. E

References in corpus (9)

• The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence
• Magnetic Helicity Conservation and Astrophysical Dynamos
• Dynamic nonlinearity in large scale dynamos with shear
• Gravitational instability of finite isothermal spheres
• Dynamical Quenching of the ${\alpha }^2$ Dynamo
• The effect of hyperdiffusivity on turbulent dynamos with helicity
• Search for non-helical disc dynamos in simulations
• Understanding Helical Magnetic Dynamo Spectra with a Nonlinear Four-Scale Theory
• Apparent suppression of turbulent magnetic dynamo action by a dc magnetic field

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• Magnetic helicity and cosmological magnetic field
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• Suppression of small scale dynamo action by an imposed magnetic field
• Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation
• Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence
• Dynamo effect in unstirred self-gravitating turbulence
• Bihelical Magnetic Relaxation and Large Scale Magnetic Field Growth
• Turbulent magnetic decay controlled by two conserved quantities
• Importance of magnetic helicity in dynamos
• Distribution function of nuclei from $e^{\pm }$ scattering in the presence of a strong primordial magnetic field