Dynamo instability and feedback in a stochastically driven system
In §2 and 3, the feedback mechanism in the magnetohydrodynamic context is considered. It is supposed that a velocity field lacking reflexional symmetry is generated in an electrically conducting fluid by a random body force of known statistical properties.Conditions are then conducive to the growth of large scale magnetic field perturbations. The growth is limited by the fact that the growing Lorentz force progressively modifies the statistical structure of the velocity field, until ultimately a statistical equilibrium is achieved. It is shown that in this equilibrium the magnetic energy density may exceed the kinetic energy density by a factor O(L/ℓ) ≫ 1, where L is the scale of the magnetic field, and ℓ the scale of the turbulence.
KeywordsVelocity Field Fourier Component Eddy Diffusivity Kinetic Energy Density Reflexional Symmetry
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