Analytic solution of an oscillatory migratory alpha^2 stellar dynamo

Abstract

Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant alpha effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant alpha. We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant alpha, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries. We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions. The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of alpha. The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant alpha.

arXiv comment7 pages, 4 figures, published in A&A

References in corpus (17)

• Astrophysical magnetic fields and nonlinear dynamo theory
• The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence
• Dynamic nonlinearity in large scale dynamos with shear
• Effects of enhanced stratification on equatorward dynamo wave propagation
• Small-scale magnetic helicity losses from a mean-field dynamo
• On the cause of solar-like equatorward migration in global convective dynamo simulations
• Large scale dynamos with helicity loss through boundaries
• Dynamo-driven plasmoid ejections above a spherical surface
• Oscillatory migrating magnetic fields in helical turbulence in spherical domains
• Oscillatory mean-field dynamos with spherically symmetric, isotropic alpha
• Turbulent dynamos in spherical shell segments of varying geometrical extent
• Magnetic helicity transport in the advective gauge family
• Intense bipolar structures from stratified helical dynamos
• Turbulent reconnection of magnetic bipoles in stratified turbulence
• Mean-Field Modeling of ${\alpha }^2$-Dynamo Coupled with Direct Numerical Simulations of Rigidly Rotating Convection
• Robustness of oscillatory ${\alpha }^2$ dynamos in spherical wedges
• Sharp magnetic structures from dynamos with density stratification

Cited by in corpus (10)

• Advances in mean-field dynamo theory and applications to astrophysical turbulence
• Estimating activity cycles with probabilistic methods II. The Mount Wilson Ca H&K data
• Turbulent processes and mean-field dynamo
• Stellar dynamos in the transition regime: multiple dynamo modes and anti-solar differential rotation
• Magnetic helicity and fluxes in an inhomogeneous alpha squared dynamo
• Budget equations and astrophysical nonlinear mean-field dynamos
• Reality of inverse cascading in neutron star crusts
• Magnetic helicity fluxes in dynamos from rotating inhomogeneous turbulence
• Shaping core dynamos in A-type stars: The role of dipolar fossil fields
• Magnetic dynamos powered by white dwarf superficial convection