Analytic solution of an oscillatory migratory α2 stellar dynamo
Abstract
Context. Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant α effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant α.
Aims: We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant α, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries.
Methods: We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions.
Results: 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 α.
Conclusions: 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 α.
- Publication:
-
Astronomy and Astrophysics
- Pub Date:
- February 2017
- DOI:
- 10.1051/0004-6361/201630033
- arXiv:
- arXiv:1611.02671
- Bibcode:
- 2017A&A...598A.117B
- Keywords:
-
- dynamo;
- magnetohydrodynamics (MHD);
- magnetic fields;
- Sun: magnetic fields;
- stars: magnetic field;
- Astrophysics - Solar and Stellar Astrophysics;
- Physics - Fluid Dynamics
- E-Print:
- 7 pages, 4 figures, published in A&