## Mean magnetic field and energy balance of Parker's surface-wave dynamo
We study the surface-wave dynamo proposed by Parker (1993) as a
model for the solar dynamo, by solving equations for the mean magnetic
field , as well as for the mean 'magnetic energy
tensor' . This tensor provides information about
the energy balance, rms field strengths and correlation coefficients
between field components. The main goal of this paper is to check
whether the equations for and
are compatible, i.e. whether both have
"reasonable" solutions for a set of "reasonable" parameters. We apply
the following constraints: has a period of 22
years and, taking into account the effect of period variations, a
decay time of 10 dynamo periods, and is
marginally stable. We find that under these constraints, the equations
for and are compatible
only if, apart from turbulent transport out of the dynamo region, an
additional energy sink is introduced. If this extra term is omitted,
then marginal stability of requires a turbulent
diffusion in the convection zone of the order
cm
## Contents- 1. Introduction
- 2. Mean-field dynamo theory and resistive dissipation
- 3. The mean magnetic field
- 3.1. Equations
- 3.2. Boundary conditions
- 3.3. Solutions
- 3.4. Parameters
- 4. The mean magnetic energy
- 4.1. Equations
- 4.2. Boundary conditions
- 4.3. Constraints on the parameters
- 4.4. Solution of Eqs. (43- 44)
- 5. Case A: no resistive dissipation ()
- 6. Case B: uniform resistive dissipation ()
- 6.1. Parameters
- 6.2. Solutions
- 6.3. Root mean square magnetic field strength
- 7. Case C: reduced dissipation in the overshoot layer ()
- 8. Summary and discussion
- Acknowledgements
- Appendix
- Appendix A: dispersion relation for the mean magnetic field
- Appendix B: expressions for the mean magnetic energy tensor
- Appendix C: boundary conditions for the mean magnetic energy tensor
- References
© European Southern Observatory (ESO) 1997 Online publication: May 26, 1998 |