Dynamics of Magnetic Flux Tubes and the Solar Dynamo

A magnetic flux tube is treated as a body in addition to a confined field. As a field, both the cyclonic convection (α-effect) and differential rotation (Ω-effect) play a role. As a body, the tube experiences not only a buoyant force, but also a dynamic pressure of downflows above the tube. When these two dynamic effects are incorporated into the αΩ dynamo equation by adding to it two diffusion terms, we obtain the dynamic equation of a flux tube. We solve this equation by using the linear perturbation theory. The main findings are: (i) unlike the pure magnetic field, the magnetic field in the flux tube can grow up to a critical value in the convection zone when downflows are present; (ii) like the solar dynamo theory, the period is determined by the cyclonic convection and the differential rotation; (iii) the growth of the magnetic field in the flux tube is caused by both the αΩ-effect and the anti-diffusion effect due to the dynamic pressure of downflows; (iv) a magnetic flux tube has an ascending phase marked by a positive growth rate, and a decay phase marked by a nonpositive growth rate; (v) two branches of the butterfly diagram occur naturally as two branches of the magnetic flux tube wave. These results are in good agreement with the relevant observations, including helioseimic observations. Subject headings: Sun: interior — Sun: magnetic fields