The strength and polarity of the solar magnetic field change during the solar activity cycle, as does the direction of the magnetic field in the convective zone. Moreover, the magnetic field has a different structure (direction) in the different parts of the convective zone.
Solar magnetic fields are thought to be generated in the thin transition region (called the overshoot region) between the solar convective and radiative zones, somewhere about 200,000 km below the visible solar surface. The magnetic field in the overshoot region is mostly horizontal. The classical Babcock model (see, p14, p826 in [2]) gives an idealized description of the solar magnetic field evolution. In the framework of this empirical model, the large-scale magnetic field of the Sun is idealized as a north-south dipole (at the beginning of every solar cycle). Under the surface, field lines go down to the bottom of the convective zone near the N and S solar poles and pass along meridians in the overshoot region. The solar equator rotates faster than its poles (solar differential rotation). Because of the high electric conductivity of solar plasma, magnetic field lines follow plasma flows (the frozen-in condition), and, gradually, they became twisted into spirals by the differential rotation. Thus, near the maximum of solar activity, the magnetic field lines in the overshoot region are horizontal but they are tilted to the meridians. At that time the Sun resembles a ball of twine. (Look around for a figure showing the Babcock model (eg, p826 in [2]). That would help you to understand what I am talking about).
Apart from that, magnetic field lines in the bottom of the convective zone are lifted up (or drawn down) and twisted by the convective flows (the twist is a result of the Coriolis force action). Thus, although magnetic fields in the overshoot region remain mostly horizontal, they become highly twisted and braided.
The magnetic fields also get organized into isolated flux tubes. The mutual action of the differential rotation and twist amplifies the magnetic field. Eventually, a portion of the flux tube may become buoyant and erupt, generating a pair of sunspots of opposite polarity (bipolar active region) in the photosphere. In the convective zone, the magnetic field of this erupted flux tube is mostly vertical (see, eg [3] for a discussion of the shape of magnetic flux tube in the convective zone). Recent numerical calculations (eq, [4]) also predict that interacting with the plasma in the convective zone, a rising magnetic flux tube may fragment into several smaller flux tubes, twisted in the opposite direction.
Magnetic fields remain frozen-in the solar plasma throughout the convective zone. At the top of each convective cell, plasma flows from the center of the cell toward its boundary. Under such conditions, the weak vertical magnetic fields sweep from the center of the convective cells and concentrate in the boundaries between cells (eg, [5]). The chromospheric network commonly observed on the quiet Sun is the result of this flux redistribution by the supergranular convective motions. The typical horizontal size of the supergranular cells is about 20,000 km and every cell is surrounded by a vertical magnetic field. If the vertical size of the supergranular cell is close to its horizontal size, one should expect to see mostly vertical magnetic fields, concentrated in the boundaries of the supergranular cells up to about 20,000 km under the photosphere. Below that, the magnetic field is, probably, not so regular.
Recent numerical simulations (eg, [6]) show a complexity of the convective flows in the convective zone. The convective cells are irregular in shape, non radial, and they show opposite flow vorticity, etc. Since the magnetic field is frozen in the plasma, one should expect to see no regular structure of the weak magnetic field in this part of the convective zone, at least not on a small spatial scale.
The existing computational resources do not allow us to simulate evolution of the magnetic fields in the convective zone in great detail. Present numerical simulations concentrate either on the short-time plasma-magnetic field interaction in a small limited volume somewhere in the convective zone [6], or study the evolution of the solar magnetic field over the whole solar cycle in an idealized axisymmetric case. The examples of the axisymmetric numerical simulations showing direction of the magnetic field in the convection zone as well as its evolution may be found in [7,8]. Although the axisymmetric models show some agreement with the observations, a snap-shot of the convective zone should reveal a much more complicated structure of the magnetic field there.
References:
1. Several methods have been proposed to derive characteristics of the magnetic field under the solar surface, e.g. Duvall, T. et al, Sol. Physics, 1997, 170, 63.
2. Review papers in the "Solar Interior and Atmosphere", Eds. A.N. Cox, W.C. Livingston, M.S. Matthews, 1991, The Univ. of Arizona Press
3. Fan, Y. et al, 1994, ApJ, 436, 907
4. Longcope D.W., et al, 1996, ApJ, 464, 999
5. Galloway, D.J., Moore, D.R., 1979, Geophys. Astrophys. Fluid Dyn., 12 73
6. Brummell, N.H., et al, 1996, ApJ, 473, 494
7. Stix, M., 1976, in Proc. IAU Symp. 71, p.367
8. Rudiger, G., Brandenburg, A., A&A, 1995, 296, 557
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