In this paper, the two-scale analytical method of mean field electrodynamics and some research results, such as α, β effects and α2, α-w solar dynamo models, are reviewed.

The solar dynamo, which explains the origin and the evolution of all magnetic fields observed on the sun, is the fundamental and essential question of Solar Physics.

In comparison with typical solar spots, three distinct features of starspots, huge area, long life-time and the possibility for them to emerge in polar region, have given a striking challenge to the solar dynamo theory.

A relic field can help us to explain many asymmetries in solar activities, such as the north-south asymmetries of solar magnetic activities, active longitudes and holes, low-latitude coronal holes, Maunder minimum, etc. In addition it can affect the distribution and evolution of solar surface magnetic field by changing the boundary conditions of solar dynamo.

As a result, it is still uncertain where and how the solar dynamo operates.

(I)CMEs are multi-dimensional, multi-parameter, and multi-scale phenomena related to the solar dynamo, corona, and heliosphere.

Planetary influences are ruled out; the variability is intrinsic and is described by the solar dynamo.

In this paper we demonstrate that resonance may play a crucial role in the dynamics of the climate system, by using the output from a nonlinear solar dynamo model as a weak input to a simplified climate model.

A key feature of this procedure is that the original time series is first transformed into a symmetrical space where the dynamics of the solar dynamo are unfolded in a better way, thus improving the model.

The magnetic fluid in the solar convection zone tends to be driven to float by the magnetic buoyancy of the toroidal magnetic field, which is produced by the ω-effect of the solar dynamo. Consequently, phenomena of active regions in bipolar magnetic fields of sunspots will be formed on the surface of the sun.We see that the dimension of a buoyant magnetic fluid-mass which produces bipolar sunspots, may be large enough as to be comparable to the supergranulation, and meanwhile, that turbulence in this mass...

The magnetic fluid in the solar convection zone tends to be driven to float by the magnetic buoyancy of the toroidal magnetic field, which is produced by the ω-effect of the solar dynamo. Consequently, phenomena of active regions in bipolar magnetic fields of sunspots will be formed on the surface of the sun.We see that the dimension of a buoyant magnetic fluid-mass which produces bipolar sunspots, may be large enough as to be comparable to the supergranulation, and meanwhile, that turbulence in this mass may probably exist as indicated by the decaying time of sunspot magnetic fields. Therefore, it is possible for us to describe the buoyant process of a magnetic fluid-mass as a motion of mean flow. Since a solar radial gradient of turbulent magnetic diffusivity is there in the solar convection zone (Stix, 1976, Fig. 1), the difference of turbulent magnetic diffusivity across the boundary of the fluid mass will grow up with the increasing height of elevation. Thus, a large gradient of turbulent magnetic diffusivity comes to exist at the boundary of this mass during it striving its way up.Generally speaking, the elevating magnetic fluid will form an irregularly shaped fluid mass of convective material. Our purpose is only to study the magnetic characteristics at the boundary of the fluid mass when it traversed the toroidal field. Therefore, we discuss merely an idealized model of spherical fluid mass with average radius γ0 and equilibrium elevating velocity vc, neglecting other fine characteristics of irregular shaping of the mass and its possible inner circulations etc.The magnetic Reynolds number of the elevating process for a fluid mass is Rm=vcγ0/η, here η is the turbulent magnetic diffusivity. Our result is for the motion with small magnetic Reynolds number, Rm<1. We have noticed from the well-known induction equation that the toroidal magnetic field is to be disturbed by the striking gradient of the turbulent magnetic diffusivity across the boundary of the fluid mass after its passing over. We develop the induction equation in the coordinate system moving with the elevating fluid mass. Taking the total magnetic field as B', we have B' = B* + B, here B* is the toroidal magnetic field and B is the additional magnetic field induced by the disturbance of the fluid mass. Substituting B'=B* + it into the induction equation, we get equation (3.5) which describes the magnetic field B. By use of the condition of cylindrical symmetry in this problem, we solve equation ' (3.5) finally to achieve formula (3.22). It is clearly shown that a magnetic flux ring has formed around the surface of the fluid mass (Pig. 4). The final result is that two oppositely polarized magnetic regions will emerge on the surface of the sun as the magnetic ring is brought to the top of solar convection zone by the elevating fluid mass. According to this reason, we attempt to explain the phenomena why the bipolar magnetic fields of sunspots are concentrated in small bundles of high field strength. By means of the characteristics of the magnetic ring and toroidal magnetic field, other characteristics of bipolar magnetic field of sunspots may also be explained extensively.''

According to the ω-effect of the solar dynamo theory, a very strong toroidal magnetic field is produced in the solar convection zone. The fluid mass in the solar convection zone tends to rise by the magnetic buoyancy of the toroidal magnetic field. We discussed, in the paper [5] , that the gradient of the magnetic diffusivity on the surface of rising fluid mass must have disturbed the toroidal, magnetic field. This disturbance attempts to concentrate toroidal magnetic field on the surface of...

According to the ω-effect of the solar dynamo theory, a very strong toroidal magnetic field is produced in the solar convection zone. The fluid mass in the solar convection zone tends to rise by the magnetic buoyancy of the toroidal magnetic field. We discussed, in the paper [5] , that the gradient of the magnetic diffusivity on the surface of rising fluid mass must have disturbed the toroidal, magnetic field. This disturbance attempts to concentrate toroidal magnetic field on the surface of fluid mass because there is a large gradient of magnetic diffusivity on its surface, thus a sunspot magnetic flux ring is formed around the surface of, the fluid mass.The instability in the development of sunspot magnetic ring in the disturbance as mentioned above is further studied with the hydromagnetic perturbation equations in this paper. We get the conclusion that there is an instable mode in the perturbation equations. The reason of this instability is as follows: When the temperature (equiv. magnetic diffusivity et seq.) is disturbed in somewhere, the toroidal magnetic field will be disturbed and concentrated at that place where there is a large gradient of temperature. This concentrating of the toroidal magnetic field causes an increase in magnetic pressure and a decrease in gas pressure which consequentially induces a decrease in temperature and an increase in the gradient of temperature with the adiabatic process. The increased gradient of temperature results a further concentration of toroidal magnetic field. The relationship of mutual promoting between the magnetic field and the temperature is now called magnetic diffusion instability.

In this paper, the two-scale analytical method of mean field electrodynamics and some research results, such as α, β effects and α2, α-w solar dynamo models, are reviewed. The main difficulties both in observation and in theory are pinpointed, and the other solar dynamo models are briefly described.