Study On The Influence Of The Electrical Conductivity At Boundary On Alpha Effect Of Hydromagnetic Self-excited Dynamo Action

There exist magnetic fields in most of celestial bodies in the universe, including planets, stars, and galaxies. The generation and evolvement of the cosmic magnetic fields has been a major problem in the field of physics and astrophysics. At present, it is generally believed that geomagnetic field, solar magnetic field and other celestial bodies’ field are generated by the hydromagnetic self-excited dynamo action. Liquid metal was used as a coolant in the fast breeder reactor and magnetic confinement fusion reactor, where the magnetic Reynolds number can be up to20orders of magnitude. It is possible to provoke self-excited dynamo action, and the self-excited magnetic field will change the flow of the liquid metal, which may cause serious accident. Therefore, the investigation of the hydromagnetic self-excited dynamo action is of great scientific significance and application value.In the past decades, the successful liquid sodium dynamo experiments have aroused growing interest in the experiment research and numerical simulation of dynamo action. However, the mechanism of dynamo action is still a mystery. Therefore, it is of great importance to investigate the mechanism of the self-excited dynamo action. Up to now the mean field dynamo theory is fundamental to the dynamo theory. The alpha effect is the core of the mean field dynamo theory. The past research shows that the alpha effect can successfully explain the Karlsruhe experimental results. The VKS experiment reveals that the electrical conductivity of the side wall has a significant impact on the dynamo action. However, there is no much report on the study of the influence of the electrical conductivity of the side wall on the Karlsruhe dynamo experiment in particular and the alpha effect in general. Therefore, in the present work the main focus is on the impact of the electrical conductivity of the side wall on the various alpha effects based on the mean field theory and the cylindrical geometry.The integral equation approach has successfully addressed the thorny non-local boundary condition problem which is encountered in the numerical simulation of dynamo action, and has been examined by the Riga, Karlsruhe and VKS experiments. Furthermore, it has played a key role in the VKS experiment. Therefore, in the present work the integral equation approach will be employed to study the Karlsruhe experiment and the alpha effect.In the present work, we attempt to investigate the influence of electricity conductivity of side wall of the cylindrical vessel on the critical magnetic Reynolds number of dynamo actions driven by various alpha effects. It is found that with the increase of the electricity conductivity of the side wall, the critical magnetic Reynolds number declines. The critical magnetic Reynolds numbers for axisymmetric mode decreases more slowly than the equatorial mode, but reach the limit value earlier.It is found that both the electricity conductivity of side wall and the inhomogeneity of the alpha effect are important factors on the symmetry of self-excited magnetic field. The original successful Karlsruhe experiment is driven by the alpha effect with its inhomogeneity parameter value taking the value1, an equatorial magnetic field with an azimuthal wave number m=1is always the dominant mode when the electrical conductivity of the side wall varies. If the self-excited dynamo action is driven by the isotropous alpha effect, when the relative electricity conductivity is greater than5.4, an equatorial magnetic field with an azimuthal wave number m=1is the dominant mode, otherwise a steady axisymmetric field with an azimuthal wave number m=0predominates the magnetic field. If the self-excited dynamo action is forced by an alpha effect with its inhomogeneity parameter value taking value0.5, when the relative electricity conductivity is greater than2.2, an equatorial magnetic field with an azimuthal wave number m=1is the dominant mode, otherwise a steady axisymmetric field with an azimuthal wave number m=0predominates the magnetic field.