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Negative Magnetic Diffusivity beta replacing alpha effect in Helical Dynamo

The alpha effect is known to be an indispensable energy source of the poloidal magnetic field in the sun or planet. However, the alpha effect is quenched as the magnetic field grows due to the conservation of magnetic helicity. With these conventional understanding, what indeed generates and sustains the observed poloidal magnetic field remains a mystery. To solve this contradiction between theory and real nature, we derived a semi-analytic representation of alpha and beta using large scale magnetic helicity and energy. Applying the simulation data to alpha and beta, we found that the negative beta effect is a promising substitution of the quenched alpha effect. However, since the negative beta effect contradicts the conventional dynamo theory, we derived the new beta expression referring to the field structure model. This analytic result with the field relation between velocity U and magnetic field B shows that the beta effect in the helical system is not a fixed one. Rather, it plays a variable and dynamic role in dynamo depending on the interaction between the poloidal velocity field and relative strength of the large scale magnetic field.