  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.
