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.

中文翻译：

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负磁扩散系数 β 替代螺旋发电机中的 α 效应

众所周知，阿尔法效应是太阳或行星极向磁场不可或缺的能量来源。然而，由于磁螺旋守恒，随着磁场的增长，α 效应会消失。有了这些传统的理解，究竟是什么产生和维持了所观察到的极向磁场仍然是个谜。为了解决理论与现实之间的这一矛盾，我们使用大规模磁螺旋和能量推导出了 alpha 和 beta 的半解析表示。将模拟数据应用于 alpha 和 beta，我们发现负 beta 效应是淬灭 alpha 效应的有希望的替代。然而，由于负贝塔效应与传统的发电机理论相矛盾，我们根据场结构模型推导出了新的贝塔表达式。这一对速度 U 和磁场 B 之间场关系的解析结果表明，螺旋系统中的 β 效应不是固定的。相反，它根据极向速度场与大尺度磁场的相对强度之间的相互作用，在发电机中发挥可变和动态的作用。