标题： 轴对称发电机由环形体积中修改的欧姆定律维持 显示英文标题

标题： Axisymmetric Dynamos Sustained by a Modified Ohm's Law in a Toroidal Volume

摘要： 这项工作解决了一个在发电机理论中的重大挑战：轴对称磁场长期放大和维持的可能性。 我们引入了一个新模型，该模型允许磁场所存在非平凡的轴对称稳态解，特别是在发电机主要在流体壳层内部一个“近似球形”的环形体积内运行时。 在这个模型中，欧姆定律被推广以包括来自电子碰撞的耗散力，该力倾向于使壳层的速度与内核和外幔的旋转速度对齐。 我们的研究结果表明，在这种情况下，Cowling定理和中性点论证被修改，从而导致适合的环向流动选择下的磁能增长。 从我们的模型中出现的全局平衡磁场表现出偶极特征。 此处开发的模型的核心见解是，如果将额外的力纳入欧姆定律，对称发电机将成为可能。 显示英文摘要

摘要： This work tackles a significant challenge in dynamo theory: the possibility of long-term amplification and maintenance of an axisymmetric magnetic field. We introduce a novel model that allows for non-trivial axially-symmetric steady-state solutions for the magnetic field, particularly when the dynamo operates primarily within a ``nearly-spherical'' toroidal volume inside a fluid shell surrounding a solid core. In this model, Ohm's law is generalized to include the dissipative force, arising from electron collisions, that tends to align the velocity of the shell with the rotational speed of the inner core and outer mantle. Our findings reveal that, in this context, Cowling's theorem and the neutral point argument are modified, leading to magnetic energy growth for a suitable choice of toroidal flow. The global equilibrium magnetic field that emerges from our model exhibits a dipolar character. The central insight of the model developed here is that if an additional force is incorporated into Ohm's law, symmetric dynamos become possible.