Exploring the origin and properties of magnetic fields is crucial to the development of many fields such as physics, astronomy and meteorology. We focus on the edge element approximation and theoretical analysis of celestial dynamo system with quasi-vacuum boundary conditions. The system not only ensures that the magnetic field on the spherical shell is generated from the dynamo model, but also provides convenience for the application of the edge element method. We demonstrate the existence, uniqueness and stability of the solution to the system by the fixed point theorem. Then, we approximate the system using the edge element method, which is more efficient in dealing with electromagnetic field problems. Moreover, we also discuss the stability of the corresponding discrete scheme. And the convergence is demonstrated by later numerical tests. Finally, we simulate the three-dimensional time evolution of the spherical interface dynamo model, and the characteristics of the simulated magnetic field are consistent with existing work.

翻译：探索磁场的起源与性质对于物理学、天文学和气象学等诸多领域的发展至关重要。本文聚焦于准真空边界条件下天体发电机系统的边单元近似及其理论分析。该系统不仅确保球壳上的磁场由发电机模型产生，还为边单元方法的应用提供了便利。我们通过不动点定理证明了该系统解的存在性、唯一性和稳定性。随后，采用在处理电磁场问题方面更具效率的边单元方法对系统进行近似。此外，我们还讨论了相应离散格式的稳定性，并通过后续数值试验验证了其收敛性。最后，我们模拟了球形界面发电机模型的三维时间演化过程，所模拟磁场的特征与已有研究结果一致。