Dynamo action is considered in the region between two differentially rotating infinite discs. The boundaries may be insulating, perfectly conducting or ferromagnetic. In the absence of a magnetic field, various well-known self-similar flows arise, generalising that of von Kármán. Magnetic field instabilities with the same similarity structure are sought. The kinematic eigenvalue problem is found to have growing modes for $R{e}_m>R_c\simeq 100$. The growth rate is real for the perfectly conducting and ferromagnetic cases, but may be complex for insulating boundaries. As $R{e}_m\to \mathrm{\infty }$ it is shown that the dynamo can be fast or slow, depending on the flow structure. In the slow case, the growth rate is governed by a magnetic boundary layer on one of the discs. The growing field saturates in a solution to the nonlinear dynamo problem. The bifurcation is found to be subcritical and nonlinear dynamos are found for $R{e}_m\gtrsim 0.7R_c$. Finally, the flux of magnetic energy to large r is examined, to determine which solutions might generalise to dynamos between finite discs. It is found that the fast dynamos tend to have inward energy flux, and so are unlikely to be realised in practice. Slow dynamos with outward flux are found. It is suggested that the average rotation rate should be non-zero in practice.

在两个不同旋转的无限圆盘之间的区域中考虑了发电机作用。边界可以是绝缘的、完全导电的或铁磁性的。在没有磁场的情况下，会出现各种众所周知的自相似流，概括了冯卡门的流。寻找具有相同相似结构的磁场不稳定性。发现运动学特征值问题具有增长模式$R{e}_{米}>R_C\simeq 100$. 对于完美导电和铁磁情况，增长率是真实的，但对于绝缘边界可能很复杂。作为$R{e}_{米}\to \mathrm{\infty }$结果表明，发电机可以快速或慢速，具体取决于流动结构。在缓慢的情况下，生长速率由其中一个圆盘上的磁性边界层控制。不断增长的领域在非线性发电机问题的解决方案中饱和。发现分岔是亚临界的，并且发现了非线性发电机$R{e}_{米}\gtrsim 0.7R_C$. 最后，检查到大r的磁能通量，以确定哪些解决方案可以推广到有限圆盘之间的发电机。发现快速发电机往往具有向内的能量通量，因此在实践中不太可能实现。发现了具有向外通量的慢发电机。建议在实践中平均旋转速率应为非零。