The dynamo effect is a class of macroscopic phenomena responsible for generation and maintaining magnetic fields in astrophysical bodies. It hinges on hydrodynamic three-dimensional motion of conducting gases and plasmas that achieve high hydrodynamic and/or magnetic Reynolds numbers due to large length scales involved. The existing laboratory experiments modeling dynamos are challenging and involve large apparatuses containing conducting fluids subject to fast helical flows. Here we propose that electronic solid-state materials -- in particular, hydrodynamic metals -- may serve as an alternative platform to observe some aspects of the dynamo effect. Motivated by recent experimental developments, this paper focuses on hydrodynamic Weyl semimetals, where the dominant scattering mechanism is due to interactions. We derive Navier-Stokes equations along with equations of magneto-hydrodynamics that describe transport of Weyl electron-hole plasma appropriate in this regime. We estimate the hydrodynamic and magnetic Reynolds numbers for this system. The latter is a key figure of merit of the dynamo mechanism. We show that it can be relatively large to enable observation of the dynamo-induced magnetic field bootstrap in experiment. Finally, we generalize the simplest dynamo instability model -- Ponomarenko dynamo -- to the case of a hydrodynamic Weyl semimetal and show that the chiral anomaly term reduces the threshold magnetic Reynolds number for the dynamo instability.

中文翻译：

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流体动力Weyl金属的发电机效应和湍流

发电机效应是一类宏观现象，负责在天体物理体中产生和维持磁场。它取决于导电气体和等离子体的流体动力学三维运动，由于涉及较大的长度尺度，该运动实现了很高的流体动力学和/或磁性雷诺数。现有的对动力学进行建模的实验室实验具有挑战性，涉及大型设备，这些设备中包含受快速螺旋流作用的导电流体。在这里，我们提出电子固态材料-特别是流体动力金属-可以作为观察发电机动力学某些方面的替代平台。受近期实验研究的推动，本文重点研究了流体动力学的Weyl半金属，其主要的散射机理是由于相互作用引起的。我们推导了Navier-Stokes方程以及磁流体动力学方程，这些方程描述了在这种情况下适合的Weyl电子空穴等离子体的传输。我们估计该系统的流体动力学和磁雷诺数。后者是发电机机构性能的关键指标。我们表明，它可以相对较大，以便在实验中观察发电机感应的磁场自举。最后，我们将最简单的发电机不稳定模型Ponomarenko发电机推广到流体动力学Weyl半金属的情况，并表明手性异常项降低了发电机不稳定的阈值雷诺数。我们估计该系统的流体动力学和磁雷诺数。后者是发电机机构性能的关键指标。我们表明，它可以相对较大，以便在实验中观察发电机感应的磁场自举。最后，我们将最简单的发电机不稳定模型Ponomarenko发电机推广到流体动力学Weyl半金属的情况，并表明手性异常项降低了发电机不稳定的阈值雷诺数。我们估计该系统的流体动力学和磁雷诺数。后者是发电机机构性能的关键指标。我们表明，它可以相对较大，以便在实验中观察发电机感应的磁场自举。最后，我们将最简单的发电机不稳定模型Ponomarenko发电机推广到流体动力学Weyl半金属的情况，并表明手性异常项降低了发电机不稳定的阈值雷诺数。