Gómez Daniel O, Mininni Pablo D, Dmitruk Pablo
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Sep;82(3 Pt 2):036406. doi: 10.1103/PhysRevE.82.036406. Epub 2010 Sep 27.
Magnetic field generation by dynamo action is often studied within the theoretical framework of magnetohydrodynamics (MHD). However, for sufficiently diffuse media, the Hall effect may become non-negligible. We present results from three-dimensional simulations of the Hall-MHD equations subjected to random nonhelical forcing. We study the role of the Hall effect in the dynamo efficiency for different values of the Hall parameter. For small values of the Hall parameter, the small-scale dynamo is more efficient, displaying faster growth and saturating at larger amplitudes of the magnetic field. For larger values of the Hall parameter, saturation of the magnetic field is reached at smaller amplitudes than in the MHD case. We also study energy transfer rates among spatial scales and show that the Hall effect produces a reduction of the direct energy cascade at scales larger than the Hall scale, therefore leading to smaller energy dissipation rates. Finally, we present results stemming from simulations at large magnetic Prandtl numbers, which is the relevant regime in the hot and diffuse interstellar medium. In the range of magnetic Prandtl numbers considered, the Hall effect moves the peak of the magnetic energy spectrum as well as other relevant magnetic length scales toward the Hall scale.
通过发电机作用产生磁场的研究通常是在磁流体动力学（MHD）的理论框架内进行的。然而，对于足够稀薄的介质，霍尔效应可能变得不可忽略。我们展示了对受随机非螺旋强迫作用的霍尔磁流体动力学方程进行三维模拟的结果。我们研究了霍尔效应在不同霍尔参数值下对发电机效率的作用。对于较小的霍尔参数值，小尺度发电机效率更高，显示出更快的增长并在更大的磁场振幅下达到饱和。对于较大的霍尔参数值，磁场在比磁流体动力学情况更小的振幅下达到饱和。我们还研究了空间尺度之间的能量传输率，并表明霍尔效应在大于霍尔尺度的尺度上导致直接能量级联的减少，从而导致更小的能量耗散率。最后，我们展示了在大磁普朗特数下模拟的结果，这是热且稀薄的星际介质中的相关情况。在所考虑的磁普朗特数范围内，霍尔效应将磁能谱的峰值以及其他相关的磁长度尺度向霍尔尺度移动。
