论文标题
统计运动学发电机的现场理论方法
A field theory approach to the statistical kinematic dynamo
论文作者
论文摘要
地磁场的变化发生在从毫秒到数百万年的广泛时间尺度上发生。卫星测量的出现允许详细研究短时间的地磁场行为，但是由于古磁记录的稀疏性，理解长时间的演变仍然具有挑战性。本文介绍了一个田间理论框架，用于研究磁场的产生，这是由于随机流体运动的结果。通过构建随机运动发电机模型，我们得出了磁场的统计特性，可以将其与古磁记录的观测值进行比较。流体速度被视为随机迫使服从高斯统计。使用Martin-Siggia-Rose-Janssen-de Dominicis（MSRJD）形式主义，我们计算平均磁场响应函数。从中，我们获得了对磁扩散性湍流贡献的估计，并发现它与平均场扰动理论的结果一致。该框架在随机背景下研究地磁领域有很大的希望。
Variations in the geomagnetic field occur on a vast range of time scales, from milliseconds to millions of years. The advent of satellite measurements has allowed for detailed studies of the short timescale geomagnetic field behaviour, but understanding the long timescale evolution remains challenging due to the sparsity of the paleomagnetic record. This paper introduces a field theory framework for studying magnetic field generation as a result of stochastic fluid motions. By constructing a stochastic kinematic dynamo model, we derive statistical properties of the magnetic field that may be compared to observations from the paleomagnetic record. The fluid velocity is taken to act as a random forcing obeying Gaussian statistics. Using the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) formalism, we compute the average magnetic field response function. From this we obtain an estimate for the turbulent contribution to the magnetic diffusivity, and find that it is consistent with results from mean-field dynamo theory. This framework presents much promise for studying the geomagnetic field in a stochastic context.
