具有中尺度起伏的平均场电动力学的推导和精度
Derivation and precision of mean field electrodynamics with mesoscale fluctuations
摘要：
平均场电动力学（MFE）有助于对天体物理或实验室系统的长期、大尺度波动特性进行实际建模。从业者通常假设平均量和波动量之间存在宽尺度分离，以证明系综和空间或时间平均值的相等性。然而，实际系统通常不表现出这种尺度分离。这就提出了两个问题：（1）在中尺度波动的存在下，MFE的适当的广义方程是什么？(II)MFE的理论预测有多精确？我们解决这两个问题，首先推导出不同类型的平均MFE方程，以及中尺度校正项，取决于平均尺度的平均值的变化尺度的比率。然后，我们表明，即使这些条款是小的，预测的MFE仍然可以有一个显着的精度误差。该误差有发电机输入参数的内在贡献，以及观测和理论通过测量核投影的方式差异的滤波贡献。最小化这些贡献之和可以产生最佳平均尺度，使理论最大化精确度。在与观测进行比较时，精确度误差很重要，因为它量化了预测能力的分辨率。我们重申这些原则的银河发电机，评论更广泛的影响，并确定进一步工作的可能性。
英文摘要：
Mean field electrodynamics (MFE) facilitates practical modeling of secular, large scale properties of astrophysical or laboratory systems with fluctuations.Practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages.Often however, real systems do not exhibit such scale separation. This raises two questions: (I) what are the appropriate generalized equations of MFE in the presence of mesoscale fluctuations? (II) how precise are theoretical predictions from MFE? We address both by first deriving the equations of MFE for different types of averaging, along with mesoscale correction terms that depend on the ratio of averaging scale to variation scale of the mean. We then show that even if these terms are small, predictions of MFE can still have a significant precision error. This error has an intrinsic contribution from the dynamo input parameters and a filtering contribution from differences in the way observations and theory are projected through the measurement kernel.Minimizing the sum of these contributions can produce an optimal scale of averaging that makes the theory maximally precise.The precision error is important to quantify when comparing to observations because it quantifies the resolution of predictive power. We exemplify these principles for galactic dynamos, comment on broader implications, and identify possibilities for further work.
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