磁能计算的准确性
Accuracy of magnetic energy computations
摘要：
对于磁驱动事件，系统的磁能是推动动力学演化的主要能量库。在太阳背景下，自由能是空间天气预报中用来预测活动区喷发性的主要指标之一。因此，在太阳大气的三维模型中，例如在日冕场重建或数值模拟中，需要对磁能进行可靠的估计。当磁场为正螺线管时，系统的能量表示为其势能与自由能之和（汤姆逊定理）是严格有效的。对于离散网格上的数值实现，该性质可能仅近似满足。我们发现，不完美的solenoidality诱导的能量，可能导致误解的量的自由能存在于一个磁配置的条款。我们认为，在螺线管和nonsolenoidal部分的能量的分解，允许明确的估计nonsolenoidal的贡献的能量。我们将这种分解应用于太阳物理学中广泛使用的六种典型情况。我们量化到什么程度的汤姆逊定理是不满意时，近似螺线管领域使用。能量上的量化误差从可忽略到显著误差不等，取决于非螺线管分量的程度。我们确定的主要来源的错误和分析的影响，增加了一个变量的分歧，各种螺线管领域。最后，我们提出病理非物理的情况下，估计的自由能似乎是负的，在以前的一些作品中发现的，我们确定这种错误的来源是存在一个有限的分歧。我们提供了一种方法，量化的影响，有限的分歧，在数值领域，连同其来源的详细诊断。
英文摘要：
For magnetically driven events, the magnetic energy of the system is the prime energy reservoir that fuels the dynamical evolution. In the solar context, the free energy is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. A trustworthy estimation of the magnetic energy is therefore needed in three-dimensional models of the solar atmosphere, eg in coronal fields reconstructions or numerical simulations. The expression of the energy of a system as the sum of its potential energy and its free energy (Thomson's theorem) is strictly valid when the magnetic field is exactly solenoidal. For numerical realizations on a discrete grid, this property may be only approximately fulfilled. We show that the imperfect solenoidality induces terms in the energy that can lead to misinterpreting the amount of free energy present in a magnetic configuration. We consider a decomposition of the energy in solenoidal and nonsolenoidal parts which allows the unambiguous estimation of the nonsolenoidal contribution to the energy. We apply this decomposition to six typical cases broadly used in solar physics. We quantify to what extent the Thomson theorem is not satisfied when approximately solenoidal fields are used. The quantified errors on energy vary from negligible to significant errors, depending on the extent of the nonsolenoidal component. We identify the main source of errors and analyze the implications of adding a variable amount of divergence to various solenoidal fields. Finally, we present pathological unphysical situations where the estimated free energy would appear to be negative, as found in some previous works, and we identify the source of this error to be the presence of a finite divergence. We provide a method of quantifying the effect of a finite divergence in numerical fields, together with detailed diagnostics of its sources.
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