We investigate the ability of a nonlinear force-free code to calculate highly-twisted magnetic field configurations using the Titov and Demoulin (1999) equilibrium field as a test case. The code calculates a force-free field using boundary conditions on the normal component of the field in the lower boundary, and the normal component of the current density over one polarity of the field in the lower boundary. The code can also use the current density over both polarities of the field in the lower boundary as a boundary condition. We investigate the accuracy of the reconstructions with increasing flux-rope surface twist number $N_{\textrm{t}}$, achieved by decreasing the sub-surface line current in the model. We find that the code can approximately reconstruct the Titov-Demoulin field for surface twist numbers up to $N_{\textrm{t}} \approx 8.8$. This includes configurations with bald patches. We investigate the ability to recover bald patches, and more generally identify the limitations of our method for highly-twisted fields. The results have implications for our ability to reconstruct coronal magnetic fields from observational data.

中文翻译：

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重建高度扭曲的磁场

我们使用 Titov 和 Demoulin (1999) 平衡场作为测试案例来研究非线性无力代码计算高扭曲磁场配置的能力。该代码使用下边界场的法向分量上的边界条件和下边界场的一个极性上的电流密度的法向分量计算无力场。该代码还可以使用下边界中场的两个极性上的电流密度作为边界条件。我们通过减少模型中的次表面线电流来研究随着磁通绳表面扭曲数 $N_{\textrm{t}}$ 的增加重建的准确性。我们发现代码可以近似重建 Titov-Demoulin 场，表面扭曲数高达 $N_{\textrm{t}} \approx 8.8 $。这包括带有秃斑的配置。我们研究了恢复秃斑的能力，更普遍地确定了我们的方法对高度扭曲场的局限性。这些结果对我们从观测数据重建日冕磁场的能力有影响。