The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces like plasma pressure gradient and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relation between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently of large interests, as accurate measurements of the photospheric field become available from ground-based (for example SOLIS) and space-born (for example Hinode and SDO) instruments. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma.

中文翻译：

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无太阳磁场

太阳电晕的结构和动力学主要由磁场决定。在电晕的大多数区域中，磁力是如此占优势，以至于所有非磁力（例如等离子压力梯度和重力）都可以以最低的顺序被忽略。当洛伦兹力消失时，该模型假设称为无力场假设。这可以通过消除电流（导致势场）或使电流与磁场线共对准来实现。首先，我们讨论一种数学上更简单的方法，即磁场和电流与一个全局常数成比例，即所谓的线性无力场近似。但是，在一般情况下，磁场与电流之间的关系是非线性的，只有在特殊情况下才能找到解析解，例如1D或2D配置。为了在3D中构建逼真的非线性无力日冕磁场模型，需要进行复杂的数值计算，并且必须从对太阳光球中磁场矢量的测量中获得边界条件。由于从地面（例如SOLIS）和太空（例如Hinode和SDO）仪器可以获得对光球场的精确测量，因此这种方法目前引起了广泛关注。如果我们可以获得准确的无力日冕磁场模型，那么我们就可以计算出电晕中的自由磁能，该量对于预测耀斑和日冕物质抛射非常重要。磁场线的3D结构知识也有助于我们解释其他日冕观测，例如辐射日冕等离子体的EUV图像。