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 such as plasma pressure gradients 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 relationship 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 a large area of research, as accurate measurements of the photospheric field are available from ground-based observatories such as the Synoptic Optical Long-term Investigations of the Sun and the Daniel K. Inouye Solar Telescope (DKIST) and space-born, e.g., from Hinode and the Solar Dynamics Observatory. 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.

日冕的结构和动力学由磁场决定。在日冕的大多数区域中，磁力占据主导地位，以至于所有非磁力（例如等离子体压力梯度和重力）都可以在最低级别上忽略不计。当洛伦兹力消失时，该模型假设称为无力场假设。这可以通过消失电流（导致势场）或电流与磁场线对齐来实现。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正比，即所谓的线性无力场近似。然而，在一般情况下，磁场和电流之间的关系是非线性的，并且仅针对特殊情况（例如一维或二维配置）找到了解析解。为了构建现实的 3D 非线性无力日冕磁场模型，需要复杂的数值计算，并且必须通过测量太阳光球层中的磁场矢量来获得边界条件。这种方法目前是一个很大的研究领域，因为可以从地面观测站（例如太阳综合光学长期研究站和丹尼尔·K·井上太阳望远镜（DKIST）和太空观测站）获得光球场的精确测量。例如，诞生于日之出和太阳动力学观测站。如果我们能够获得准确的无力日冕磁场模型，我们就可以计算日冕中的自由磁能，这个量对于预测耀斑和日冕物质抛射非常重要。了解磁场线的 3D 结构也有助于我们解释其他日冕观测结果，例如辐射日冕等离子体的 EUV 图像。