CEDAR: Euler potentials for field-aligned and shell currents in the ionosphere

地球的电离层是高层大气中带电粒子浓度相对较高的部分，主要是由于太阳辐射。这一区域距地球表面约50公里至1000公里，具有复杂的电动力学过程，对从表面磁场到空间辐射的广泛领域都有重要影响。PI寻求聘请本科生研究人员研究电离层中的场向电流，在电离层中，电流沿着地球的磁力线流动。这项工作将使学生学习如何分析和解释电离层数据。PI还旨在通过由美国物理研究所组织的一系列研讨会，招募来自不同背景的少数族裔学生进入物理学专业。PI计划使用欧拉势，它可以从磁场中解析得出，并应用于跟踪电流流线和带电粒子轨迹。这个项目将使用欧拉势从地面和空间观测中重建壳电流，这是以前从未做过的。该项目对于理解电离层-磁层-热层耦合很重要。将首次对电离层中的电流系统进行分析描述。研究结果将有助于规划和管理低空卫星以及预测GPS信号中断。该项目的主要预期成果是找到电离层中的壳层电流分布，这对于可靠地计算焦耳加热很重要。该项目有三个目标：1)确定电离层及其附近磁场的欧拉势，2)使用欧拉势计算带电粒子的运动，3)使用欧拉势寻找电流流线。从电离层数据和经验模型可以得到具有良好时间和空间分辨率的场向电流(FAC)和感应磁场变化。然而，FAC和壳电流(SLC)之间的合并还没有确定。这些方法在电离层中的应用将使电离层电流建模更加可靠，更接近实际。该方法可以定义每条磁场线并跟踪随时间的变化。也可以监控场向电流的形成和演化。建议的欧拉势方法可以解析地找到感应磁场，这是一个比Biot-Savart积分更容易和更快的过程。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The Earth’s ionosphere is the part of the upper atmosphere that has a relatively high concentration of charged particles, largely due to solar radiation. This region, from about 50 km to 1000 km above the Earth’s surface, has complex electro-dynamic processes that have important effects in a wide range of areas from the surface magnetic field to radiation in space. The PI seeks to engage undergraduate researchers to study the field-aligned currents in the ionosphere, in which the electric current flows along the Earth’s magnetic field lines. This work will allow the students to learn how to analyze and interpret ionospheric data. The PI also aims to recruit minority students into Physics from different backgrounds via a series of workshops organized by the American Institute of Physics. The PI plans to use Euler potentials which can be derived analytically from magnetic field and applied for tracing current streamlines and charged particles trajectories. This project will use Euler potentials to reconstruct shell currents from ground-based and space-based observations, which has not been done before. This project is important for understanding ionosphere-magnetosphere-thermosphere coupling. An analytical description of electric current systems in the ionosphere will be given for the first time. The results will be useful for planning and managing low-altitude satellites and predicting GPS signal disruptions. The main expected outcome of the project is to find shell currents distribution in the ionosphere, important for reliable calculations of Joule heating. This project has three objectives: 1) To determine Euler potentials for the magnetic field in the ionosphere and in its vicinity, 2) To use the Euler potentials for calculation of charged particle motion, and 3) To find electric current streamlines using the Euler potentials. Field-aligned currents (FAC) and induced magnetic field variations with good temporal and spatial resolution can be obtained from Ionospheric data and empirical models. However, the merging between FAC and shell currents (SLC) is not determined. The application of the methods in the ionosphere will make the ionospheric currents modeling more reliable and closer to reality. This method can define each magnetic field line and track changes over time. The formation and evolution of field-aligned currents can be monitored as well. The proposed Euler potentials method can find the induced magnetic field analytically, which is a much easier and faster process that the Biot-Savart integration.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.