合唱波是一種極低頻波，容易在磁層赤道區域產生，它們能與內磁層的電子產生波粒交互作用，進而影響此區域電子的損失和加速過程。合唱波的特性是不連續波元，每個波元持續幾百毫秒後結束發展。當一個波元開始產生時，前一個波元還沒結束，這個波元稱作重疊波元，否則就是非重疊波元。過去有很多人研究合唱波波前的行進方向，他們大多數集中於行進方向的角度統計或地方時分布，其結果都顯示合唱波波前的行進方向並非都是平行於磁場傳播的，有些與磁場呈現大角度的傳播方向。根據這個結果，同一個地點量測到的不同合唱波波元可能會來自不同來源。最小變異分析是用來找出一個物理向量中變化最小的方向，因合唱波是平面圓形極化電磁波，我們可利用最小變異量分析找出磁場變化最小的方向，即電磁波波前傳播的方向。我們將分析THEMIS衛星高解析度磁場資料，使用最小變異量分析估計低頻帶合唱波波前的行進方向。每個合唱波事件包含多重合唱波波元，其來源是否相同仍然未知。如果這些波元有相同的行進方向，則它們來自相同的來源。此外透過這些具有相同傳播方向的波元之起始與結束時間，可以區分出重疊與非重疊波元。這個研究可以幫助我們釐清合唱波波元的特性，以及了解合唱波的產生和發展機制。 ;Chorus waves, typically generated in the equatorial region, are a type of very low frequency waves. These waves can interact with electrons in the inner magnetosphere, resulting in the loss and acceleration of the electrons. The characteristics of chorus waves are discrete elements. Each element lasts a few hundred milliseconds and stops growing. If one element starts before the previous one ends, this element is called an overlapped element, and otherwise, it is called a non-overlapped element. Many people studied the propagation direction of chorus waves. Most of them focused on the statistics and local distributions of the propagation direction, reporting that not all the propagation directions are aligned with the magnetic fields and the aligning angle could be large for some cases. Therefore, the elements observed at the same place could be originated from difference sources. Minimum Variance Analysis (MVA) is a technique that helps determine the direction of a physical quantity that has minimum variance. Since chorus is a type of circularly polarized planed electromagnetic waves, the MVA can be used to find the minimum-variance direction of the magnetic fields, that is, the propagation direction of the chorus waves. In the proposed work, we will analyze high-resolution magnetic fields obtained from the THEMIS probes to determine the propagation direction of chorus waves with the MVA. Each chorus event contains multiple chorus elements and their sources may be different. If the determined propagation directions of the elements are the same, these elements are originated from the same source. Overlapped and non-overlapped elements can be determined according to the starting and ending times of elements. The proposed work can help us sort out the characteristics of chorus elements and understand the generation and development of chorus waves.
