離子環狀速度分佈通常是在輻射帶以及靠近磁赤道的地方被衛星觀測到，本篇論文即是去探討磁尾來源的氫離子飄移至輻射帶後是否能形成離子環狀速度分佈。當磁尾來源的氫離子越接近地球時，會因為磁矩守恆，讓垂直磁場的速度不斷增加，這些帶有很高速度的離子，在進入輻射帶後，垂直速度的能量會大於飄移速度的能量，因此在磁場方向的等向性分佈即使經過飄移運動看起來還是會呈現等向性分佈，因此這些粒子可能是產生離子環狀速度分佈的原因。
在本篇論文的模擬中，使用Tsyganenko(T01)和地球偶極磁場模型，並根據太陽風資料，加入一個晨昏方向的電場來模擬離子的運動。我們在磁赤道的黃昏測放置一個觀察點，並記錄氫離子通過該觀測點的速度。初始條件方面，我們在磁尾來源使用每一組20顆氫離子，搭配相同初速度(v_∥,v_⊥)以及不同相位角度來當作初始條件，並採用連續方程式的概念來計算磁尾來源的氫離子到達觀測點的密度貢獻，再使用辛普森定理計算出這些氫離子的速度分佈，並將結果與觀測點的馬克斯威廉速度分佈結合比較。結果顯示，當我們將磁尾來源的氫離子總數量增加後，在觀測點垂直於磁場的速度分佈環的形狀會更加明顯。

Ion ring velocity distribution have been sometimes observed by the satellite in the radiation belts and near the magnetic equator. In this study, we would explore magnetotail of hydrogen ions as a possible source of ion ring velocity distributions after ions drift from magnetotail to the radiation belts. When the magnetotail ions drift toward the Earth, their perpendicular velocities increase because the magnetic field that they encounter increases while the magnetic moment is an invariant. These ions, with high perpendicular speed but relatively low perpendicular drift velocity in the radiation belts, undergo gyration about the magnetic field direction. Under the presumption of gyrotropic condition these particles may form an ion ring velocity distribution.

In our simulations, we use Tsyganenko model T01 and the Earth's dipole field model for the magnetic field, and add a dawn-to-dusk electric field in accordance with E=-V_wind×B_wind , obtained from the solar wind data of velocity V_wind and magnetic field B_wind to simulate the motion of the ions. We set an observation site of the magnetic equator on the dusk side of the inner magnetosphere to record the hydrogen ion velocities in the simulations. For the initial conditions, we use magnetotail hydrogen ions in groups of 20, the ions in each groups sharing the same parallel velocity v_∥ and perpendicular velocity v_⊥ but with different gyration phases. Continuity equation is used to calculate the density contribution from the hydrogen ions of the magnetotail source when they reach the observation site with various velocities. The velocity distribution for these ions are calculated and then added to the Maxwillian distribution at the observed site to check if an ion velocity distribution results. The simulations show that when we increase the total number of hydrogen ions in the magnetotail source, the ring shape in the velocity distribution in the direction perpendicular to the magnetic field become are clearer.

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