地球磁層觀測到的合唱波(chorus waves)屬於電磁波，它們的波頻率範圍低於一個電子回旋頻率，卻遠高於一個質子回旋頻率。其中合唱波最引人注目的一個特徵就是在0.5個電子回旋頻率處有一個缺口(frequency gap)，也就是動態頻譜不連續。過去的研究認為0.5個電子回旋頻率的波發生Landau Damping，而導致動態頻譜關係圖(dynamic spectra)中的合唱波中在此頻率處有一個頻率缺口。然而，沒有發生頻率缺口的合唱波也被觀測到。本論文中，我們想要研究在電子質子雙流體電漿裡中低頻波的群速度分布，進而了解波能量的擴散情形。根據群速度分佈資訊來模擬準電磁波的區域擾動源所造成的動態頻譜關係，其中準電磁波表示電磁分量大於靜電分量。我們的理論結果指出快波(fast-mode)波頻率在0.5個電子回旋頻率附近的準電磁波都近乎沿背景磁場傳播，因為它們的群速度分布顯示ray angles非常地小，其中ray angles為群速度傳播方向與背景磁場方向的夾角大小。因此，我們提出當接收器與準電磁波的區域擾動源在同一條磁力管上時，沒有頻率缺口的電磁合唱波就會被觀測到。我們的結果也指出頻率缺口的寬度隨著ray angles變大而變寬。然而，我們也看到另一種沒有頻率缺口的合唱波，它們低於0.5個電子回旋頻率的波(lower-band waves)屬於準靜電波。除了升頻的合唱波外，我們也研究了降頻的哨波。我們找到兩種類型的電磁哨波解。一個是由快波模所得到的low-k_⊥ 哨波，它的群速度與相速度的方向都是近乎沿背景磁場。另一個則是由中速波模(intermediate-mode)所得到的high-k_⊥哨波，它的群速度也是近乎沿背景磁場，但相速度的方向卻是近乎垂直背景磁場。這種high-k_⊥哨波解可以解釋近期的文獻報告稱在地磁緯度11度也觀測到由閃電產生之哨波。

Chorus waves are rising-tone electromagnetic waves with a frequency less than the electron cyclotron frequency but higher than the ion cyclotron frequency. The most noticeable feature of the chorus waves is the frequency gap at half the electron cyclotron frequency on the dynamic spectrum. Previous studies usually attribute the frequency gap to the Landau damping processes. However, chorus waves without a frequency gap have also been observed. In this thesis, the low- and medium-frequency waves in the ion-electron two-fluid plasma are studied in great detail. We examine the expansions of wave energy based on the group-velocity distribution of these waves. We mimic the dynamic spectra of the quasi-electromagnetic waves based on the Friedrichs’ diagrams of the group-velocity distribution when the waves are generated by a localized broadband disturbance. Our theoretical results indicate that the quasi-electromagnetic fast-mode waves have an extremely small expansion angle when the wave frequency is around half the electron cyclotron frequency. Therefore, we propose that the rising-tone electromagnetic chorus waves without a frequency gap can only be observed when the receiver is located in the same flux tube as the source disturbances of the chorus waves. Our results also indicate that the bandwidth of the frequency gap of the electromagnetic chorus waves increases with increasing ray angles of the waves. The group-velocity distributions of the quasi-electrostatic waves in the ion-electron two-fluid plasma have also been studied. No frequency gap is found in the dynamic spectrum of the rising-tone chorus waves when the lower-band waves are quasi-electrostatic. This result is consistent with recent observations. In addition to the rising-tone chorus waves, we also examine the falling tone whistler waves. We obtain two types of falling-tone electromagnetic whistler wave solutions. One of them is the well-known fast-mode low-k_⊥whistler waves, which is characterized by highly field-aligned group velocities and phase velocities. The other is the intermediate-mode high-k_⊥ whistler waves, which is characterized by highly field-aligned group velocity, but with phase velocity nearly perpendicular to the background magnetic field. The high-k_⊥ whistler waves can explain the recent observations of lightning-induced whistler waves at 11 degrees magnetic latitude.

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