帶電粒子束在科學、醫學、工業以及軍事上面有很多的用途。因此
對於帶電粒子束各種特性的掌握度越高，在應用上的設計與現象的解釋
就越有幫助。而空間電荷效應限制帶電粒子束的總電荷數，且直接影響
電子束的品質，因此這方面研究也成為真空電子學的重要之研究議題。
帶電粒子束所注入、加速與形成的區域主要分為加速區或飄移區。
通常是在加速區陰極產生帶電粒子，經過加速腔體把帶電粒子加速到一
定的能量，再導入飄移區。然而，空間電荷極限電流會限制帶電粒子束
通過腔體的最大電流。空間電荷極限電流就是來自於帶電粒子束在腔體
中的空間電荷效應對於系統的限制。這幾年來由於科技的進步，帶電粒
子束的能量越來越高，束寬越來越窄。傳統用來估計空間電荷極限電流
的公式已不敷使用，因此必須對於理論加以修正。
經過這幾十年來的發展，空間電荷極限電流的理論已經可以考慮相
對論性效應、有限束寬粒子束與短脈衝等幾何效應。但仍然有許多議題
尚未被探討。首先，目前的理論都只考慮靜電模型，電磁效應基本上是
忽略不考慮的。因此我們先利用了電磁的二維粒子式電漿模擬來研究電
磁效應對於加速區空間電荷極限電流的影響。我們發現在短脈衝且有限
束寬的情況下，電磁效應是不能忽略的。我們的研究結果也指出靜電模
型的適用範圍為長脈衝的粒子束，或是短脈衝但大束寬的粒子束。
目前大部分的研究都是探討加速區的空間電荷極限電流，但對於飄
移區，就相對較少人研究。因此我們針對飄移區，發展了二維長脈衝相
對論性的空間電荷極限電流理論， 並研究了超過極限電流時帶電粒子束
的動力學行為。我們透過二維靜電粒子式電漿模擬來驗證我們的理論，
i
也探討如何在模擬中決定極限電流。
而後我們發展了一套二維長脈衝的統一理論把加速區與飄移區連結
起來， 並研究其空間電荷極限電流以及大於極限時的動力學行為。理
論也說明了何時我們可以把系統視為加速區，何時能視為飄移區。研究
結果指出二維的空間電荷極限電流主要由幾何效應所主導， 而當注入電
流超過極限時，則是由粒子入射的初始速度來主導系統的動力學行為。
除了長脈衝粒子束外，我們也利用了一維的電荷薄片模型研究了電
子束團在加速區以及飄移區的最大電荷密度。電子束團可應用在時間解
析的電子顯微鏡、自由電子雷射、Smith-Purcell 輻射...等機制， 也因此空間電荷效應在電子束團的應用上扮演著很重要角色。我們發展了一套方法能夠很快地決定在腔體中最適當的電荷密度，以避免電子束團抵達陽極的時序不會因空間電荷效應被破壞。此方法也可以用在相對論性的範疇，因此可適用性非常廣。
本論文針對空間電荷極限電流的理解在深度與廣度上的提升。此
外，理論模型以及模擬方法也有助於相關應用的發展與研究。

Charged particle beams have intensive applications on science, medicine, industry and military. Hence, much more information and understandings from charged particle beams, much more advantages on the practical designs and explanations of phenomena. Space charge effect limits the total number of charges and affects the beam quality of the charged particle beam directly, so that the study of this research topic becomes an important research issue in vacuum electronics. Basically, the injection, acceleration and the formation of a charged
particle beams are operated in accelerating regions or drift regions. The charge particle sources are usually generated from cathode and accelerated up to the designed energy in the accelerating region, and then injected into the drift region for the practical use. However, Space Charge Limited (SCL) Current would limit the maximum current across the accelerating
region or drift region. The SCL current results from the limit due to the space charge effect of the charge particle beam in the system. Thanks to the improvements of science and technology, the charge particle beams have much higher energy and thinner beam width. The traditional formula to estimate the SCL current is no longer available, and thus needs to be modied. In the past few decades, the theory of the SCL current has been revised extensively to consider various effects such as nite emission area, short pulse length, relativistic effects, and etc. However, there are still many issues need to be discussed. First of all, the current theories only consider
the electrostatic (ES) model and ignore the electromagnetic (EM) effects. Thus we rst used the two-dimensional (2D) EM particle-in-cell (PIC) simulation to study the EM effects on the SCL current in an accelerating region. We found that EM effects cannot be ignored when a short-pulse and nite-width charge particle beam is considered. Our research results
also indicated that ES model is only available for long-pulse cases or short-pulse beams but with larger width.
The most of the research regarding the SCL current focus on the accelerating region, but the drift region draws less attentions. For this reason, we developed a 2D ES relativistic SCL current theory for drift region, and also studied the dynamical behavior when the injected current exceeds the
threshold. It is veried by 2D ES PIC simulation, and the determination
of SCL current in the simulation was also discussed.
We further developed a 2D long-pulse unied theory to combine the accelerating region and drift region. The SCL current and the dynamical behavior when the injected current exceeds the threshold were derived, and the transition from the accelerating region to the drift region also studied. The theoretical analysis shows that the 2D SCL current is mainly determined by the geometrical effects, but the dynamical behaviors of the current flow are mainly determined by the initial velocity at higher current density exceeding the SCL current density.
Besides the long pulse charge particle beam, a charge sheet model was also proposed for the study of the maximum charge density of an electron pulse train injected to in an accelerating region or a drift region with uniform temporal pulse separation. An electron pulse train can be applied to the time resolved electron microscopy, Smith-Purcell radiation and free electron lasers, thus the space charge effect of an electron pulse train plays an important role for the applications. We developed a efficient way to determine the maximum charge density without the temporal distortion when the pulse train arriving at the anode. The method can also be applied in relativistic regime and has wide range applications.
This dissertation deepens and widens the understanding of SCL current. Moreover, these theoretical models and simulation methods are useful for the researches and developments of the future corresponding applications.

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