本論文旨在設計 mini-Tokamak 的中心螺線管電流波形，以產生電漿擊穿所需的環形迴路電壓，並進一步驅動電漿電流至 10 kA，同時將電漿加熱至 10 eV。隨時間變化的中心螺線管電流會在真空腔的內外壁中誘發渦電流，而這些渦電流將影響迴路電壓。為此，我們建立了一套數值模型，可用來計算托克馬克各組件的電阻與電感，並求得真空腔壁中感應的渦電流及其對迴路電壓的影響。模擬結果顯示，渦電流在初期會抑制迴路電壓，但其效應將迅速衰減，在 0.5 ms 後影響降至 5% 以下。因此，中心螺線管電流的作用時間應超過 0.5 ms，以降低渦電流干擾。此外，我們建立了一個模型，用以計算電漿電流與溫度在歐姆加熱下的變化。電漿電阻採用新古典理論計算，而電離率則使用一套混合模型求得，此模型結合經驗公式與 ADAS 資料庫中的係數，可描述從弱電離狀態至完全電離過程中的電離行為。為在粒子密度 n = 10¹⁷ m⁻³（對應氣壓約 10⁻⁵ Torr）且磁力線連接長度為 500 m的條件下實現擊穿，所需的環形迴路電壓約為 0.046 V。在此條件下，中心螺線管的電流變化率需大於 289 A/ms。為使 mini-Tokamak（主半徑 85 mm、短半徑 55 mm、橢圓延展率 κ = 1.82）中的電漿溫度達到 10 eV，中心螺線管電流應先於 10 ms 內線性由 5.4 kA 降至 0 kA，再於接續 40 ms 內由 0 kA 緩降至 −1.5 kA。在不考慮粒子流失及其所造成的能量流失的條件下，此中心螺線管電流波形可使電漿溫度在 40 ms 內維持於 10 eV。

This thesis presents the design of the central solenoid current profile of the mini-Tokamak to generate the toroidal loop voltage required for plasma breakdown and to subsequently drive the plasma current to 10 kA and heat the plasma to 10 eV. The time-varying current induces eddy currents in the inner and outer vacuum-vessel walls, which in turn affect the loop voltage. A numerical model is developed to compute the resistance and inductance of the tokamak components, the induced eddy currents and the loop voltage, with the effects of eddy currents in the vacuum-vessel wall included. The calculations show that eddy currents initially suppress the loop voltage but decay rapidly, with their influence reducing to below 5% after 0.5 ms. Consequently, the solenoid current should be maintained longer than 0.5 ms to minimize eddy current effects. In addition, a time-dependent plasma model is constructed to calculate plasma current and temperature evolution due to Ohmic heating. Plasma resistance is calculated based on neoclassical resistivity, and the ionization fraction is obtained using a hybrid model that combines collisional model from empirical formula with coefficients from the ADAS database. This formulation enables estimation of ionization behavior from the initial weakly ionized state to a fully ionized plasma. To achieve breakdown at a particle density of n = 1017 m−3 (corresponding to a pressure of 10−5 Torr) with a connection length of 500 m, a loop voltage of approximately 0.046 V is required. Under these conditions, the central solenoid current change rate must exceed 289 A/ms. Furthermore, to achieve a plasma temperature of 10 eV in the mini-Tokamak with a major radius of 85 mm, minor radius of 55 mm, and elongation κ = 1.82, the central solenoid current should decrease linearly from 5.4 kA to 0 kA in 10 ms, followed by a ramp from 0 kA to –1.5 kA in 40 ms. When the particle losses and the corresponding energy losses are neglected, the plasma temperature can be maintained at 10 eV for 40 ms.

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