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系統識別號 U0026-3008201615564600
論文名稱(中文) 質子環之質子密度與速度對波之不穩定性之影響
論文名稱(英文) Influence of the Proton Density and Velocity of the Proton Ring Velocity Distribution on the Instabilities of Waves
校院名稱 成功大學
系所名稱(中) 太空與電漿科學研究所
系所名稱(英) Institute of Space and Plasma Sciences
學年度 104
學期 2
出版年 105
研究生(中文) 孫聖翔
研究生(英文) Shen-Hsiang Sun
學號 LA6991099
學位類別 碩士
語文別 中文
論文頁數 146頁
口試委員 指導教授-談永頤
口試委員-汪愷悌
口試委員-楊雅惠
中文關鍵字 質子環狀速度分布 
英文關鍵字 proton ring velocity distributions 
學科別分類
中文摘要 離子環狀速度分布除了觀測研究外,多探討離子環狀速度分布與磁層其他電磁波之關係與影響。本篇論文將依循Perraut et al. [1982]之研究,電漿為冷電漿,分布函數假設為一個狄拉克函數且波的行進方向與背景磁場垂直,經由Vlasov equation求得行列式,再由數值分析進一步探討當質子環狀速度分布的密度與速度變化時對波的不穩定性造成之影響。
首先藉由將Vlasov equation線性化,將擾動項與非擾動項分離出來,接著利用特徵法找出一階擾動分布函數,再利用Maxwell’s equations與擾動電流密度求得電漿之行列式,即可使用此行列式求出此電漿之色散關係。
求得行列式後,我們利用數值分析來求解色散關係。首先利用行列式繪製ω_r-ω_j等高線圖,其中等高線之值即為色散方程之絕對值|D|,利用觀察等高線圖,尋找封閉且向內收縮之等高線圖,當D→0時即代表找到一個色散關係之解。再利用牛頓法由此解的位置出發尋找其他解的位置,最終即可繪製出一張ω-k圖,亦即找出色散關係之各個解。
在此篇論文中,在 ρ=0.02時: 並無不穩定性現象; 波的速度隨U_⊥/V_A 增加而略微下降,當U_⊥/V_A =0.8、1.25、1.4時此波為Alfvén wave,在U_⊥/V_A =1.4時有阻尼的現象。偏振為左、右旋橢圓偏振,阻尼為右旋偏振。在 ρ=0.2時: 波出現擾動態,不穩定性現象隨著波數提高而增強,U_⊥/v_A 的增加能擴展擾動態產生的範圍(R~4.26→R~2.1、Λ_⊥~5.5→Λ_⊥∼3.6)。波的偏振方面在非擾動時為橢圓偏振、右旋圓偏振及類線偏振,當擾動時其偏振振幅隨時間而增加,偏振方向擾動態皆為左旋偏振。
在此篇論文中質子環狀速度分布的不穩定性現象中,質子環密度是造成擾動的主要變因,而質子環速度則對不穩定性現象無顯著影響。
英文摘要   This study extends the work by Perraut et al. [1982] to investigate how proton ring velocity distributions affect the instabilities of waves. We assume that the proton velocity distributions consist of two populations: one forming the cold plasma and one forming a cold ring at finite perpendicular velocity U_⊥, both populations with velocity distributions represented by Dirac delta functions. Wave propagates in the perpendicular direction with background magnetic field. We obtain first-order perturbed distribution function from Vlasov equation (kinetic theory) by method of Characteristics, and derive the dielectic tensor by using first-order perturbed current density and Maxwell’s equations. We numerically determine the dispersion relation mainly by Newton’s method, also using contour plots to provide new initial guess. Then we obtain two kind of waves: one is Bernstein mode-like waves (occurring at the harmonics of proton gyrofrequency), the other one is non-dispersive waves. When ρ, the density ratio between the proton ring and the cold proton population is 0.02, there are instabilities, the group velocity of the waves decreases as the ratio between U_⊥ and Alfvén speed v_A increases. Alfvén waves satisfy the dispersion relation when ρ=0.02 and U_⊥/v_A =0.8,1.25,1.4.
Bernstein mode-like waves are of right-handed elliptically polarization or left-handed elliptically polarization. When ρ=0.02 and U_⊥/v_A =1.4, right-hand polarized non-dispersive waves are damped. There are instabilities when ρ=0.2. Increase in the ratio of U_⊥/v_A can increase the range of the wave numbers of unstable waves (R~4.26→R~2.1、Λ_⊥~5.5→Λ_⊥∼3.6, where R is the normailized frequency, Λ_⊥ is the normalized perpendicular wave number). Bernstein mode-like waves in the ρ=0.2 case have three kind of polarizations: right-handed elliptically polarization, left-handed elliptically polarization and linear-like polarized. The influence of the proton ring velocity distribution on the instabilities of waves is dominated by the proton ring density.
論文目次 摘要 I
Abstract III
誌謝 IX
圖目錄 XI
第一章 序論 1
第一節 背景介紹 1
1. 磁層(Magnetosphere) 1
2. 離子環狀速度分布(Ion Ring Velocity Distribution) 2
第二節 研究動機 4
第二章 理論推導 5
第一節 Vlasov equation 5
第二節 一階擾動分布函數(first-order perturbed distribution function) fα1 6
第三節 一階擾動電流密度(first-order perturbed current density) J1 11
第四節 行列式(Determinant) D 12
第五節 色散關係(Dispersion relation) 18
第三章 數值計算 22
第一節 牛頓法(Newton’s method) 22
第二節 等高線圖法(Contour Plot) 23
第三節 使用自動化牛頓法求解色散方程 25
第四章 數值計算結果與討論 27
第一節 ρ=0.02時之色散關係 27
1. ρ=0.02、U_⊥/v_A =0.2 27
2. ρ=0.02、U_⊥/v_A =0.8 36
3. ρ=0.02、U_⊥/v_A =1.25 41
4. ρ=0.02、U_⊥/v_A =1.4 44
第二節 ρ=0.2時之色散關係 50
1. ρ=0.2、U_⊥/v_A =0.2 50
2. ρ=0.2、U_⊥/v_A =0.8 55
3. ρ=0.2、U_⊥/v_A =1.25 59
4. ρ=0.2、U_⊥/v_A =1.4 63
第三節 討論 68
第五章 總結 69
參考文獻 70
附錄1 71
附錄2 89
附錄3 126
參考文獻 Gary, S. P., K. Liu, and D. Winske (2011), Bernstein instability driven by suprathermal protons in the ring current, J. Geophysical. Res. 116. A08215.
Gurnett, D. A. (1976), Plasma Wave Interactions With Energetic Ions Near the Magnetic Equator, American. Geophysical. Union. 2765-2770.
Kuz'menkov L.S. and M.I. Sitnov, Bernstein mode formation in weak magnetic field. Phys.Lett.A 1984, v.100, pp.141-143.
Newberger, B. S. (1982), New sum rule for products of Bessel functions with application to plasma physics, J. Math. Phys. 23. 1278-1281.
Perraut, S., A. Roux, P. Robert, and R. Gendrin (1982), A Systematic Study of ULF Waves Above F_(H^+ ) From GEOS 1 and 2 Measurements and Their Relations With Proton Ring Distributions, J. Geophysical. Res. 87. 6219-6236.
Russell, C.T., R.E. Holzer, and E.J. Smith (1970), OGO3 Observations of ELF Noise in the Magnetoshpere, 2. The Nature of the Equatorial Noise, J. Geophysical. Res. 75. 755-768.
Thorne, R. M. (2010), Radiation belt dynamics: The importance of wave particle interactions, J. Geophysical. Res. 37. L22107.
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