博碩士論文 90643002 詳細資訊




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姓名 林承忠(Cheng-Chung Lin)  查詢紙本館藏   畢業系所 太空科學研究所
論文名稱
(Fast Magnetosonic Shocks in the interplanetary Space and Magnetosphere)
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摘要(中) 在本論文中,我們針對兩個與快震波相關的研究做討論: (1)磁尾產生冷O+離子束(cold O+ beam or COB)的新機制,(2)分析行星際空間快震波(fast magnetosonic shock)的新方法。這兩個研究簡述如下:
(1)磁尾產生冷O+離子束(COB)的機制:
在地球磁尾腔/磁尾電漿篷(lobe/mantle)的COB觀測顯示,來自電離層的O+離子會流向磁尾遠端(40 – 200 RE),在磁尾中這些離子擁有高的流動能量(~ 1 – 20 keV)與低的垂直磁場熱能(~ 70 – 210 eV)。在這裡,我們提出一個包含非絕熱(non-adiabatic)震波加熱與絕熱演變(adiabatic evolution)加速過程的COB產生機制。我們利用理論分析與混合粒子模擬(hybrid simulation)探討震波加熱過程,結果發現在震波經過電漿後,重離子得到了很高的垂直磁場熱能。在震波加熱後, 重離子的垂直熱能接著在磁尾的絕熱演變過程中被大量轉換成平行磁場的流動能量,此流動能量大小大致可以與觀測相符。我們發現,如果在磁層極區(polar magnetosphere)中有弱的震波(Alfvén馬赫數MA ~ 1.05 – 1.2),即可將O+離子加熱到觀測的能量規模。這些弱震波可能由行星際震波/不連續結構與地球磁層交互作用而產生。
(2)分析行星際空間快震波的新方法:
在這裡我們提出一個新的震波擬合(fitting)方法,可以從觀測資料中得到滿足非均向(anisotropic)Rankine-Hugoniot關係式的解。新方法利用Monte Carlo計算方式與最小平方差技巧,用到的參數有上下游磁場、電漿密度、電漿熱壓比(plasma beta)、電漿非均向參數、W (上下游電漿流速差, V2 – V1)與?t (兩衛星觀測到同震波的時間差)。我們定義一個損失函數(loss function),此函數定義為觀測值與預測值差的總合,我們要的解就是使損失函數為最小值的解。對於無法擬合的震波,我們在Rankine-Hugoniot關係式中加了兩個新的參數項,一個加在法向(normal)動量方程式,另一個加在能量方程式中。這兩個新參數在系統中代表多出來的法向動量與熱流(heat flow),而新方法會得出這兩個參數的值。我們利用幾個假想的震波資料檢驗新方法,同時也將新方法運用在兩個被WIND與Geotail衛星觀測到的行星際震波,驗證了新方法可以得出精確的震波法向量(shock normal),且可以運用於垂直與平行震波。
由於在此我們假設He2+離子速度偏移量很小,未將此效應考慮在擬合計算模型中,所以新方法只能在震波中He2+離子速度偏移量很小且可被忽略的情形下使用。我們發現,當偏移量很大時,共平面特性可能無法成立。由WIND衛星在黃道面附近的震波觀測我們得知,偏移所造成的偏移壓力(slippage pressure)通常遠小於熱壓,可以被忽略,所以新方法可以運用於絕大多數在黃道面附近觀測到的快震波。
摘要(英) In this dissertation, we focus on two studies for fast shocks: 1) a new model for generating the observed cold O+ beam in the geomagnetic tail lobe, and 2) a new method for analysis of interplanetary shocks. These two studies are described briefly below:
(1) The model for generating the observed cold O+ beam:
Observations of cold O+ beams (COBs) in the lobe/mantle region of Earth’’s magnetotail showed that O+ ions originating from the ionosphere can stream into the distant tail (40 – 200 RE). These O+ ions have a high parallel streaming energy (~ 1 – 20 keV) and low perpendicular thermal energy (~ 70 – 210 eV) in the distant tail. Here we propose that the non-adiabatic shock heating of O+ ions in the polar magnetosphere and the subsequent adiabatic evolution of ion velocity can lead to the occurrence of COBs in the tail lobe. The heating and acceleration of heavy O+ ions by fast shocks are studied by a theoretical analysis and hybrid simulations. It is found that after the passing of fast shock, heavy ions gain a large perpendicular thermal energy. After heating, the adiabatic evolution in the tail lobe can transfer a major part of perpendicular thermal energy to the observed parallel streaming energy. We have found that weak fast shocks in the polar magnetosphere with Alfvén Mach number MA ~ 1.05 – 1.2 can lead to the observed streaming energy associated with COBs. Weak fast shocks in the magnetosphere can be generated by the interaction of interplanetary shocks/discontinuities with Earth’’s magnetosphere. Escaping ionospheric O+ ions can gain enough energy from shock heating to account for observations of COBs.
(2) The method for analysis of interplanetary shocks:
Here we present a novel procedure for shock fitting of the one-fluid anisotropic Rankine-Hugoniot relations and of the time difference between two spacecraft observations in the case of small He2+ slippage. A Monte Carlo calculation and a minimization technique are used. The observed variables including the up- and downstream magnetic fields, plasma densities, plasma betas, plasma anisotropies, W (the difference between the down- and upstream velocities, W=V2-V1), and delta_t (the time difference between two spacecraft observations) are used in our procedure where V is defined as the center of mass velocity of plasmas. A loss function based on a difference between the calculated and the observed values is defined, and the best-fit solution is found by searching for the minimum loss function value. For shocks that cannot be fitted well, we introduce two new parameters in the modified RH relations, one in the normal momentum flux and the other in the energy flux equations. These two parameters are interpreted as the equivalent “normal momentum” and “heat” fluxes needed in the RH relations. Their amounts can be estimated from our procedure. Several synthetic shocks are given to verify our procedure. We also apply this procedure to two interplanetary shocks observed by both the WIND and Geotail spacecraft. The results demonstrate that our method works for both the synthetic and the real shocks. We have shown that our method can provide accurate shock normal estimations for perpendicular and parallel shocks as well.
Given that our model is based on the RH relations that do not include the effect of He2+ slippage, it can only be applied to the cases with an ignorable slippage pressure tensor. We found that when the slippage pressure is large, the magnetic coplanarity property may not be valid. We have investigated the pressure tensor due to alpha particle slippage using the WIND spacecraft data. It is found that in general the slippage pressure is small in comparison with the thermal pressure of the system and can be ignored. Thus, our model can be applied to most interplanetary shocks observed near the ecliptic plane.
關鍵字(中) 關鍵字(英) ★ shock heating
★ shock fitting
★ COB
★ fast magnetosonic shock
★ RH relations
★ MHD shock
★ fast shock
論文目次 Title page
Abstract i
摘要 iii
致謝 v
Table of Contents vi
List of Tables viii
List of Figures ix
Ch 1 Introduction 1
1.1 Cold O+ Beam (COB) in the Magnetospheric Tail Lobe 1
1.2 Shock Analysis Methods 3
Ch 2 Basic MHD Equations for Shocks 8
2.1 MHD equations for anisotropic plasma 8
2.2 Rankine-Hugoniot (RH) Relations 10
2.2.1 Conventional RH relations 10
2.2.2 RH relations with additional terms 15
2.3 Fast Shock Solution 17
Ch 3 A Mechanism of Generating Cold O+ Beam (COB) 21
3.1 Observation 21
3.2 Non-adiabatic Shock Heating in Polar Magnetosphere 23
3.2.1 Perpendicular energization of ions across fast shocks 23
3.2.2 Verifying in hybrid simulations 30
3.3 Adiabatic Evolution in Tail Lobe 34
3.3.1 Ion’s adiabatic evolution along geomagnetic field line 34
3.3.2 Geomagnetic field and plasma model in polar magnetosphere and tail lobe 37
3.3.3 Comparison between observations and shock heating result 40
3.4 Discussion and Summary 43
3.4.1 Comments on Seki models 43
3.4.2 Existence of shocks in magnetosphere 46
3.4.3 Summary 48
Ch 4 A New Shock Analysis Approach Using Monte Carlo Calculation 50
4.1 The New Fitting Approach 50
4.1.1 Method A 52
4.1.2 Method B 57
4.2 Tests of the Method Using Synthetic Shocks 59
4.2.1 An oblique shock with zero ?G and ?Q 59
4.2.2 Errors in ?G, ?Q, and fast Mach number 73
4.2.3 An oblique shock with significant ?G and ?Q 77
4.2.4 Perpendicular and parallel shocks (with zero ?G and ?Q) 79
4.2.5 Single spacecraft method 83
4.2.6 Fitting for the subset of the RH relations 83
4.3 Error Analysis 84
4.3.1 Systematic errors 84
4.3.2 Array size 87
4.4 Applications to Interplanetary Shocks 89
4.4.1 Spacecraft data 89
4.4.2 One-fluid plasma moments 90
4.4.3 The Oct. 19, 1995 shock 91
4.4.4 The March 23, 1995 shock 98
4.5 Discussion 101
4.5.1 Issue in uniqueness of solution 101
4.5.2 Alpha particle slippage at interplanetary shocks 103
4.5.3 Effect of alpha slippage to the RH relations: Invalidation of coplanarity 108
4.5.4 Possible origins of ?G and ?Q 109
4.5.5 Monte Carlo method and its potential 110
4.6 Summary 110
Ch 5 Summary 113
5.1 Generation of COB 113
5.2 New Shock Fitting Method 114
References 116
Appendix A Magnetic Coplanarity 126
Appendix B Solution for Isotropic RH Relations 127
Appendix C Parametric Equations for the Anisotropic RH Relations 129
Appendix D Mach Numbers 132
Appendix E Perpendicular Shock Solution 134
Appendix F Slippage Pressure Tensor in Solar Wind 136
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指導教授 李羅權、趙寄昆
(Lou-Chuang Lee、Jih Kwin Chao)
審核日期 2006-7-16
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