博碩士論文 90249002 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:13 、訪客IP:54.161.118.57
姓名 羅英奕(Ying-Yi Lo)  查詢紙本館藏   畢業系所 天文研究所
論文名稱 宇宙射線和磁流動力系統之不穩定性
(Instability of the Cosmic Rays and MHD Waves System)
相關論文
★ 宇宙射線在球形震波的加速★ 重力透鏡效應造成的類星體-星系關聯與星系-星系相關函數
★ 星際物質演化的研究★ 宇宙射線在恆星風的自相似解
★ 分子雲演化的二維模型★ 以2MASS近紅外資料研究太陽附近的疏散星團
★ 以二微米巡天觀測近紅外資料研究本銀河系結構★ 橢圓星系中基礎平面及等效半徑的多波段研究
★ 初生星團的生存率★ 橢圓星系外型與紅移關聯之研究
★ 在不同均功參數下星團的擴散及核心的形成★ 兩微米巡天數星所取得的銀河系資訊
★ A numerical simulation survey on the outflow from the Galactic center★ Galaxy Cluster Dynamics and Modified Newtonian Dynamics
★ Strong Gravitational Lensing in Modified Newtonian Dynamics★ The destiny of a binary system under different mass loss scenarios
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 從歷史上,我們學到如三國時關公入千軍萬馬取上將首級如「探囊取物」、唐朝郭子儀「單騎退敵」,等等。這些人雖然為數不多,但卻扮演著關鍵性的角色。就如同自然界中,宇宙射線雖然在數量上很少,但卻有相當高的能量,而是否對宇宙有一定的影響?本論文以解析和數值模擬的方法,研究宇宙射線和電漿耦合的系統。
第一章提出一自洽的方程組,作為我們的模型。它們相互影響,彼此襯托,以流體的方式描繪出宇宙射線,電漿,磁場和波的關係。於第二章利用解析的方法,討論此模型的穩定性。除了對參數空間在一般及極限情況下外,也對第一章模型的穩態解,廣泛而深入的探究模型在線性微擾方面的種種。之前的研究已知由熱電漿、宇宙射線及反向艾爾文波(Alfvén waves)構成的宇宙射線-電漿系統,顯示系統對由宇宙射線驅動的磁聲(magnetoacoustic)不穩定性非常敏感。加入正、反向的艾爾文波能量方程後,形成一個四流體-即熱電漿和宇宙射線外,再加入正、反向的艾爾文波。此時,二階費米(Fermi)效應自然就會出現在這系統中。這系統能量交換有三種:(一)、波的能量由宇宙射線透過自我激發的效應產生,(二)、波則藉由二階費米加速將能量傳送給宇宙射線,(三)、宇宙射線壓力梯度與波的壓力梯度則傳遞能量給電漿;反之亦然。第三章則省略模型中波的效應,利用 MOCCT 數值的方法(對法拉第方程,是先求出電場),模擬在星系盤面上三維的 Parker 不穩定性。對宇宙射線擴散項先用 Biconjugate gradient stabilized (BICGStab)方法,再以修正的Lax-Wendroff 方法求得宇宙射線能量密度。我們在解 MHD 方程上用修正的 Lax-Wendroff 方法,而在針對解宇宙射線擴散方程上選擇了隱性(implicit)的 BICGStab 方法。所以整體而言,我們是利用混合(hybrid)數值方法。在非線性演化期間,我們發現了一些特性。當擴散係數遞減時,宇宙射線的壓力分佈從原來的均勻分佈變成集中在磁泡的足點附近;同時,宇宙射線的壓力梯度迫使磁泡的頂端變得比較大。於是,向下掉落的物質被壓力梯度所阻,因此減緩了不穩定的成長。此外,在演化末期,三維模擬由於交換不穩定(interchange instability)的參與,其結果與二維非常不同。
摘要(英) In histroy, there are only few people who have very high positive energy, however, they trun the table in critical time. Analoginally, the cosmic rays with the energy density is larger than plasma and magnetic field, it should participate in and influence the evolutin of astronomical enviroments, despite they are rare. This thesis investigates a self-consistent hydrodynamical model, which comprises magnetized thermal plasma, cosmic rays, forward and backward propagating Alfvén waves.
Chapter 1 introduces our four-fluids model, begin from the cosmic ray transport equation, after frames trasformation and includes the relation between scattering frequencies and gwowth rate of Alfvén waves, intergal the momentum, then toward the hydrodynamics model.
In chpater 2, we study the stability of our model and discuss basic linearly and analytically. Prior rsearch indicated there is magneto-acoustic instability driven by cosmic ray and backward Alfvén wave excited by streaming instability. As the result by adding the forward Alfvén wave, the second order Fermi acceleration effect arises in our four-fluid model (i.e. cosmic ray, plasma, forward and backward Alfvén waves), spontaneousness. This cosmic-ray plasma and waves system exchange energy among cosmic ray, plasma and waves via: (1) waves gain energy from self-excite effect by cosmic ray; (2) the second order Fermi effect transfer energy from waves to cosmic ray, and (3) The work done by pressure gradient of cosmic ray and waves lead the plasma gain energy from cosmic ray and waves,vice versa.
In chapter 3, by using the MOCCT (Method of Characteristics/Constrained Transport) MHD code, we exploits a 3D numerical simulation, points on the Parker instability, but ingores the effects of self-gravity and waves. After sloved the diffusion term of cosmic ray energy equation via BICGStab (Biconjugate gradient stabilized) method, then obtained the convection trem and other MHD equations by modified Lax-Wendroff method. In general, we stduy 3D Parker instability including the cosmic ray effect with a hybrid numerical method.
During the epoach of non-linear stage, we found some characteristics: the cosmic ray pressure distribution is rather nonuniform. Cosmic rays tend to accumulate near the footpoint of the magnetic loop, and the cosmic ray pressure gradient force toward the top of the loop becomes larger. The falling motion of matter is then impeded by the cosmic ray pressure gradient force, and the growth rate of the Parker instability decreases. For 3D case, at near the end of evolution, due to the interchange mode participate in the system, the results are very different between 3D and 2D.
關鍵字(中) ★ 不穩定性
★ 磁流動力
★ 宇宙射線
關鍵字(英) ★ instability
★ MHD
★ cosmic ray
論文目次 Chinese Abstract i
Abstract iii
Chinese Acknowledgments v
Acknowledgments vii
Contents ix
1 Model 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Scattering of Cosmic Rays . . . . . . . . . . . . . . . . 3
1.1.2 Streaming Instability . . . . . . . . . . . . . . . . . . . 5
1.2 The Cosmic Ray Transport Equation . . . . . . . . . . . . . . 5
1.2.1 Transform to The Original Frame of Reference . . . . . 7
1.2.2 Relation Between Scattering Frequencies and Growth
Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Toward The Hydrodynamics . . . . . . . . . . . . . . . . . . . 11
1.3.1 Complete Set of Equations . . . . . . . . . . . . . . . . 13
1.4 Nonlinear Test Particle Picture . . . . . . . . . . . . . . . . . 15
1.5 Steady State Solution . . . . . . . . . . . . . . . . . . . . . . . 18
2 Instability Analysis of Cosmic Rays And Waves System 1
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.1 The Concept of Stability . . . . . . . . . . . . . . . . . 23
2.2 Methods to Study Instability . . . . . . . . . . . . . . . . . . . 26
2.2.1 Energy Principle . . . . . . . . . . . . . . . . . . . . . 27
2.2.2 Interchange Instability . . . . . . . . . . . . . . . . . . 29
2.2.3 Normal Mode Analysis . . . . . . . . . . . . . . . . . . 30
2.2.4 An Example . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.5 Generalized Hermite-Biehler theorem . . . . . . . . . . 32
2.2.6 Routh-Hurwitz Stability Criterion . . . . . . . . . . . . 33
2.2.7 Sylvester matrix . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Linear Stability Analysis on The Four-
uid Model . . . . . . . 12
2.4 Results I { Special Case . . . . . . . . . . . . . . . . . . . . . 39
2.4.1 Nonlinear Test Particle Picture Case . . . . . . . . . . 39
2.4.2 Perpendicular perturbations (mu = 0) Case . . . . . . . 48
2.4.3 Unidirectional wave system (P+w0 = 0 or P-w0 = 0) . . . 49
2.4.4 Large cosmic ray pressure (Pc0 >> (P+w0 + P-w0)) . . . . . 50
2.4.5 Vanishing cosmic ray pressure (Pc0 ~ 0) . . . . . . . . 52
2.4.6 Large wavenumber (k lD) . . . . . . . . . . . . . . . 52
2.4.7 Vanishing wavenumber (~k ~ 0) . . . . . . . . . . . . . 53
2.5 Results II General cases . . . . . . . . . . . . . . . . . . . . 54
2.5.1 (e-; ec)-plane . . . . . . . . . . . . . . . . . . . . . . . 54
2.5.2 (e-; ~k)-plane. . . . . . . . . . . . . . . . . . . . . . . . 54
2.5.3 (e-; mu)-plane . . . . . . . . . . . . . . . . . . . . . . . . 55
2.5.4 (mu; ~k)-plane . . . . . . . . . . . . . . . . . . . . . . . . 55
2.5.5 (mu; betaw)-plane . . . . . . . . . . . . . . . . . . . . . . . 55
2.5.6 ( betas; beta w)-plane . . . . . . . . . . . . . . . . . . . . . . 56
2.5.7 (~nug0; betaw)-plane . . . . . . . . . . . . . . . . . . . . . . 56
2.6 Results III { An Example . . . . . . . . . . . . . . . . . . . . 57
3 3D Simulation of Parker Instability with Cosmic Ray 65
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.1 Lax-Wendroff Method . . . . . . . . . . . . . . . . . . 68
3.1.2 Time Splitting And BICGstab Method . . . . . . . . . 69
3.1.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . 73
3.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 76
3.3 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.4 Initial Condition . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.5.1 kappa = 200 . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.5.2 kappa = 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4 Summary 97
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
A Linearized Equations for System 107
B Coefficient for Polynomial 111
C Criteria for real roots of a quartic equation 115
D Lax-wendroff Metods 117
E BICGstab Method 119
參考文獻 [1] Achterberg, A., Blandford, R. D., and Periwal, V. Two-Fluid
Models Of Cosmic Ray Shock Acceleration. Astronomy and Astrophysics
132 (1984), 97-104.
[2] Aharonian, F. A.and Akhperjanian, A. G., Aye, K.,
Bazer-Bachi, A. R., Beilicke, M., Benbow, W., Berge,
D., Berghaus, P., Bernlohr, K., Bolz, O., Boisson, C.,
Borgmeier, C., Breitling, F., Brown, A. M., Bussons Gordo,
J., Chadwick, P. M., Chitnis, V. R., Chounet, L., Cornils, R.,
Costamante, L., Degrange, B., Djannati-Ata, A., Drury,
L. O., Ergin, T., Espigat, P., Feinstein, F., Fleury, P.,
Fontaine, G., Funk, S., Gallant, Y. A., Giebels, B.,
Gillessen, S., Goret, P., Guy, J., Hadjichristidis, C.,
Hauser, M., Heinzelmann, G., Henri, G., Hermann, G., Hinton,
J. A., Hofmann, W., Holleran, M., Horns, D., de Jager,
O. C., Jung, I., Khelifi, B., Komin, N., Konopelko, A.,
Latham, I. J., Le Gallou, R., Lemoine, M., Lemi ere, A.,
Leroy, N., Lohse, T., Marcowith, A., Masterson, C., Mc-
Comb, T. J. L., de Naurois, M., Nolan, S. J., Noutsos, A.,
Orford, K. J., Osborne, J. L., Ouchrif, M., Panter, M., Pelletier,
G., Pita, S., Pohl, M., Puhlhofer, G., Punch, M.,
Raubenheimer, B. C., Raue, M., Raux, J., Rayner, S. M., Redondo,
I., Reimer, A., Reimer, O., Ripken, J., Rivoal, M.,
Rob, L., Rolland, L., Rowell, G., Sahakian, V., Sauge, L.,
Schlenker, S., Schlickeiser, R., Schuster, C., Schwanke, U.,
Siewert, M., Sol, H., Steenkamp, R., Stegmann, C., Tavernet,
J.-P., Theoret, C. G., Tluczykont, M., van der Walt,
D. J., Vasileiadis, G.and Vincent, P., Visser, B., Volk, H. J.,
and Wagner, S. J. High-Energy Particle Acceleration In The Shell
Of A Supernova Remnant. Nature 432 (2004), 75-77.
[3] Bernstein, I. B., Frieman, E. A., Kruskal, M. D., and Kusrud, R. M. An Energy Principle For Hydromagnetic Stability Problems.
Proceedings of the Royal Society A 244 (1958), 17-40.
[4] Bhattacharyya, S. P., Chapellat, H., and Keel, L. H. Robust
Control: The Parametric Approach. Prentice Hall, 1995.
[5] Dewar, R. L. Interaction between HydromagneticWaves And A Time-
Dependent, Inhomogeneous Medium. Physics of Fluids 13 (1970), 2710-
2720.
[6] Dobbs, C. L., and Price, D. J. Magnetic Fields And The Dynamics
Of Spiral Galaxies. Monthly Notices of the Royal Astronomical Society
383 (2008), 497-512.
[7] Faber, T. E. Fluid Mechanics For Physicisits. Cambridge University
Press, 1997.
[8] Ferdinand, F. An Inhomogeneous Eigenvalue Problem. Journal of
Computational and Applied Mathmarics 167 (2004), 243-249.
[9] Franco, J., Kim, J., Alfaro, E. J., and Hong, S. S. The Parker
Instability In Three Dimensions: Corrugations And Superclouds Along
The Carina-Sagittarius Arm. The Astrophysical Journal 570 (2002),
647-655.
[10] Fukui, Y., Yamamoto, Y., Fujishita, M., Kudo, M., Torii,
K., Nozawa, S., Takahashi, K., Matsumoto, R., Machida, M.,
Kawamura, A., Yonekura, Y., Mizuno, N., Onishi, T., and
Mizuno, A. Molecular Loops In the Galactic Center: Evidence for
Magnetic Flotation. Science 314 (2006), 106.
[11] Gerard, L. G. S., and Diederik, R. BICGSTAB(L) For Linear
Equations Involving Unsymmetric Matrices With Complex. Electronic
Transactions on Numerical Analysis 1 (1993), 11-32.
[12] Hanasz, M., and Lesch, H. The Dynamical Coupling Of Cosmic
Rays And Magnetic Field In Galactic Disks. Astrophysics and Space
Science 281 (2002), 289-292.
[13] Heavens, A. F. Ecient Particle Acceleration In Shocks. Royal As-
tronomical Society, Monthly Notices 210 (1984), 813-827.
[14] Horbury, T., Forman, M., and Oughton, S. Spacecraft Observations
Of Solar Wind Turbulence: An Overview. Plasma Physics and
Controlled Fusion 47 (2005), B703-B717.
[15] Hughes, D. W., and Cattaneo, F. A New Look At The Instability
Of A Strati ed Horizontal Magnetic Field. Geophysical & Astrophysical
Fluid Dynamics 39 (1987), 65-81.
[16] Jiang, I. G., Chan, K. W., and Ko, C. M. Hydrodynamic Approach
To Cosmic Ray Propagation. I. Nonlinear Test Particle Picture.
Astronomy and Astrophysics 307 (1996), 903-914.
[17] Jones, F. C., and Ellison, D. C. The Plasma Physics Of Shock
Acceleration. Space Science Reviews 58 (1991), 259-346.
[18] Jones, T. W., and Kang, H. Time-Dependent Evolution Of Cosmic-
Ray-Mediated Shocks In The Two-Fluid Model. The Astrophysical Jour-
nal 363 (1990), 499-514.
[19] Jury, E. I. From J. J. Sylvester to Adolf Hurwitz: A History Review.
In Stability Theory Hurwitz Centenary Conference Centro Stefano Fran-
scini, Ascona (1995), R. Jeltsch and M. Mansour, Eds., pp. 53-65.
[20] Kim, W., Ostriker, E. C., and Stone, J. M. Three-Dimensional
Simulations Of Parker, Magneto-Jeans, and Swing Instabilities In Shearing
Galactic Gas Disks. The Astrophysical Journal, Volume 581, Issue
2, pp. 1080-1100 581 (2002), 1080-1100.
[21] Ko, C. M. A Note on The Hydrodynamical Description of Cosmic Ray
Propagation. Astronomy and Astrophysics 259 (1992), 377-381.
[22] Ko, C. M. Cosmic-Ray-Modi ed Shocks. Advances in Space Research
15 (1995), 149-158.
[23] Ko, C. M. Hydrodynamic Approach To Cosmic Ray Propagation. II.
Nonlinear Test Particle Picture In A Shocked Background. Astronomy
and Astrophysics 340 (1998), 605-616.
[24] Ko, C. M. Continuous So0lutions Of The Hydrodynamic Approach To
Cosmic-Ray Propagation. Journal of Plasma Physics 65 (2001), 305-
317.
[25] Ko, C. M., and Jeng, A. T. Magnetohydrodynamics Instability
Driven By Cosmic Rays. Journal of Plasma Physics 52 (1994), 23-42.
[26] Kulsrud, R. M., and Cesarsky. The E ectiveness of Instabilities
for The Con nement of High Energy Cosmic Rays in The Galactic Disk.
Astrophysical Letters 8 (1971), 189.
[27] Kulsrud, R. M., and Pearce, W. P. The E ect of Particle-wave
Interactions on The Propagation of Cosmic Rays. The Astrophysical
Journal 156 (1969), 445-469.
[28] Kuwabara, T., and Ko, C. M. Parker-jeans instability of gaseous
disks including the e ect of cosmic rays. The Astrophysical Journal 636
(2006), 290-302.
[29] Landau, L. D., and Lifshtiz, E. M. Fluid Mechanics. Pergamon
Press, 1987. Translated from the Russion by J. B. Sykes and W. H.
Reid.
[30] Lindqusit, S. On the Stability of Magneto-Hydrostatic Fields. Physics
Review 83 (1951), 307-311.
[31] Lo, Y. Y., and Ko, C. M. Stability of A System with Cosmic Rays
and Waves. Astronomy and Astrophysics, Volume 469 (2007), 829-837.
[32] Longair, M. S. High Energy Astrophysics, second ed., vol. 2. Cambridge
University Press, 1994.
[33] Malkov, M. A. Analytic Solution for Nonlinear Shock Acceleration
in the Bohm Limit. The Astrophysical Journal 485 (1997), 638-654.
[34] Malkov, M. A. Bifurcation, E ciency, and the Role of Injection in
Shock Acceleration with the Bohm Di usion. The Astrophysical Journal
491 (1997), 584-595.
[35] Marchuk, G. I. Method of Numerical Mathematics, vol. 2. Springer-
Verlag, New York,Heidelberg, Berlin, 1975.
[36] Matsumoto, T., Nakamura, F., and Hanawa, T. Gravitational
instability of magnetized lamentary clouds. 2: Rotation. In In ESA,
Fourth International Toki Conference on Plasma Physics and Controlled
Nuclear Fusion (1993), pp. 349-352.
[37] Morris, M. Galactic Prominences on the Rise. Science 314 (2006),
70-71.
[38] Ostrowski, M. Eciency of The Second-order Fermi Acceleration At
Parallel Shock Wave. Astronomy and Astrophysics 283 (1994), 344-348.
[39] Padmanabhan, T. Theoretical Astrophysics, vol. I: Astrophysical Processes.
Cambridge university Press, 2000
[40] Parker, E. N. The Dynamical State of the Interstellar Gas and Field.
Astrophysical Journal 145 (1966), 811-833.
[41] Press, W. H., Teukolsky, S. A., Vetterling, W. T., and
Flanney, B. P. Numerical Rrcipes in C, second ed. Press Syndicate
of the University of Cambridge, 1006.
[42] Priest, E. N. Solar Magnetohydrodynamics. D. Reidel Publishing
Company, P.O. Box 17, 3300 AA Dordrecht, Holland, 1987.
[43] Robert, R., and Rosier, C. Long Range Predictability of Atmospheric
Flows. Nonlinear Processes in Geophysics 8 (2001), 55-67.
[44] S., L. M., and Hong, S. S. ans Kim, J. Three-Dimensional Simulations
of the Jens-Parker Instability. Journal of The Korean Astronomical
Society 34 (2001), 285-287.
[45] Shibata, K., Tajima, T., Matsumoto, R., Horiuchi, T.,
Hanawa, T., Rosner, R., and Uchida, Y. Nonlinear Parker Instability
of Isolated Magnetic Flux in A Plasma. The Astrophysical Journal
338 (1989), 471-492.
[46] Skilling, J. Cosmic Rays in The Galaxy: Convection or Di usion.
The Astrophysical Journal 170 (1971), 265-273.
[47] Skilling, J. Cosmic Ray Streaming. I - E ect of Alfven Waves on
Particles. Royal Astronomical Society, Monthly Notices 172 (1975), 557-
566.
[48] Skilling, J. Cosmic Ray Streaming. III - Self-consistent Solutions.
Royal Astronomical Society, Monthly Notices 173 (1975), 255-269.
[49] Tanuma, S., Yokoyama, T., Kudoh, T., and Shibata, K. Magnetic
Reconnection Triggered by the Parker Instability in the Galaxy:
Two-dimensional Numerical Magnetohydrodynamic Simulations and
Application to the Origin of X-Ray Gas in the Galactic Halo. The
Astrophysical Journal 582 (2003), 215-229.
[50] Webb, G. M., Zank, G. P., Kaghashvili, E. K., and
Ratkiewicz, R. E. Magnetohydrodynamics waves in non-uniform
ows I: A Variational Approach. J. Plasma Physics 71 (2005), 785-
809.
[51] Yan, H., and Lazarian, A. Cosmic-Ray Scattering and Streaming
In Compressible Magnetohydrodynamic Turbulence. The Astrophysical
Journal 614 (2004), 757-769.
[52] Yang, L., and Xia, B. An Explicit Criterion to Determine The Number
Of Roots In An Interval Of A Polynominal. Progress In Nature
Science 10, 12 (2000), 897-910.
指導教授 高仲明(Chung-Ming Ko) 審核日期 2009-7-15
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明