NONLINEAR EVOLUTION OF KINETIC ALFVEN WAVES TURBULENCE IN SPACE
PLASMAS
SACHIN KUMAR
Z J
~s~~re OF TEC~N~~O~
CENTRE FOR ENERGY STUDIES
INDIAN INSTITUTE OF TECHNOLOGY, DELHI
JANUARY - 2010
NONLINEAR EVOLUTION OF KINETIC ALFVEN WAVES TURBULENCE IN SPACE
PLASMAS
Sachin 7(umar
CENTRE FOR ENERGY STUDIES
Submitted
in fulfillment of the requirements for the award of the degree of
Doctor of 2'FiiCosop/Iy
to the
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73
INDIAN INSTITUTE OF TECHNOLOGY DELHI
JANUARY - 2010
Dedicatei to Eon d ganesfia,
My Supervisor and 9Wy (Parents
O Indian Institute of Technology Delhi, New Delhi-2010
Certificate
This is to certify that the thesis entitled "Nonlinear evolution of kinetic Alfven waves turbulence in space plasmas" being submitted by Mr. Sachin Kumar to the Indian Institute of Technology Delhi, for the award of the degree of `Doctor of Philosophy' in Centre for Energy Studies, is a record of bonafide research work carried out by him. Mr. Sachin Kumar has worked under my guidance and supervision and has fulfilled the requirements for the submission of this thesis, which to my knowledge has reached the requisite standard.
The results contained in this work have not been submitted in part or full, to any other University or Institute for the award of any degree.
Prof. R. P. Sharma
Centre for Energy Studies
Indian Institute of Technology Delhi
Hauz Khas, New Delhi-110016
Acknowledgement
In the first place, I would like to thank my supervisor — Prof. R. P. Sharma for his supervision, advice, and guidance from the very early stage of this research as well as giving me extraordinary experiences throughout the work. Above all and the most needed, he provided me unflinching encouragement and support in various ways. His truly researcher intuition has made him as a constant oasis of ideas and passions in plasma physics, which exceptionally inspire and enrich my growth as a student, a researcher want to be. I am indebted to him more than he knows.
I thank to my other committee members, Prof. A. Chandra, Dr. H. D. Pandey and Prof. Y. Nath for their helpful suggestions and comments during my study. I wish to express my sincere thanks to Prof. S. C. Kaushik, Head, CES, Prof. A.
Chandra, Chairman, CRC, Prof. T. S. Bhatti, Secretary, CRC, Dr. H.D. Pandey and all faculty members of CES for their valuable suggestions, advices and approval of my thesis work.
I am particularly grateful to my colleagues Dr. Karuna Batra, Dr. Hemam Dinesh Singh, Dr. Prashant Kumar Chauhan, Sanjay Kumar, Prerana Sharma, Navin,
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Monika, Sangita, Alok, Nidhi and Ruchika who created friendly and productive atmosphere in our Plasma Simulation Lab. I am also grateful to my friends Charu Dwivedi and Virendra Singh for their moral support throughout my research period.
I am endlessly thankful to my parents, sisters for all love and care they gave me.
At last, I want to devote this thesis to my lord Shree Ganesha, whose blessings are always with me.
Sachin Kumar January-2010
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Abstract
This thesis presents the nonlinear evolution of kinetic Alfven waves (KAWs) to investigate the coherent structures formation, chaos, power spectra, particle heating and its application to various solar and magnetospheric plasmas. The research is focused on the dispersive properties as well as the Landau damping of KAW and its effects on magnetic coherent structures (filaments) and the power spectra. These coherent structures formation and turbulence spectra are found to play an important role in the heating and energization of plasma particles.
Numerical simulations of the nonlinear KAW dynamics when the nonlinearity arises due to ponderomotive effects and Joule heating by taking the adiabatic/nonadiabatic response of the background density have been performed (using pseudospectral method). The nonlinear dynamical equations satisfy the modified nonlinear Schrodinger equation (MNLS) in adiabatic case and it is modified Zakharov system of equations (MZSE) in non-adiabatic case by coupling the KAW with ion acoustic wave. The simulations were performed at different initial conditions i.e. longitudinal periodic perturbation, transverse periodic perturbation and random perturbation of the main KAW. The spatial and temporal evolution of dynamical equations have been studied at different transverse wave numbers to analyze the magnetic field intensity profiles, density and magnetic field propagations, phase portraits and power spectra. In the second
MIA
chapter of the proposed thesis, I have studied the nonlinear properties of KAWs satisfying the MNLS in the presence of ponderomotive and Joule heating nonlinearity modification of the background density in the non-paraxial regime. It has been found that the KAWs breaks up into filamentary structures with high intensity magnetic field inside. The wave shows chaotic behavior as the transverse wavenumber changes. The power spectra get deviated from the observed Kolmogorov k 5"3 scaling. In the third chapter, the author has investigated the spatial evolution of KAWs turbulence (using MNLS) having the applications in magnetospheric plasmas. The effect of Landau damping of KAW on filamentary structure as well as on the spectral index of spectra has been studied. The spectral index has been found to be deviated from -5/3 scaling. Particle heating in these turbulent structures has also been calculated by using velocity space diffusion coefficient in Fokker-Planck equation. In the fourth chapter, the temporal evolution of KAWs turbulence (using MNLS) in the presence of Landau damping has been studied. Using, Fokker-Planck equation, the author has calculated the particle heating in solar corona. In the fifth chapter of the thesis, the author has solved numerically the model equations for the nonlinear interaction between of KAWs and ion acoustic waves in the intermediate-fl (thermal to background magnetic pressures ratio) plasmas in the paraxial regime. The nonlinear dynamical equations satisfy the MZSE by taking the non-adiabatic response of the background density. The localized magnetic filamentary structures are found in
solar corona alongwith the density dips and humps associated with the KAWs.
The power spectra of magnetic field fluctuations indicate that the nonlinear interactions may be redistributing energy among higher wavenumbers. This type of nonlinear interaction may be responsible for heating of the solar corona. In the sixth chapter, the author has studied nonlinear interaction between KAW and ion acoustic wave in the non-paraxial regime. Filamentation of KAW and the turbulent spectra have been presented in intermediate- /3 plasmas at heliocentric distances (0.3AU <_ r <1 .OAU ). The author found that these growing filaments and steeper turbulent spectra (of power law k_s , 5 / 3 <_ S <_ 3) can be responsible for plasma heating and particle acceleration in solar wind. Particle heating in these small-scale filamentary structures has also been calculated by using velocity space diffusion coefficient in Fokker-Planck equation.
Contents
Certificate i
Acknowledgement iii
Abstract iv
List of figures xi
Chapter 1. Introduction 1-40
1.1 MHD Model 3
1.2 Two Fluid Model 7
1.3 Kinetic Model 9
1.4 Turbulence in Space Plasmas 13
1.5 Role of kinetic Alfven Waves in Space Plasmas
1.4.1 Solar Corona 19
1.4.2 Magnetospheric Plasmas 22
1.4.3 Solar Wind 24
1.6 Spacecraft Observations 27
1.7 Alfven Wave Filamentation 32
1.8 Numerical Technique 33
1.8 Objective of the Thesis 35
Chapter Wise Summary 35
vii
Publications 39
References 40
Chapter 2. Nonlinear evolution of kinetic Alfven waves and the turbulent
spectra 47-74
2.1 Introduction 47
2.2 Model Equations 50
2.3 Numerical Simulations 53
2.4 Simplified Model 59
2.5 Discussion and Conclusion 62
References 73
Chapter 3. Kinetic Alfven waves turbulence in the Earth's magnetosphere 75-95
3.1 Introduction 75
3.2 Model Equations 77
3.3 Numerical Simulation 81
3.4 Particle Acceleration 84
3.5 Summary and Conclusions 88
viii
References 94 Chapter 4. Landau damped kinetic Alfven waves and coronal heating
96- 109
4.1 Introduction 4.2 Model Equations 4.3 Numerical Simulation 4.4 Results and Discussion
4.5 Particle Acceleration 4.6 Summary
References
Chapter 5. Nonlinear Excitation of short scale turbulence in solar corona
by kinetic Alfven waves 110-131
5.1 Introduction 110
5.2 Ion Acoustic Wave dynamics 113
5.3 Kinetic Alfven Wave dynamics 115
5.4 Numerical Simulations 118
5.5 Summary 122
References 130
96 97 99 100 102 103 108
ix
Chapter 6. Turbulence in Solar Wind Plasmas 132-156
6.1 Introduction 132
6.2 Ion Acoustic Wave dynamics 135
6.3 Kinetic Alfven Wave dynamics 138
6.4 Numerical Simulations 140
6.5 Concluding Remarks 148
References 155
Chapter 7. Summary and Scope of the Work 157-158
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