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E-grāmata: Advanced Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas

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(Katholieke Universiteit Leuven, Belgium), (Katholieke Universiteit Leuven, Belgium),
  • Formāts: PDF+DRM
  • Izdošanas datums: 29-Apr-2010
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9780511718076
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Advanced Magnetohydrodynamics: With Applications to Laboratory and Astrophysical PlasmasPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 29-Apr-2010
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9780511718076
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"Following on from the companion volume Principles of Magnetohydrodynamics, this textbook analyzes the applications of plasma physics to thermonuclear fusion and plasma astrophysics from the single viewpoint of MHD. This approach turns out to be ever more powerful when applied to streaming plasmas (the vast majority of visible matter in the Universe), toroidal plasmas (the most promising approach to fusion energy), and nonlinear dynamics (where it all comes together with modern computational techniques and extreme transonic and relativistic plasma flows). The textbook interweaves theory and explicit calculations of waves and instabilities of streaming plasmas in complex magnetic geometries. It is ideally suited to advanced undergraduate and graduate courses in plasma physics and astrophysics"--Provided by publisher.

Following on from the companion volume principles of Magnetohydrodynamics, this textbook analyzes the applications of plasma physics to thermonuclear fusion and plasma astrophysics from the single viewpoint of MHD. This approach turns out to be ever more powerful when applied to streaming plasmas (the vast majority of visible matter in the Universe), toroidal plasmas (the most promising approach to fusion energy), and nonlinear dynamics (where it all comes together with modern computational techniques and extreme transonic and relativistic plasma flows).

The textbook interweaves theory and explicit calculations of waves and instabilities of streaming plasmas in complex magnetic geometries. It is ideally suited to advanced undergraduate and graduate courses in plasma physics and astrophysics.

"...a unique and outstanding volume on theoretical magnetohydrodynamics... The reader is carefully and clearly guided on a mathematical journey through the essential arguments, which serves as a concise road map across the vast territory of mathematical plasma kinetics... an outstanding contribution to the subject of MHD theory and its applications..." Gene Parker Journal of Fluid Mechanics

"...an engaging text... The authors present many examples to good effect, and derive results efficiently and clearly from fundamental relationships... The authors' clarity inspires eagerness to dig into derivations and examples..." E. J. Zeta American Journal of Physics

Recenzijas

From the companion volume: 'Goedbloed and Poedts have written a unique and outstanding volume on theoretical magnetohydrodynamics The reader is carefully and clearly guided on a mathematical journey through the essential arguments, which serves as a concise road map across the vast territory of mathematical plasma kinetics the present volume is an outstanding contribution to the subject of MHD theory and its applications. Supplemented with [ the companion volume], it might well become the definitive treatise on the subject.' Gene Parker, Journal of Fluid Mechanics ' an engaging text The authors present many examples to good effect, and derive results efficiently and clearly from fundamental relationships. Units (mksA) are, blessedly, explicit. The authors' clarity inspires eagerness to dig into derivations and examples Goedbloed and Poedts have thoughtfully asterisked those sections that are optional for a first course in MHD ' E. J. Zeta, American Journal of Physics

Papildus informācija

Following on from Principles of Magnetohydrodynamics, this textbook is for advanced undergraduate and graduate courses in plasma physics and astrophysics.
Preface xiii
Part III Flow and dissipation
1(244)
12 Waves and instabilities of stationary plasmas
3(46)
12.1 Laboratory and astrophysical plasmas
3(10)
12.1.1 Grand vision: magnetized plasma on all scales
3(3)
12.1.2 Differences between laboratory and astrophysical plasmas
6(6)
12.1.3 Plasmas with background flow
12(1)
12.2 Spectral theory of stationary plasmas
13(22)
12.2.1 Basic equations
13(3)
12.2.2 Frieman-Rotenberg formulation
16(6)
12.2.3 Self-adjointness of the generalized force operator
22(5)
12.2.4 Energy conservation and stability
27(8)
12.3 Solution paths in the complex w plane
35(12)
12.3.1 Opening up the boundaries
35(5)
12.3.2 Approach to eigenvalues
40(7)
12.4 Literature and exercises
47(2)
13 Shear flow and rotation
49(78)
13.1 Spectral theory of plane plasmas with shear flow
49(22)
13.1.1 Gravito-MHD wave equation for plane plasma flow
49(6)
13.1.2 Kelvin-Helmholtz instabilities in interface plasmas
55(4)
13.1.3 Continua and oscillation theorem R for real eigenvalues
59(6)
13.1.4 Complex eigenvalues and the alternator
65(6)
13.2 Case study: flow-driven instabilities in diffuse plasmas
71(22)
13.2.1 Rayleigh-Taylor instabilities of magnetized plasmas
73(3)
13.2.2 Kelvin-Helmholtz instabilities of ordinary fluids
76(9)
13.2.3 Gravito-MHD instabilities of stationary plasmas
85(6)
13.2.4 Oscillation theorem C for complex eigenvalues
91(2)
13.3 Spectral theory of rotating plasmas
93(11)
13.3.1 MHD wave equation for cylindrical flow
93(5)
13.3.2 Local stability
98(4)
13.3.3 WKB approximation
102(2)
13.4 Rotational instabilities
104(19)
13.4.1 Rigid rotation of incompressible plasmas
104(8)
13.4.2 Magneto-rotational instability: local analysis
112(6)
13.4.3 Magneto-rotational instability: numerical solutions
118(5)
13.5 Literature and exercises
123(4)
14 Resistive plasma dynamics
127(50)
14.1 Plasmas with dissipation
127(8)
14.1.1 Conservative versus dissipative dynamical systems
127(1)
14.1.2 Stability of force-free magnetic fields: a trap
128(7)
14.2 Resistive instabilities
135(15)
14.2.1 Basic equations
135(3)
14.2.2 Tearing modes
138(11)
14.2.3 Resistive interchange modes
149(1)
14.3 Resistive spectrum
150(12)
14.3.1 Resistive wall mode
150(5)
14.3.2 Spectrum of homogeneous plasma
155(3)
14.3.3 Spectrum of inhomogeneous plasma
158(4)
14.4 Reconnection
162(13)
14.4.1 Reconnection in 2D Harris sheet
162(6)
14.4.2 Petschek reconnection
168(1)
14.4.3 Kelvin-Helmholtz induced tearing instabilities
169(2)
14.4.4 Extended MHD and reconnection
171(4)
14.5 Literature and exercises
175(2)
15 Computational linear MHD
177(68)
15.1 Spatial discretization techniques
178(26)
15.1.1 Basic concepts for discrete representations
180(2)
15.1.2 Finite difference methods
182(4)
15.1.3 Finite element method
186(10)
15.1.4 Spectral methods
196(5)
15.1.5 Mixed representations
201(3)
15.2 Linear MHD: boundary value problems
204(13)
15.2.1 Linearized MHD equations
204(2)
15.2.2 Steady solutions to linearly driven problems
206(3)
15.2.3 MHD eigenvalue problems
209(2)
15.2.4 Extended MHD examples
211(6)
15.3 Linear algebraic methods
217(8)
15.3.1 Direct and iterative linear system solvers
217(3)
15.3.2 Eigenvalue solvers: the QR algorithm
220(1)
15.3.3 Inverse iteration for eigenvalues and eigenvectors
221(1)
15.3.4 Jacobi-Davidson method
222(3)
15.4 Linear MHD: initial value problems
225(15)
15.4.1 Temporal discretizations: explicit methods
225(8)
15.4.2 Disparateness of MHD time scales
233(1)
15.4.3 Temporal discretizations: implicit methods
234(2)
15.4.4 Applications: linear MHD evolutions
236(4)
15.5 Concluding remarks
240(1)
15.6 Literature and exercises
241(4)
Part IV Toroidal plasmas
245(160)
16 Static equilibrium of toroidal plasmas
247(60)
16.1 Axi-symmetric equilibrium
247(22)
16.1.1 Equilibrium in tokamaks
247(5)
16.1.2 Magnetic field geometry
252(4)
16.1.3 Cylindrical limits
256(4)
16.1.4 Global confinement and parameters
260(9)
16.2 Grad-Shafranov equation
269(15)
16.2.1 Derivation of the Grad-Shafranov equation
269(2)
16.2.2 Large aspect ratio expansion: internal solution
271(6)
16.2.3 Large aspect ratio expansion: external solution
277(7)
16.3 Exact equilibrium solutions
284(15)
16.3.1 Poloidal flux scaling
284(5)
16.3.2 Soloviev equilibrium
289(4)
16.3.3 Numerical equilibria
293(6)
16.4 Extensions
299(5)
16.4.1 Toroidal rotation
299(2)
16.4.2 Gravitating plasma equilibria
301(1)
16.4.3 Challenges
302(2)
16.5 Literature and exercises
304(3)
17 Linear dynamics of static toroidal plasmas
307(48)
17.1 "Ad more geometrico"
307(8)
17.1.1 Alfven wave dynamics in toroidal geometry
307(1)
17.1.2 Coordinates and mapping
308(1)
17.1.3 Geometrical-physical characteristics
309(6)
17.2 Analysis of waves and instabilities in toroidal geometry
315(19)
17.2.1 Spectral wave equation
315(3)
17.2.2 Spectral variational principle
318(1)
17.2.3 Alfven and slow continuum modes
319(3)
17.2.4 Poloidal mode coupling
322(4)
17.2.5 Alfven and slow ballooning modes
326(8)
17.3 Computation of waves and instabilities in tokamaks
334(18)
17.3.1 Ideal MHD versus resistive MHD in computations
334(6)
17.3.2 Edge localized modes
340(4)
17.3.3 Internal modes
344(3)
17.3.4 Toroidal Alfven eigenmodes and MHD spectroscopy
347(5)
17.4 Literature and exercises
352(3)
18 Linear dynamics of stationary toroidal plasmas
355(50)
18.1 Transonic toroidal plasmas
355(2)
18.2 Axi-symmetric equilibrium of transonic stationary states
357(17)
18.2.1 General equations and toroidal rescalings
357(8)
18.2.2 Elliptic and hyperbolic flow regimes
365(1)
18.2.3 Expansion of the equilibrium in small toroidicity
366(8)
18.3 Equations for the continuous spectrum
374(18)
18.3.1 Reduction for straight-field-line coordinates
374(4)
18.3.2 Continua of poloidally and toroidally rotating plasmas
378(7)
18.3.3 Analysis of trans-slow continua for small toroidicity
385(7)
18.4 Trans-slow continua in tokamaks and accretion disks
392(10)
18.4.1 Tokamaks and magnetically dominated accretion disks
393(3)
18.4.2 Gravity dominated accretion disks
396(1)
18.4.3 A new class of transonic instabilities
397(5)
18.5 Literature and exercises
402(3)
Part V Nonlinear dynamics
405(186)
19 Computational nonlinear MHD
407(80)
19.1 General considerations for nonlinear conservation laws
408(25)
19.1.1 Conservative versus primitive variable formulations
408(7)
19.1.2 Scalar conservation law and the Riemann problem
415(5)
19.1.3 Numerical discretizations for a scalar conservation law
420(10)
19.1.4 Finite volume treatments
430(3)
19.2 Upwind-like finite volume treatments for 1D MHD
433(21)
19.2.1 The Godunov method
434(6)
19.2.2 A robust shock-capturing method: TVDLF
440(6)
19.2.3 Approximate Riemann solver type schemes
446(5)
19.2.4 Simulating 1D MHD Riemann problems
451(3)
19.3 Multi-dimensional MHD computations
454(19)
19.3.1 Δ · B = 0 condition for shock-capturing schemes
455(6)
19.3.2 Example nonlinear MHD scenarios
461(5)
19.3.3 Alternative numerical methods
466(7)
19.4 Implicit approaches for extended MHD simulations
473(11)
19.4.1 Alternating direction implicit strategies
474(1)
19.4.2 Semi-implicit methods
475(6)
19.4.3 Simulating ideal and resistive instability developments
481(1)
19.4.4 Global simulations for tokamak plasmas
482(2)
19.5 Literature and exercises
484(3)
20 Transonic MHD flows and shocks
487(56)
20.1 Transonic MHD flows
487(3)
20.1.1 Flow in laboratory and astrophysical plasmas
487(1)
20.1.2 Characteristics in space and time
488(2)
20.2 Shock conditions
490(17)
20.2.1 Special case: gas dynamic shocks
492(6)
20.2.2 MHD discontinuities without mass flow
498(2)
20.2.3 MHD discontinuities with mass flow
500(5)
20.2.4 Slow, intermediate and fast shocks
505(2)
20.3 Classification of MHD shocks
507(22)
20.3.1 Distilled shock conditions
507(6)
20.3.2 Time reversal duality
513(7)
20.3.3 Angular dependence of MHD shocks
520(7)
20.3.4 Observational considerations of MHD shocks
527(2)
20.4 Stationary transonic flows
529(11)
20.4.1 Modeling the solar wind-magnetosphere boundary
530(1)
20.4.2 Modeling the solar wind by itself
531(3)
20.4.3 Example astrophysical transonic flows
534(6)
20.5 Literature and exercises
540(3)
21 Ideal MHD in special relativity
543(48)
21.1 Four-dimensional space-time: special relativistic concepts
544(20)
21.1.1 Space-time coordinates and Lorentz transformations
544(3)
21.1.2 Four-vectors in flat space-time and invariants
547(4)
21.1.3 Relativistic gas dynamics and stress-energy tensor
551(5)
21.1.4 Sound waves and shock relations in relativistic gases
556(8)
21.2 Electromagnetism and special relativistic MHD
564(16)
21.2.1 Electromagnetic field tensor and Maxwell's equations
564(5)
21.2.2 Stress-energy tensor for electromagnetic fields
569(1)
21.2.3 Ideal MHD in special relativity
570(2)
21.2.4 Wave dynamics in a homogeneous plasma
572(5)
21.2.5 Shock conditions in relativistic MHD
577(3)
21.3 Computing relativistic magnetized plasma dynamics
580(8)
21.3.1 Numerical challenges from relativistic MHD
583(1)
21.3.2 Example astrophysical applications
584(4)
21.4 Literature and exercises
588(3)
Appendices
591(13)
A Vectors and coordinates
591(13)
A.1 Vector identities
591(1)
A.2 Vector expressions in orthogonal coordinates
592(8)
A.3 Vector expressions in non-orthogonal coordinates
600(4)
References 604(25)
Index 629
J. P. (Hans) Goedbloed is an advisor at the FOM-Institute for Plasma Physics and Professor Emeritus of theoretical plasma physics at Utrecht University. He has been a visiting scientist at laboratories in the Soviet Union, the United States, Brazil and Europe. He has taught at Campinas, Rio de Janeiro, Sćo Paulo, MIT, K. U. Leuven, and regularly at Amsterdam Free University and Utrecht University. For many years he coordinated a large-scale computational effort with the Dutch Science Organization on Fast Changes in Complex Flows involving scientists of different disciplines. Rony Keppens is a Professor at the Centre for Plasma-Astrophysics, K. U. Leuven, affiliated with the FOM-Institute for Plasma Physics 'Rijnhuizen', and a Professor at Utrecht University. He headed numerical plasma dynamics teams at Rijnhuizen and Leuven, and is frequently invited to lecture on computational methods in astrophysics. His career started with research posts at the National Center for Atmospheric Research, Boulder, and the Kiepenheuer Institute for Solar Physics, Freiburg. His expertise ranges from solar physics to high energy astrophysics, includes parallel computing, grid-adaptivity and visualization of large-scale simulations. Stefaan Poedts is full Professor in the department of mathematics at K. U. Leuven. He graduated in Leuven, was a postdoctoral researcher at the Max-Planck-Institut für Plasmaphysik, Garching, a senior researcher at FOM-Institute for Plasma Physics 'Rijnhuizen', and a research associate at the Centre for Plasma Astrophysics, K. U. Leuven. His research interests include solar astrophysics, space weather, thermonuclear fusion and MHD stability. He teaches both basic math courses and advanced courses on plasma physics of the Sun and numerical simulation, and is currently president of the European Solar Physics Division of the EPS.
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