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El. knyga: Magnetohydrodynamics of Laboratory and Astrophysical Plasmas

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  • Formatas: EPUB+DRM
  • Išleidimo metai: 31-Jan-2019
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781108577588
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Magnetohydrodynamics of Laboratory and Astrophysical PlasmasDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 31-Jan-2019
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781108577588
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With ninety per cent of visible matter in the universe existing in the plasma state, an understanding of magnetohydrodynamics is essential for anyone looking to understand solar and astrophysical processes, from stars to accretion discs and galaxies; as well as laboratory applications focused on harnessing controlled fusion energy. This introduction to magnetohydrodynamics brings together the theory of plasma behavior with advanced topics including the applications of plasma physics to thermonuclear fusion and plasma- astrophysics. Topics covered include streaming and toroidal plasmas, nonlinear dynamics, modern computational techniques, incompressible plasma turbulence and extreme transonic and relativistic plasma flows. The numerical techniques needed to apply magnetohydrodynamics are explained, allowing the reader to move from theory to application and exploit the latest algorithmic advances. Bringing together two previous volumes: Principles of Magnetohydrodynamics and Advanced Magnetohydrodynamics, and completely updated with new examples, insights and applications, this volume constitutes a comprehensive reference for students and researchers interested in plasma physics, astrophysics and thermonuclear fusion.

This introduction to magnetohydrodynamics combines theories of plasma behaviour with applications of plasma physics to thermonuclear fusion and astrophysics, and the techniques needed to apply magnetohydrodynamics. Bringing together both parts of the two-volume first edition, it is fully updated throughout and provides a comprehensive reference.

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An introduction to magnetohydrodynamics combining theory with advanced topics including the applications of plasma physics to thermonuclear fusion and plasma astrophysics.
Preface xvii
Part I Plasma Physics Preliminaries 1(102)
1 Introduction
3(24)
1.1 Motivation
3(1)
1.2 Thermonuclear fusion and plasma confinement
4(5)
1.2.1 Fusion reactions
4(2)
1.2.2 Conditions for fusion
6(3)
1.2.3 Magnetic confinement and tokamaks
9(10)
1.3 Astrophysical plasmas
11(1)
1.3.1 Celestial mechanics
11(2)
1.3.2 Astrophysics
13(2)
1.3.3 Plasmas enter the stage
15(2)
1.3.4 The standard view of nature
17(2)
1.4 Definitions of the plasma state
19(5)
1.4.1 Microscopic definition of plasma
19(4)
1.4.2 Macroscopic approach to plasma
23(1)
1.5 Literature and exercises
24(3)
2 Elements of plasma physics
27(39)
2.1 Theoretical models
27(1)
2.2 Single particle motion
27(11)
2.2.1 Cyclotron motion
27(3)
2.2.2 Excursion: Basic equations of electrodynamics and mechanics
30(3)
2.2.3 Drifts, adiabatic invariants
33(5)
2.3 Kinetic plasma theory
38(14)
2.3.1 Boltzmann equation and moment reduction
38(5)
2.3.2 Collective phenomena: plasma oscillations
43(3)
2.3.3 Landau damping
46(6)
2.4 Fluid description
52(11)
2.4.1 From the two-fluid to the MHD description of plasmas
53(4)
2.4.2 Alfven waves
57(2)
2.4.3 Equilibrium and stability
59(4)
2.5 In conclusion
63(1)
2.6 Literature and exercises
64(2)
3 'Derivation' of the macroscopic equations
66(37)
3.1 Two approaches
66(1)
3.2 Kinetic equations
67(11)
3.2.1 Boltzmann equation
67(3)
3.2.2 Moments of the Boltzmann equation
70(2)
3.2.3 Thermal fluctuations and transport
72(3)
3.2.4 Collisions and closure
75(3)
3.3 Two-fluid equations
78(17)
3.3.1 Electron-ion plasma
78(1)
3.3.2 The classical transport coefficients
79(4)
3.3.3 Dissipative versus ideal fluids
83(3)
3.3.4 Excursion: waves in two-fluid plasmas
86(9)
3.4 One-fluid equations
95(6)
3.4.1 Maximal ordering for MHD
95(4)
3.4.2 Resistive and ideal MHD equations
99(2)
3.5 Literature and exercises
101(2)
Part II Basic Magnetohydrodynamics 103(128)
4 The MHD model
105(42)
4.1 The ideal MHD equations
105(8)
4.1.1 Postulating the basic equations
105(5)
4.1.2 Scale independence
110(2)
4.1.3 A crucial question
112(1)
4.2 Magnetic flux
113(3)
4.2.1 Flux tubes
113(1)
4.2.2 Global magnetic flux conservation
114(2)
4.3 Conservation laws
116(12)
4.3.1 Conservation form of the MHD equations
116(2)
4.3.2 Global conservation laws
118(3)
4.3.3 Local conservation of magnetic flux
121(3)
4.3.4 Magnetic helicity
124(4)
4.4 Dissipative magnetohydrodynamics
128(5)
4.4.1 Resistive MHD
128(3)
4.4.2 (Non-)conservation form of the dissipative equations
131(2)
4.5 Discontinuities
133(5)
4.5.1 Shocks and jump conditions
133(3)
4.5.2 Boundary conditions for plasmas with an interface
136(2)
4.6 Model problems
138(6)
4.6.1 Laboratory plasmas (models I-III)
138(3)
4.6.2 Energy conservation for interface plasmas
141(2)
4.6.3 Astrophysical plasmas (models IV-VI)
143(1)
4.7 Literature and exercises
144(3)
5 Waves and characteristics
147(34)
5.1 Physics and accounting
147(3)
5.1.1 Introduction
147(1)
5.1.2 Sound waves
147(3)
5.2 MHD waves
150(9)
5.2.1 Symmetric representation in primitive variables
150(2)
5.2.2 Entropy wave and magnetic field constraint
152(3)
5.2.3 Reduction to velocity representation: three waves
155(2)
5.2.4 Dispersion diagrams
157(2)
5.3 Phase and group diagrams
159(10)
5.3.1 Basic concepts
159(2)
5.3.2 Application to the MHD waves
161(4)
5.3.3 Asymptotic properties
165(1)
5.3.4 Self-gravity and contraction in homogeneous media
166(3)
5.4 Characteristics
169(10)
5.4.1 The method of characteristics
169(2)
5.4.2 Classification of partial differential equations
171(2)
5.4.3 Characteristics in ideal MHD
173(6)
5.5 Literature and exercises
179(2)
6 Spectral theory
181(50)
6.1 Stability: intuitive approach
181(5)
6.1.1 Two viewpoints
181(2)
6.1.2 Linearization and Lagrangian reduction
183(3)
6.2 Force operator formalism
186(10)
6.2.1 Equation of motion
186(4)
6.2.2 Hilbert space
190(1)
6.2.3 Proof of self-adjointness of the force operator
191(5)
6.3 Spectral alternatives
196(4)
6.3.1 Mathematical intermezzo
196(2)
6.3.2 Initial value problem in MHD
198(2)
6.4 Quadratic forms and variational principles
200(6)
6.4.1 Expressions for the potential energy
200(2)
6.4.2 Hamilton's principle
202(1)
6.4.3 Rayleigh-Ritz spectral variational principle
203(1)
6.4.4 Energy principle
204(2)
6.5 Further spectral issues
206(7)
6.5.1 Normal modes and the energy principle
206(1)
6.5.2 Proof of the energy principle
207(2)
6.5.3 r-stability
209(1)
6.5.4 Returning to the two viewpoints
210(3)
6.6 Extension to interface plasmas
213(16)
6.6.1 Boundary conditions at the interface
215(3)
6.6.2 Self-adjointness for interface plasmas
218(1)
6.6.3 Extended variational principles
219(2)
6.6.4 Application to the Rayleigh-Taylor instability
221(8)
6.7 Literature and exercises
229(2)
Part III Standard Model Applications 231(204)
7 Waves and instabilities of inhomogeneous plasmas
233(59)
7.1 Hydrodynamics of the solar interior
233(6)
7.1.1 Radiative equilibrium model
234(3)
7.1.2 Convection zone
237(2)
7.2 Hydrodynamic waves and instabilities of a gravitating slab
239(9)
7.2.1 Hydrodynamic wave equation
239(2)
7.2.2 Convective instabilities
241(1)
7.2.3 Gravito-acoustic waves
242(3)
7.2.4 Helioseismology and MHD spectroscopy
245(3)
7.3 MHD wave equation for a gravitating magnetized plasma slab
248(17)
7.3.1 Preliminaries
248(4)
7.3.2 MHD wave equation for a gravitating slab
252(6)
7.3.3 Gravito-MHD waves
258(7)
7.4 Continuous spectrum and spectral structure
265(14)
7.4.1 Singular differential equations
265(4)
7.4.2 Alfven and slow continua
269(4)
7.4.3 Oscillation theorems
273(5)
7.4.4 Cluster spectra
278(1)
7.5 Gravitational instabilities of a magnetized plasma slab
279(10)
7.5.1 Energy principle for a gravitating plasma slab
280(3)
7.5.2 Interchanges in shearless magnetic fields
283(2)
7.5.3 Interchange instabilities in sheared magnetic fields
285(4)
7.6 Literature and exercises
289(3)
8 Magnetic structures and dynamics of the solar system
292(33)
8.1 Plasma dynamics in laboratory and nature
292(1)
8.2 Solar magnetism
293(20)
8.2.1 The solar cycle
294(6)
8.2.2 Magnetic structures in the solar atmosphere
300(9)
8.2.3 Inspiration from solar magnetism
309(1)
8.2.4 Solar wind and heliosphere
309(4)
8.3 Space weather
313(8)
8.3.1 Technological and economic implications
313(1)
8.3.2 Coronal mass ejections
314(3)
8.3.3 Numerical modelling of space weather
317(3)
8.3.4 Solar wind and planetary magnetospheres
320(1)
8.4 Perspective
321(1)
8.5 Literature and exercises
322(3)
9 Cylindrical plasmas
325(47)
9.1 Equilibrium of cylindrical plasmas
325(5)
9.1.1 Diffuse plasmas
325(4)
9.1.2 Interface plasmas
329(1)
9.2 MHD wave equation for cylindrical plasmas
330(9)
9.2.1 Derivation of the MHD wave equation for a cylinder
330(6)
9.2.2 Boundary conditions for cylindrical interfaces
336(3)
9.3 Spectral structure
339(9)
9.3.1 One-dimensional inhomogeneity
339(2)
9.3.2 Cylindrical model problems
341(6)
9.3.3 Cluster spectra
347(1)
9.4 Stability of cylindrical plasmas
348(21)
9.4.1 Oscillation theorems for stability
348(5)
9.4.2 Stability of plasmas with shearless magnetic fields
353(4)
9.4.3 Stability of force-free magnetic fields
357(4)
9.4.4 Stability of the 'straight tokamak'
361(8)
9.5 Literature and exercises
369(3)
10 Initial value problem and wave damping
372(27)
10.1 Implications of the continuous spectrum
372(1)
10.2 Initial value problem
373(7)
10.2.1 Reduction to a one-dimensional representation
373(3)
10.2.2 Restoring the three-dimensional picture
376(4)
10.3 Damping of Alfven waves
380(6)
10.3.1 Green's function
381(3)
10.3.2 Spectral cuts
384(2)
10.4 Quasi-modes
386(6)
10.5 Leaky modes
392(5)
10.6 Literature and exercises
397(2)
11 Resonant absorption and wave heating
399(36)
11.1 Ideal MHD theory of resonant absorption
399(18)
11.1.1 Analytical solution of a simple model problem
399(6)
11.1.2 Role of the singularity
405(9)
11.1.3 Resonant 'absorption' versus resonant 'dissipation'
414(3)
11.2 Heating and wave damping in tokamaks and coronal loops
417(6)
11.2.1 Tokamaks
417(1)
11.2.2 Coronal loops and arcades
418(1)
11.2.3 Numerical analysis of resonant absorption
419(4)
11.3 Alternative excitation mechanisms
423(9)
11.3.1 Foot point driving
424(3)
11.3.2 Phase mixing
427(1)
11.3.3 Applications to solar and magnetospheric plasmas
428(4)
11.4 Literature and exercises
432(3)
Part IV Flow and Dissipation 435(180)
12 Waves and instabilities of stationary plasmas
437(36)
12.1 Laboratory and astrophysical plasmas
437(8)
12.1.1 Grand vision: magnetized plasma on all scales!
437(3)
12.1.2 Laboratory and astrophysical plasmas
440(1)
12.1.3 Interchanges and the Parker instability
441(4)
12.2 Spectral theory of stationary plasmas
445(17)
12.2.1 Plasmas with background flow
445(3)
12.2.2 Frieman-Rotenberg formulation
448(5)
12.2.3 Self-adjointness of the generalized force operator
453(3)
12.2.4 Energy conservation and stability
456(6)
12.3 The Spectral Web
462(9)
12.3.1 Opening up the boundaries
462(4)
12.3.2 Oscillation theorems in the complex plane
466(5)
12.4 Literature and exercises
471(2)
13 Shear flow and rotation
473(52)
13.1 Spectral theory of plane plasmas with shear flow
473(13)
13.1.1 Gravito-MHD wave equation for plane plasma flow
473(5)
13.1.2 Kelvin-Helmholtz instabilities in interface plasmas
478(2)
13.1.3 Continua and the real oscillation theorem
480(4)
13.1.4 Spectral Web and the complex oscillation theorem
484(2)
13.2 Analysis of flow-driven instabilities in plane plasmas
486(12)
13.2.1 Rayleigh-Taylor instabilities of magnetized plasmas
488(1)
13.2.2 Kelvin-Helmholtz instabilities of ordinary fluids
489(5)
13.2.3 Combined instabilities of magnetized plasmas
494(4)
13.3 Spectral theory of rotating plasmas
498(8)
13.3.1 MHD wave equation for cylindrical flow in 3D
498(2)
13.3.2 Reduction to a second order differential equation
500(2)
13.3.3 Singular expansions
502(3)
13.3.4 Doppler-Coriolis shift and solution path
505(1)
13.4 Rayleigh-Taylor instabilities in rotating theta-pinches
506(7)
13.4.1 Hydrodynamic modes (k = 0)
507(4)
13.4.2 Magnetohydrodynamic modifications (k # 0)
511(2)
13.5 Magneto-rotational instability in accretion discs
513(10)
13.5.1 Analytical preliminaries
514(4)
13.5.2 Numerical Spectral Web solutions
518(5)
13.6 Literature and exercises
523(2)
14 Resistive plasma dynamics
525(44)
14.1 Plasmas with dissipation
525(7)
14.1.1 Conservative versus dissipative dynamical systems
525(1)
14.1.2 Stability of force-free magnetic fields: a trap
525(7)
14.2 Resistive instabilities
532(12)
14.2.1 Basic equations
532(2)
14.2.2 Tearing modes
534(9)
14.2.3 Resistive interchange modes
543(1)
14.3 Resistive spectrum
544(10)
14.3.1 Resistive wall mode
544(4)
14.3.2 Spectrum of homogeneous plasma
548(3)
14.3.3 Spectrum of inhomogeneous plasma
551(3)
14.4 Reconnection
554(9)
14.4.1 Reconnection in a 2D Harris sheet
554(4)
14.4.2 Petschek reconnection
558(1)
14.4.3 Kelvin-Helmholtz induced tearing instabilities
559(1)
14.4.4 Extended MHD and reconnection
560(3)
14.5 Excursion: Hall-MHD wave diagrams
563(3)
14.6 Literature and exercises
566(3)
15 Computational linear MHD
569(46)
15.1 Spatial discretization techniques
569(19)
15.1.1 Basic concepts for discrete representations
571(1)
15.1.2 Finite difference methods
572(4)
15.1.3 Finite element method
576(7)
15.1.4 Spectral methods
583(3)
15.1.5 Mixed representations
586(2)
15.2 Linear MHD: boundary value problems
588(11)
15.2.1 Linearized MHD equations
589(1)
15.2.2 Steady solutions to linearly driven problems
590(3)
15.2.3 MHD eigenvalue problems
593(1)
15.2.4 Extended MHD examples
594(5)
15.3 Linear MHD: initial value problems
599(13)
15.3.1 Temporal discretizations: explicit methods
599(7)
15.3.2 Disparateness of MHD time scales
606(1)
15.3.3 Temporal discretizations: implicit methods
606(2)
15.3.4 Applications: linear MHD evolutions
608(4)
15.4 Concluding remarks
612(1)
15.5 Literature and exercises
612(3)
Part V Toroidal Geometry 615(132)
16 Static equilibrium of toroidal plasmas
617(50)
16.1 Axi-symmetric equilibrium
617(18)
16.1.1 Equilibrium in tokamaks
617(4)
16.1.2 Magnetic field geometry
621(3)
16.1.3 Cylindrical limits
624(3)
16.1.4 Global confinement and parameters
627(8)
16.2 Grad-Shafranov equation
635(12)
16.2.1 Derivation of the Grad-Shafranov equation
635(2)
16.2.2 Large aspect ratio expansion: internal solution
637(5)
16.2.3 Large aspect ratio expansion: external solution
642(5)
16.3 Exact equilibrium solutions
647(13)
16.3.1 Poloidal flux scaling
647(5)
16.3.2 Soloviev equilibrium
652(3)
16.3.3 Numerical equilibria
655(5)
16.4 Extensions
660(4)
16.4.1 Toroidal rotation
660(2)
16.4.2 Gravitating plasma equilibria
662(1)
16.4.3 Challenges
663(1)
16.5 Literature and exercises
664(3)
17 Linear dynamics of static toroidal plasmas
667(40)
17.1 "Ad more geometrico"
667(7)
17.1.1 Alfven wave dynamics in toroidal geometry
667(1)
17.1.2 Coordinates and mapping
667(1)
17.1.3 Geometrical-physical characteristics
668(6)
17.2 Analysis of waves and instabilities in toroidal geometry
674(16)
17.2.1 Spectral wave equation
674(2)
17.2.2 Spectral variational principle
676(1)
17.2.3 Alfven and slow continuum modes
677(3)
17.2.4 Poloidal mode coupling
680(3)
17.2.5 Alfven and slow ballooning modes
683(7)
17.3 Computation of waves and instabilities in tokamaks
690(14)
17.3.1 Ideal MHD versus resistive MHD in computations
690(5)
17.3.2 Internal modes
695(2)
17.3.3 Edge localized modes
697(4)
17.3.4 Toroidal Alfven eigenmodes and MHD spectroscopy
701(3)
17.4 Literature and exercises
704(3)
18 Linear dynamics of toroidal plasmas with flow
707(40)
18.1 Transonic toroidal plasmas
707(2)
18.2 Axi-symmetric equilibrium of transonic stationary states
709(13)
18.2.1 Equilibrium flux functions
709(3)
18.2.2 Equilibrium variational principle and rescaling
712(3)
18.2.3 Elliptic and hyperbolic flow regimes
715(1)
18.2.4 Expansion of the equilibrium in small toroidicity
716(6)
18.3 Equations for the continuous spectrum
722(15)
18.3.1 Reduction for straight-field-line coordinates
722(3)
18.3.2 Continua of poloidally and toroidally rotating plasmas
725(6)
18.3.3 Analysis of trans-slow continua for small toroidicity
731(6)
18.4 Trans-slow continua in tokamaks and accretion discs
737(7)
18.4.1 Tokamaks and magnetically dominated accretion discs
738(2)
18.4.2 Gravity dominated accretion discs
740(2)
18.4.3 Trans-slow Alfven continuum instabilities
742(2)
18.5 Literature and exercises
744(3)
Part VI Nonlinear Dynamics 747(172)
19 Turbulence in incompressible magneto-fluids
749(31)
19.1 Incompressible hydrodynamics preliminaries
749(9)
19.1.1 The incompressible hydro model
749(2)
19.1.2 Two-dimensional formulations
751(1)
19.1.3 'Wave' analysis for incompressible Euler
751(2)
19.1.4 Energy equation and Kolmogorov scaling
753(3)
19.1.5 Selected numerical examples
756(2)
19.2 Incompressible magnetohydrodynamics
758(6)
19.2.1 Governing equations
758(1)
19.2.2 Elsasser formulation
759(1)
19.2.3 Kinematic MHD modelling
760(1)
19.2.4 Dynamo aspects
761(3)
19.3 Waves in incompressible MHD
764(7)
19.3.1 Linear wave analysis
765(1)
19.3.2 Nonlinear wave solutions and conservation laws
766(2)
19.3.3 MHD turbulence scaling laws
768(3)
19.4 Incompressible MHD simulations
771(5)
19.4.1 Structure formation in incompressible MHD studies
772(2)
19.4.2 Dynamo aspects continued
774(2)
19.5 Extension to compressible MHD and concluding remarks
776(2)
19.6 Literature and exercises
778(2)
20 Computational nonlinear MHD
780(57)
20.1 General considerations for nonlinear conservation laws
780(17)
20.1.1 Conservative versus primitive variable formulations
780(6)
20.1.2 Scalar conservation law and the Riemann problem
786(4)
20.1.3 Numerical discretizations for scalar conservation
790(6)
20.1.4 Finite volume treatments
796(1)
20.2 Upwind-like finite volume treatments for one-dimensional MHD
797(16)
20.2.1 The Godunov method
798(4)
20.2.2 A robust shock-capturing method: TVDLF
802(5)
20.2.3 Approximate Riemann solver schemes
807(4)
20.2.4 Simulating 1D MHD Riemann problems
811(2)
20.3 Multi-dimensional MHD computations
813(14)
20.3.1 nabla · B = 0 condition for shock-capturing schemes
814(5)
20.3.2 Example nonlinear MHD scenarios
819(3)
20.3.3 Alternative numerical methods
822(5)
20.4 Implicit approaches for extended MHD simulations
827(7)
20.4.1 Semi-implicit methods
828(4)
20.4.2 Simulating ideal and resistive instabilities
832(1)
20.4.3 Global simulations for tokamak plasmas
833(1)
20.5 Literature and exercises
834(3)
21 Transonic MHD flows and shocks
837(42)
21.1 Transonic flows
837(9)
21.1.1 Characteristics and shocks
838(2)
21.1.2 Gas dynamic shocks
840(5)
21.1.3 Misnomers
845(1)
21.2 MHD shock conditions
846(8)
21.2.1 MHD discontinuities without mass flow
846(2)
21.2.2 MHD discontinuities with mass flow
848(4)
21.2.3 Slow, intermediate and fast shocks
852(2)
21.3 Advanced classification of MHD shocks
854(17)
21.3.1 Distilled shock conditions
854(5)
21.3.2 Time reversal duality
859(6)
21.3.3 Angular dependence of MHD shocks
865(5)
21.3.4 Observational considerations of MHD shocks
870(1)
21.4 Example astrophysical transonic flows
871(5)
21.5 Literature and exercises
876(3)
22 Ideal MHD in special relativity
879(40)
22.1 Four-dimensional space-time: special relativistic concepts
879(16)
22.1.1 Space-time coordinates and Lorentz transformations
880(2)
22.1.2 Four-vectors in flat space-time and invariants
882(3)
22.1.3 Relativistic gas dynamics and stress-energy tensor
885(4)
22.1.4 Sound waves and shock relations in relativistic gases
889(6)
22.2 Electromagnetism and special relativistic MHD
895(13)
22.2.1 Electromagnetic field tensor and Maxwell's equations
895(5)
22.2.2 Ideal MHD in special relativity
900(2)
22.2.3 Wave dynamics in a homogeneous plasma
902(4)
22.2.4 Shock conditions in relativistic MHD
906(2)
22.3 Computing relativistic magnetized plasma dynamics
908(7)
22.3.1 Numerical challenges from relativistic MHD
910(1)
22.3.2 Pulsar Wind Nebulae modelling
911(4)
22.4 Outlook: General relativistic MHD simulations
915(1)
22.5 Literature and exercises
916(3)
Appendices 919(18)
A Vectors and coordinates
919(12)
A.1 Vector identities
919(1)
A.2 Vector expressions in orthogonal coordinates
920(7)
A.3 Vector expressions in non-orthogonal coordinates
927(4)
B Tables of physical quantities
931(6)
References 937(27)
Index 964
Hans Goedbloed is Advisor of the Dutch Institute for Fundamental Energy Research (DIFFER), 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, Massachusetts Institute of Technology, Katholieke Universiteit Leuven, Amsterdam Free University and Utrecht University. For many years he coordinated an interdisciplinary and largescale computational effort with the Dutch Science Organisation on 'Fast Changes in Complex Flows.' Rony Keppens is Professor and Division Chair at the Centre for mathematical Plasma-Astrophysics, Katholieke Universiteit Leuven. He headed numerical plasma dynamics teams at FOM-Institute for Plasma Physics 'Rijnhuizen' (now DIFFER) and Leuven and frequently lectures on computational methods in astrophysics. His career started at the National Center for Atmospheric Research, Boulder, and the Kiepenheuer Institute for Solar Physics, Freiburg. He held a professorship at Utrecht University and a concurrent professorship at Nanjing University. His expertise ranges from solar to high energy astrophysics and includes parallel computing and grid-adaptivity. Stefaan Poedts is Professor and Chair of the Department of Mathematics at Katholieke Universiteit Leuven. He was a post-doctoral researcher at the Max Planck Institute for Plasma Physics, Garching, a senior researcher at the FOM-Institute for plasma physics 'Rijnhuizen', and research associate at the Centre for mathematical Plasma-Astrophysics, Katholieke Universiteit Leuven. His research interests include solar physics, space weather, thermonuclear fusion, MHD (in)stability, and multi-fluid modelling. He teaches basic math courses, and advanced courses on plasma physics of the Sun and numerical simulation.
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