computational astrophysics: magnetic fields and charged particle dynamics 20-nov-2008
TRANSCRIPT
![Page 1: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/1.jpg)
Computational Astrophysics:Magnetic Fields and
Charged Particle Dynamics
20-nov-2008
![Page 2: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/2.jpg)
Topics this week
MagnetoHydroDynamics (MHD) Macroscopic equations Hydrodynamics MHD-approximation Ideal MHD Resistive MHD
IDL experimentarium
![Page 3: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/3.jpg)
Topics today
Macroscopic equations Density, velocity, internal energy Induction (Faraday) equation Mass, energy, and momentum conservation MHD approximation MHD equations
Demos and exercises IDL experimentarium for ideal MHD
![Page 4: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/4.jpg)
Boyd & Sanderson
Assumed background for today Chapter 3
Carefully: 3.1, 3.3. Cursory: 3.2, 3.4 Chapter 4
Carefully: 4.1, 4.2, 4.3 (intro), 4.4, 4.8. Cursory: 4.3.1-4.3.2, 4.3.4.
Read up on it, if ”a bit thin” ;-)
![Page 5: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/5.jpg)
What are the central issues today?
Basic MHD-equations Conservation of mass, momentum, and energy ”Frozen in” magnetic field in ideal MHD
Static equilibria + perturbations Potential magnetic fields Force-free magnetic fields Magnetic buoyancy
![Page 6: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/6.jpg)
Implementing
Equation of contiuity Mass conservation in fixed coordinate system:
)(/ u t
![Page 7: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/7.jpg)
Implementing
Equation of motion Momentum conservation in fixed coordinates:
No viscous stress!
Bjuuu xPt )(/)(
![Page 8: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/8.jpg)
Implementing
Energy equation Constant temperature
TPgas
![Page 9: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/9.jpg)
Implementing
Magnetic field equations for ideal MHD Induction equation
Electric field (no resistive electric field)
Electric current density:
EB t/
Bj
BuE
![Page 10: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/10.jpg)
Central theoretical topics:
Potential magnetic fields Potential no electric current!
Force-free magnetic fields Electric current J parallel to B no force
Magnetic buoyancy Internal gas pressure reduced Lower density buoyancy
![Page 11: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/11.jpg)
Central concepts
Magnetic field lines ”Frozen-in” for ideal MD
Magnetic flux surfaces Boundaries with B-field
Magnetic flux tubes Idealized picture, both useful & dangerous!
![Page 12: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/12.jpg)
Frozen-in magnetic field
![Page 13: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/13.jpg)
Magnetic field lines
![Page 14: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/14.jpg)
Flux surfaces
![Page 15: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/15.jpg)
Black Board!Black Board!Black Board!Black Board!
![Page 16: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/16.jpg)
Hands-on: IDL experimentarium for ideal MHD
No dissipation Looking for equilibria Need to damp out motions – kill kinetic energy
Play with twisted field configurations
Sunspot model (after lunch)
![Page 17: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/17.jpg)
Code piecesidl directory (library)
Interpolation inter.pro, plot_inter.pro
Differentiation stagger.pro
Drawing functions interactively draw_function.pro
Time stepping timestep.pro
Fieldlines fieldines.pro
![Page 18: Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008](https://reader036.vdocuments.mx/reader036/viewer/2022062309/56649eb05503460f94bb5811/html5/thumbnails/18.jpg)
Code piecestodays experimentarium
exercise2.pro events.pro make_widgets.pro initial_values.pro
draw_profiles.pro magnetic_field.pro visualize.pro
evolve.pro pde.pro