Download presentation
Presentation is loading. Please wait.
Published byFelix Harmon Modified over 9 years ago
1
Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008
2
Topics this week MagnetoHydroDynamics (MHD) Macroscopic equations Hydrodynamics MHD-approximation Ideal MHD Resistive MHD IDL experimentarium
3
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
4
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” ;-)
5
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
6
Implementing Equation of contiuity Mass conservation in fixed coordinate system:
7
Implementing Equation of motion Momentum conservation in fixed coordinates: No viscous stress!
8
Implementing Energy equation Constant temperature
9
Implementing Magnetic field equations for ideal MHD Induction equation Electric field (no resistive electric field) Electric current density:
10
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
11
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!
12
Frozen-in magnetic field
13
Magnetic field lines
14
Flux surfaces
15
Black Board!
16
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)
17
Code pieces idl directory (library) Interpolation inter.pro, plot_inter.pro Differentiation stagger.pro Drawing functions interactively draw_function.pro Time stepping timestep.pro Fieldlines fieldines.pro
18
Code pieces todays experimentarium exercise2.pro events.pro make_widgets.pro initial_values.pro draw_profiles.pro magnetic_field.pro visualize.pro evolve.pro pde.pro
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.