Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008.

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Presentation transcript:

Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008

Topics this week MagnetoHydroDynamics (MHD) Macroscopic equations Hydrodynamics MHD-approximation Ideal MHD Resistive MHD IDL experimentarium

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

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: , Read up on it, if ”a bit thin” ;-)

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

Implementing Equation of contiuity Mass conservation in fixed coordinate system:

Implementing Equation of motion Momentum conservation in fixed coordinates: No viscous stress!

Implementing Energy equation Constant temperature

Implementing Magnetic field equations for ideal MHD Induction equation Electric field (no resistive electric field) Electric current density:

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

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!

Frozen-in magnetic field

Magnetic field lines

Flux surfaces

Black Board!

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)

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

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