computational astrophysics: magnetic fields and charged particle dynamics 20-nov-2008
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: 4.3.1-4.3.2, 4.3.4.
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:
)(/ u t
Implementing
Equation of motion Momentum conservation in fixed coordinates:
No viscous stress!
Bjuuu xPt )(/)(
Implementing
Energy equation Constant temperature
TPgas
Implementing
Magnetic field equations for ideal MHD Induction equation
Electric field (no resistive electric field)
Electric current density:
EB t/
Bj
BuE
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!Black Board!Black Board!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 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
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