computational astrophysics: magnetic fields and charged particle dynamics 20-nov-2008

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