Astrophysical magnetic fields essentials
Brief overview of magnetic fields in the Universe:
Typical intensities and morphologies.
Magnetic fields of planets, stars, compact object, galaxies, interstellar medium, etc.
Brief overview of magnetic environments:
Stellar interiors, stellar atmospheres, interstellar medium, accretion discs, etc.
Typical plasma parameters: densities, temperatures, collisionality.
Description of magnetized plasmas:
Kinetic description: Vlasov equation.
Continuum description: Moments, two-fluids equations, MHD.
High conductivity limit:
Ideal MHD. Alfvén theorem. Consequences of the “frozen in” condition: field advection and distortion.
MHD invariants: Energy, helicity, cross helicity.
Simple solutions: MHD waves, magnetostatic equilibria, formation of singularities.
Non ideal effects:
Ohm’s law, and its generalizations.
Reconnection: Sweet-Parker reconnection, Hall-term effects, collisionless reconnection.
Dynamo action: generation of small-scale fields. Kazatsev model and its generalizations. Generation of large-scale fields and Mean Field Electrodynamics. The alpha and omega effects.
MHD turbulence. The energy cascade. Critical balance. Spontaneous alignment. The spectrum of MHD turbulence.