MAGNETOHYDRODYNAMICS

The course is aimed at providing the student the basic knowledge and the state of the art of some topics in Magnetohydrodynamics: deepened knowledge of laws of electromagnetism; knowledge of the motions of charged particles in presence of magnetic, electric or other force fields; knowledge of the concept and properties of plasma; magnetohydrodynamics approach; frozen magnetic fields; knowledge of 2D and 3D reconnection mechanisms; knowledge of dynamo theories.

The electromagnetic field. Potential magnetic field. The scalar electric potential. Faraday induction equation. Magnetic dipole field. The interplanetary magnetic field. The induced electric field. Plasma definition. Concept of temperature of a plasma. Debye distance. The oscillations of the plasma. Diffusion in a weakly ionized plasma. Diffusion in a highly ionized plasma. Collisional and non-collisional plasma. Van Allen Radiation belts. Lorentz force. Motion of particles and motion of the guiding center. Motion of a particle in a constant magnetic field. Magnetic moment. Mirror points. Adiabatic invariants. Eulerian and Lagrangian points of view. Forces acting on a fluid. Continuity equation. Equation of motion. Equation of energy conservation. System of equations of the MHD. Induction equation. Magnetic Reynolds number. Decay of the magnetic field in absence of motion. Evolution of the magnetic field in presence of motion of the fluid and with an infinite conductivity. Conservation law of the magnetic flux. Law of the frozen magnetic field. Neutral points. Current sheets. Magnetic reconnection. Dynamo mechanism. Waves: basic equations. Fundamental modes. Acoustic waves. Magnetic waves. Waves of gravity. Magnetoacustic waves. Shock waves.

• D.A. Gurnett & A. Bhattacharjee: Introduction to Plasma Physics, Cambridge University Press, 2005
• E.N. Parker, Cosmical Magnetic Fields, Clarendon Press – Oxford, 1979
• E. R. Priest : Solar magnetohydrodynamics, Reidel Publ. Co., Dordrecht, 1984
• R.M. Kulsrud: Plasma Physics for Astrophysics, Princeton University Press, 2005