MAGNETOHYDRODYNAMICS AND PLASMA PHYSICS

The course is aimed at providing the student the basic knowledge and the state of the art of some topics in Magnetohydrodynamics and Plasma Physics: 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 of the properties of plasma; magnetohydrodynamics approach; frozen magnetic fields; knowledge of 2D and 3D reconnection mechanisms.

Teaching is based on lectures.

Electromagnetism. Maxwell's Laws. Lorentz Force. Conservation Laws.

The attendance to lectures is usually mandatory.

Program of the course

Electric and magnetic fields: The electromagnetic field. Potential magnetic field. The scalar electric potential. Faraday induction equation. Dipolar magnetic field. The interplanetary magnetic field.

Plasma Physics: Plasma definition. Concept of temperature of a plasma. Debye distance. Plasma oscillations. Parameters that characterize a plasma. Diffusion in a plasma. Collisional and non-collisional plasma. Plasma kinetic description. Distribution function. Moments of the distribution function. Vlasov equation.

Theory of orbits: 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.

Magnetohydrodynamic equations: 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.

Magnetic reconnection: Neutral points. Current sheets. Sweet Parker model. Petschek model. Tearing mode instability. Coalescence instability. 3D magnetic reconnection.

• C. Chiuderi & M. Velli: Fisica del Plasma: Fondamenti e applicazioni astrofisiche, Springer - Verlag, 2012
• 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

Verification of learning will be carried out through an oral final exam. Through questions related to qualifying points of the various parts of the program, the exam is aimed at ascertaining the overall level of knowledge acquired by the candidate, as well as his/her ability to critically address the topics studied and to correlate the various parts of the program.

The final grade will equally match the knowledge shown in the qualitative and quantitative arguments, the critical view of the topics dealt with during the course and the ability to correlate the various parts of the program.

• Dipolar magnetic field and Earth magnetosphere
• Debye length and plasma electric neutrality
• Motion of a charged particle in a magnetic field
• Adiabatic Invariants
• Induction equation
• Magnetic Reynolds number
• Frozen field Law
• Properties of current sheet
• Sweet & Parker and Petschek reconnection models