Academic Year 2022/2023 - Teacher: Francesca ZUCCARELLO

Expected Learning Outcomes

The course aims to provide students with the basic elements and the state of the art of some topics of Magnetohydrodynamics and Plasma Physics: in-depth knowledge of the laws of electromagnetism; knowledge of particle motions in the presence of magnetic, electric or other force fields; knowledge of the concept and properties of plasmas; magnetohydrodynamic approach; frozen magnetic fields; knowledge of the mechanisms of magnetic reconnection in 2D and 3D. The approach followed is theoretical-observational.

Knowledge and understanding: Critical understanding of the most advanced developments in Modern Physics in both theoretical and laboratory aspects and of their interconnections, even in interdisciplinary fields. Considerable mastery of the scientific method, and understanding of the nature and research methods in Physics. During the course the student will understand the main concepts underlying Magnetohydrodynamics (MHD) and the fundamental physical mechanisms that occur in plasmas.

Applying knowledge and understanding: Ability to identify the essential elements of a phenomenon (with reference to MHD and plasmas), in terms of order of magnitude and level of approximation, and to be able to make the required approximations. Ability to use the analogy tool to apply known solutions in the field of interaction between particles and electromagnetic fields and the physics of plasmas to new problems (problem solving) and different astrophysical contexts.

Making judgments: Ability to convey own interpretations of physical phenomena, when discussing within a research team. Developing one's own sense of responsibility, through the choice of optional courses and of the final project.

Communication skills: Ability to discuss about advanced physical concepts, both in Italian and in English. Ability to present one's own research activity or a review topic both to an expert and to an non-expert audience. These skills will be developed in the context of the communication of MHD processes and plasma.

Learning skills: Ability to acquire adequate tools for the continuous update of one's knowledge and to access the specialized literature both in the field of plasma physics and MHD and in scientifically close fields.

Course Structure

Teaching is based on lectures (in English). Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course.

Required Prerequisites

Necessary knowledge: Electromagnetism. Maxwell's laws. Lorentz force. Laws of conservation.

Attendance of Lessons

Attendance at the course is usually compulsory (see the Didactic Regulations of Course of Study).

Detailed Course Content

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. 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.

Textbook Information

  • 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

Course Planning

 SubjectsText References
1Dipolar Magnetic field and Earth magnetosphereNotes provided by the teacher
2Debye length and plasma electric neutrality C. Chiuderi & M. Velli: Fisica del Plasma
3Motion of a charged particle in a magnetic fieldNotes provided by the teacher
4Adiabatic invariantsNotes provided by the teacher
5Induction equationC. Chiuderi & M. Velli: Fisica del Plasma
6Frozen field LawE. R. Priest : Solar magnetohydrodynamics
7Properties of current sheetsE. R. Priest : Solar magnetohydrodynamics
8Magnetic reconnection processE. R. Priest : Solar magnetohydrodynamics


Learning Assessment Procedures

Examination modalities: 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.

Students can start the exam by showing a topic of their choice, based on the recommended texts and on any review articles recommended by the teacher. The chosen topic can be described through a ppt presentation, in order to evaluate also the student's communication skills.

Exams may take place online, depending on circumstances.

  Criteria for awarding the final grade: The mastery shown in qualitative and quantitative description of the topics, the critical view of the topics covered during the course and the ability to correlate the various parts of the program will contribute equally to the formulation of the final grade.

Examples of frequently asked questions and / or exercises

 The questions below are not an exhaustive list but represent only a few examples.
  • 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