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Corso di laurea magistrale in

Physics

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MAGNETOHYDRODYNAMICS AND PLASMA PHYSICS

Anno accademico 2024/2025 - Docente: ALFIO MAURIZIO BONANNO

Risultati di apprendimento attesi

Course Description:

This course provides a comprehensive introduction to the dynamics of plasmas and magnetized fluids in various astrophysical and laboratory settings. It covers the theoretical framework of magnetohydrodynamics (MHD), basic plasma physics concepts, and applications to astrophysical phenomena such as solar winds, accretion disks, and stellar interiors. The course emphasizes both the mathematical techniques used to describe these systems and the physical understanding of the processes involved.



Modalità di svolgimento dell'insegnamento

Course Format:

Didattica Frontale: Interactive lectures will provide the primary theoretical foundation for the course, covering the core topics of plasma physics, MHD, and astrophysical fluid dynamics.

Laboratory Component (Optional/To Be Confirmed): Students may engage in laboratory sessions or computational labs focused on the numerical simulation of MHD and plasma systems. These lab sessions will help students apply theoretical concepts through hands-on experience with scientific computing tools like Python or MATLAB.

Prerequisiti richiesti

Prerequisites:

  • Classical Mechanics 
  • Electrodynamics 
  • Optional: Partial Differential Equations

Contenuti del corso

Week 1-2: Introduction to Plasma Physics and Magnetohydrodynamics (MHD)

  • Definition of plasmas, basic plasma parameters.
  • Single particle motion in electromagnetic fields.
  • Introduction to MHD: assumptions, scope, and relevance.
  • MHD equations: mass continuity, momentum, energy, and induction equations.

Week 3-4: Waves in Plasmas and MHD

  • Plasma oscillations, sound waves, and Alfvén waves.
  • Magnetosonic waves and fast/slow modes.
  • Dispersion relations in plasma and MHD.

Week 5-6: Equilibrium and Stability in MHD

  • Force-free fields and magnetic pressure.
  • Equilibrium configurations in astrophysical systems (magnetospheres, accretion disks).
  • Stability criteria: Rayleigh-Taylor, Kelvin-Helmholtz, and magnetic buoyancy instabilities.

Week 7-8: Magnetic Reconnection and Dynamo Theory

  • Magnetic reconnection: Sweet-Parker model, tearing mode instability.
  • Coronal heating problem and solar flares.
  • Dynamo theory: the origin of magnetic fields in stars and planets.

Week 9-10: Astrophysical Fluid Dynamics

  • Basic fluid dynamics: Navier-Stokes equation, conservation laws.
  • Compressible and incompressible flows.
  • Vorticity and turbulence in astrophysical fluids.

Week 11-12: Astrophysical Applications of MHD and Plasma Physics

  • Solar wind, coronal mass ejections, and magnetospheric dynamics.
  • MHD in accretion disks and jets.
  • Stellar and galactic magnetic fields.

Week 13-14: Advanced Topics

  • Instabilities in accretion disks: magnetorotational instability (MRI).
  • Plasma physics in the interstellar medium and galaxy clusters.
  • MHD turbulence and cascade models.

Week 15: Project Presentations and Review

  • Presentation of student projects on a selected topic in MHD, plasma physics, or astrophysical fluid dynamics.
  • Review of key concepts for the final exam.

Testi di riferimento

Textbooks and Reading Materials:

"Introduction to Plasma Physics and Controlled Fusion" by Francis F. Chen

A standard textbook covering the basics of plasma physics with a focus on both theory and applications.

"Plasma Physics for Astrophysics" by Russell M. Kulsrud

Provides a detailed look at the role of plasma physics in astrophysical systems, with emphasis on theoretical foundations.

"Magnetohydrodynamics of the Sun" by Eric Priest

An excellent resource for understanding MHD in solar physics, covering topics like magnetic reconnection and coronal heating.

"Astrophysical Fluid Dynamics" by E. T. Vishniac and D. Clarke

A comprehensive text on fluid dynamics in astrophysical contexts, from the basic equations to complex phenomena like turbulence.

"Magnetohydrodynamics" by P.H. Roberts

A classic text providing a rigorous treatment of the fundamental equations and applications of MHD.

"Fundamentals of Plasma Physics" by Paul M. Bellan

Covers the fundamental concepts of plasma physics with a focus on astrophysical and laboratory plasma processes.

"The Physics of Fluids and Plasmas: An Introduction for Astrophysicists" by Arnab Rai Choudhuri

A well-rounded introduction to both fluid dynamics and plasma physics, with numerous astrophysical applications.

Selected journal articles and review papers (provided by the instructor).

Verifica dell'apprendimento

Modalità di verifica dell'apprendimento

Here’s a syllabus for a 6-credit course titled "Magnetohydrodynamics (MHD), Plasma Physics, and Astrophysical Fluid Dynamics". The course is designed for advanced undergraduates or graduate students with a strong background in physics and applied mathematics.

Course Title:

Magnetohydrodynamics (MHD), Plasma Physics, and Astrophysical Fluid Dynamics

Course Code:

PHY 5XXX / AST 5XXX (Depending on institutional structure)

Credits:

6 Credits

Instructor:

Prof. [Instructor's Name]
Office: [Office Location]
Email: [Instructor's Email]
Office Hours: [Time & Days]

Course Description:

This course provides a comprehensive introduction to the dynamics of plasmas and magnetized fluids in various astrophysical and laboratory settings. It covers the theoretical framework of magnetohydrodynamics (MHD), basic plasma physics concepts, and applications to astrophysical phenomena such as solar winds, accretion disks, and stellar interiors. The course emphasizes both the mathematical techniques used to describe these systems and the physical understanding of the processes involved.

Prerequisites:

  • Classical Mechanics (PHY XXXX)
  • Electrodynamics (PHY XXXX)
  • Fluid Mechanics or Continuum Mechanics (PHY XXXX)
  • Partial Differential Equations (MAT XXXX)
  • Recommended: Introduction to Plasma Physics (optional)

Course Learning Outcomes:

By the end of the course, students will be able to:

  1. Formulate and solve the basic equations of magnetohydrodynamics (MHD) and plasma physics.
  2. Understand the role of magnetic fields in plasma dynamics and astrophysical processes.
  3. Analyze fluid and plasma instabilities in astrophysical contexts (e.g., Rayleigh-Taylor, Kelvin-Helmholtz, and magnetorotational instabilities).
  4. Apply MHD and plasma physics concepts to real-world astrophysical phenomena like stellar winds, magnetospheres, and accretion disks.
  5. Perform numerical simulations and interpret observational data related to plasmas and astrophysical fluid systems.

Course Outline:

Week 1-2: Introduction to Plasma Physics and Magnetohydrodynamics (MHD)

  • Definition of plasmas, basic plasma parameters.
  • Single particle motion in electromagnetic fields.
  • Introduction to MHD: assumptions, scope, and relevance.
  • MHD equations: mass continuity, momentum, energy, and induction equations.

Week 3-4: Waves in Plasmas and MHD

  • Plasma oscillations, sound waves, and Alfvén waves.
  • Magnetosonic waves and fast/slow modes.
  • Dispersion relations in plasma and MHD.

Week 5-6: Equilibrium and Stability in MHD

  • Force-free fields and magnetic pressure.
  • Equilibrium configurations in astrophysical systems (magnetospheres, accretion disks).
  • Stability criteria: Rayleigh-Taylor, Kelvin-Helmholtz, and magnetic buoyancy instabilities.

Week 7-8: Magnetic Reconnection and Dynamo Theory

  • Magnetic reconnection: Sweet-Parker model, tearing mode instability.
  • Coronal heating problem and solar flares.
  • Dynamo theory: the origin of magnetic fields in stars and planets.

Week 9-10: Astrophysical Fluid Dynamics

  • Basic fluid dynamics: Navier-Stokes equation, conservation laws.
  • Compressible and incompressible flows.
  • Vorticity and turbulence in astrophysical fluids.

Week 11-12: Astrophysical Applications of MHD and Plasma Physics

  • Solar wind, coronal mass ejections, and magnetospheric dynamics.
  • MHD in accretion disks and jets.
  • Stellar and galactic magnetic fields.

Week 13-14: Advanced Topics

  • Instabilities in accretion disks: magnetorotational instability (MRI).
  • Plasma physics in the interstellar medium and galaxy clusters.
  • MHD turbulence and cascade models.

Week 15: Project Presentations and Review

  • Presentation of student projects on a selected topic in MHD, plasma physics, or astrophysical fluid dynamics.
  • Review of key concepts for the final exam.

  1. ).

Grading Breakdown:

  • Homework Assignments: 30%
  • Midterm Exam: 20%
  • Final Exam: 30%
  • Project (including presentation): 20%

Assignments & Projects:

  • Homework will involve analytical problems on plasma physics, MHD, and fluid dynamics. Numerical simulations using Python or MATLAB may be required.
  • Project: Each student will work on a research project related to a specific astrophysical system or plasma process. The project will involve both a written report and an oral presentation.