Plasma physics and controlled fusion

A.Y. 2020/2021
Overall hours
Learning objectives
Basic preparation on phenomenological aspects, theoretical models and experimental methods in plasma physics, which allow to treat specific problems in astrophysics, in the context of controlled thermonuclear fusion and in technological plasma-based processes.
Expected learning outcomes
At the end of the course the student will be able to:
- define the plasma state, provide examples of different types of plasma and explain the parameters that characterize them;
- analyze the motion of charged particles in electric and magnetic fields;
- distinguish the single particle approach, fluid approach and kinetic statistical approach to describe different plasma phenomena;
- explain the concept of cutoff and resonance and describe various types of waves in plasmas;
- discuss the interaction between particles and waves;
- discuss technical applications of plasma and explain the most important methods for the production and diagnostics of plasma in the laboratory;
- demonstrate an understanding of the principles of confinement in a toroidal magnetic field configuration and describe the basic principles of tokamak operation;
- explain the use of thermonuclear fusion for energy production, discuss plasma confinement problems and current directions of research;
- demonstrate an understanding of the processes related to plasmas in the near Earth environment, interplanetary space and astrophysical objects.
Course syllabus and organization

Single session

Lesson period
Second semester
Synchronous remote lessons, using the Zoom platform. Notices, lesson recordings and additional material on the Ariel website.
Course syllabus
Plasmas in nature and in the laboratory. Basic parameters and typical length and frequency scales of plasmas, quasi-neutrality, Debye shielding effect.

Motion of charged particles in non-uniform electric and magnetic fields; magnetic, inertial and polarization drift. Adiabatic invariants. Magnetic mirrors. Motion of charged particles in the magnetic field of a Tokamak. Brief notes on plasma acceleration methods. Van Allen radiation belts and motion of charged particles in the Earth's magnetic field.

Kinetic description of plasma, Vlasov equation and Fokker-Planck equation. Moments of the distribution function, derivation of fluid equations. Chapman and Enskog procedure for closing fluid equations, Braginskii equations and their limiting cases: cold plasma equations and magnetohydrodynamic (MHD) equations.

Wave propagation in a homogeneous cold plasma. WKB approximation for the propagation of waves in a non-homogeneous plasma. Ray-tracing equations, propagation of radio waves in the ionosphere. Short notes on the propagation of waves in a plasma in the kinetic approach, Landau damping. Emission of radiation from a plasma: Bremsstrahlung and cyclotron radiation. Radiation transport equation.

The ideal magnetohydrodynamics, freezing of the magnetic flux. Magnetohydrodynamic waves. Examples of MHD equilibrium states, the Grad-Shafranov equation for static axisymmetric equilibria. Solar corona: Chapman's static model and Parker's dynamic model (solar wind). Examples of MHD instabilities, energy principle. Short notes of non-ideal magnetohydrodynamics and magnetic reconnection.

Nuclear fusion reactions. Ignition conditions and Lawson's criterion. Magnetic and inertial confinement systems. State of the art of research on controlled thermonuclear fusion, the ITER project.
Prerequisites for admission
Knowledge of the concepts and methods introduced in the Bachelor's Degree in Physics, in particular relating to Classical Mechanics, Electromagnetism and Mathematical Analysis.
Teaching methods
Lectures using blackboard and slides.
Teaching Resources
R. Fitzpatrick, "Plasma Physics - Introduction", CRC press, 2015
P. M. Bellan, "Fundamentals of Plasma Physics", Cambridge University Press, 2006
F. F. Chen, "Introduction to Plasma Physics and Controlled Fusion", 3rd ed., Springer, 2016
J. P. Freidberg, "Plasma physics and fusion energy", Cambridge University Press, 2007
W. M. Stacey, "Fusion plasma physics", Wiley, 2005
R. M. Kulsrud, "Plasma physics for astrophysics", Princeton University Press, 2005
C. Chiuderi, "Fisica del plasma: fondamenti e applicazioni astrofisiche", Springer, 2012
Notes on the Ariel platform.
Assessment methods and Criteria
Oral exam with questions on the topics covered in class, to check if the objectives of the course have been achieved and the student has acquired the basic knowledge of the subject.
FIS/03 - PHYSICS OF MATTER - University credits: 6
Lessons: 42 hours
Professor: Rome' Massimiliano