Plasma Physics and Controlled Fusion
A.Y. 2026/2027
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.
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.
- 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.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Natural and laboratory plasmas. Basic parameters and typical length and frequency scales of a plasma, quasi-neutrality, Debye shielding effect.
Motion of charged particles in nonuniform electric and magnetic fields; magnetic, inertial, and polarization drift. Adiabatic invariants. Magnetic mirrors. Motion of charged particles in the magnetic field of a tokamak. Introduction to plasma acceleration methods. Van Allen radiation belts and motion of charged particles in the Earth's magnetic field.
Kinetic description of the plasma, Vlasov equation and Fokker-Planck equation. Moments of the distribution function, derivation of fluid equations. Chapman-Enskog procedure for closure of 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 wave propagation in a nonhomogeneous plasma. Ray-tracing equations, radio wave propagation in the ionosphere. Introduction to wave propagation in a plasma using the kinetic approach, Landau damping. Radiation emission from a plasma: Bremsstrahlung and cyclotron radiation. Radiation transport equation.
Ideal magnetohydrodynamics, freezing of magnetic flux. Magnetohydrodynamic waves. Examples of MHD equilibrium states, the Grad-Shafranov equation for static axisymmetric equilibria. Solar corona: Chapman static model and Parker dynamic model (solar wind). Examples of MHD instabilities, the energy principle. Introduction to nonideal MHD and magnetic reconnection.
Nuclear fusion reactions. Ignition conditions and the Lawson criterion. Magnetic and inertial confinement systems. State-of-the-art research on controlled thermonuclear fusion.
Motion of charged particles in nonuniform electric and magnetic fields; magnetic, inertial, and polarization drift. Adiabatic invariants. Magnetic mirrors. Motion of charged particles in the magnetic field of a tokamak. Introduction to plasma acceleration methods. Van Allen radiation belts and motion of charged particles in the Earth's magnetic field.
Kinetic description of the plasma, Vlasov equation and Fokker-Planck equation. Moments of the distribution function, derivation of fluid equations. Chapman-Enskog procedure for closure of 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 wave propagation in a nonhomogeneous plasma. Ray-tracing equations, radio wave propagation in the ionosphere. Introduction to wave propagation in a plasma using the kinetic approach, Landau damping. Radiation emission from a plasma: Bremsstrahlung and cyclotron radiation. Radiation transport equation.
Ideal magnetohydrodynamics, freezing of magnetic flux. Magnetohydrodynamic waves. Examples of MHD equilibrium states, the Grad-Shafranov equation for static axisymmetric equilibria. Solar corona: Chapman static model and Parker dynamic model (solar wind). Examples of MHD instabilities, the energy principle. Introduction to nonideal MHD and magnetic reconnection.
Nuclear fusion reactions. Ignition conditions and the Lawson criterion. Magnetic and inertial confinement systems. State-of-the-art research on controlled thermonuclear fusion.
Prerequisites for admission
Knowledge of the concepts and methods introduced in the Bachelor's Degree in Physics, in particular in the courses of Classical Mechanics, Electromagnetism and Analysis.
Teaching methods
Lectures using blackboard and slides.
Teaching Resources
R. Fitzpatrick, "Plasma Physics - An Introduction", 2nd ed., CRC Press, 2022
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, 2010
W. M. Stacey, "Fusion plasma physics", 2nd ed. Wiley-VCH, 2012
R. M. Kulsrud, "Plasma physics for astrophysics", Princeton University Press, 2004
C. Chiuderi e M. Velli, "Fisica del plasma: fondamenti e applicazioni astrofisiche", Springer, 2012
Notes on the Ariel platform.
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, 2010
W. M. Stacey, "Fusion plasma physics", 2nd ed. Wiley-VCH, 2012
R. M. Kulsrud, "Plasma physics for astrophysics", Princeton University Press, 2004
C. Chiuderi e M. Velli, "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.
PHYS-03/A - Experimental Physics of Matter and Applications - University credits: 3
PHYS-04/A - Theoretical Physics of Matter, Models, Mathematical Methods and Applications - University credits: 3
PHYS-04/A - Theoretical Physics of Matter, Models, Mathematical Methods and Applications - University credits: 3
Lessons: 42 hours
Professor:
Rome' Massimiliano Gaetano
Professor(s)
Reception:
Friday, 9: 30-12: 30 (by appointment)
office at the Department of Physics