The course is offered in a 10-CFU version (Plasma physics I+II), to which two 5-CFU courses (Plasma physics I, Plasma Physics II) and one 8-CFU course (Plasma Physics) are offered jointly. The present detailed program defines aims, educational outcomes and syllabus for every joint course.

PLASMA PHYSICS I (5 ECTS)

The aim of this course is to provide a fundamental knowledge about the plasma state, with special focus on strongly ionized, high temperature plasmas. First, the problem is framed in the wider context of the electrodynamics of continuous media. Subsequently, after introducing the main properties and physical quantities that characterize the plasma state, the different theoretical models used in its description are derived from first principles. These models are then used to investigate specific topics, such as the collective modes and the propagation and emission of electromagnetic radiation in a plasma. The course concludes with a short introduction to the main issues related to controlled thermonuclear fusion.

PLASMA PHYSICS II (5 ECTS)

The course aims to develop some important issues of the physics of matter in the plasma state and represents a logical continuation of the course Plasma physics I. In addition to a more complete understanding of the physical properties of a plasma, the topics that are covered are also preparatory to the study of some of the most interesting and important applications of hot plasmas produced in the laboratory. To this end, the covered aspects include an introduction to the physical properties of magnetically confined plasmas, the physics of intense laser-plasma interaction and a presentation of controlled thermonuclear fusion, both magnetic and inertial. At the end of the course, visits at Research Centers (IFP-CNR Milano, ENEA Frascati, LNF-INFN Frascati) are foreseen.

PLASMA PHYSICS I

The student:

- knows the mathematical and physical methods required to develop theoretical plasma physics
- knows the main quantities definining the plasma state, together with the theoretical models suitable to describe it, with particular reference to classical, quasi-ideal plasmas
- is able to describe the main properties distinguishing the various kinds of plasma present in Nature/laboratory and to make simple estimates of the main quantities characterizing them
- is able to exploit the theoretical plasma models to develop the description of small amplitude electromagnetic wawes and collettive modes in plasmas
 

PLASMA PHYSICS II

The student:

- knows the theoretical models required to describe plasma dynamics in the non-linear and relativistic regime
- knows the main properties of magnetically confined plasmas, with main reference to equilibrium configurations also in realistic geometries
- is able to apply plasma theory to develop a description of non-linear waves in plasmas and to exploit the results to understand the main properties of the interaction between plasmas and intense laser pulses
- is able to apply the developed physical results to understand the main aspects of thermonuclear fusion research, with main reference to the properties of thermonuclear plasmas, to the conceptual scheme of a nuclear fusion power plant and to the magnetic and inertial confinement approaches

PLASMA PHYSICS I

Recalls of electromagnetism. Maxwell's equations. Lorentz force. Electrodynamic potentials. Gauge invariance. Lorenz and Coulomb gauges. Systems of Units in Electromagnetism: SI and gauss.

Electrodynamics of continuous media. Poynting's theorem, conservation of energy in linear dispersive media. Anti-hermitian component of the dielectric tensor of a medium and its absorption properties of electromagnetic energy. Conservation of energy in the presence of spatial dispersion. Propagation of electromagnetic waves in uniform and dispersive media: linear theory.

Fundamental plasma parameters. Shielding of the electric charge and the Debye length. Thermodynamic properties of a classical plasma. Plasma oscillations and plasma frequency. Electrical conductivity of a plasma. Conditions of "existence" of a plasma.

Guiding center theory. Dynamics of charged particles in constant, uniform, external electric and magnetic fields. Motion in slowly varying fields: the guiding center approximation. Drift motions. Mirror effect.

Methods for the description of a plasma. Microscopic description of a plasma: Klimontovich equation, kinetic theory, Vlasov equation. Macroscopic descriptions of a plasma: equations for the moments and multiple fluids model. Single fluid approach: Magnetohydrodynamics (MHD). Limits of validity.

Waves in a plasma I. Macroscopic approach: waves in a cold plasma, waves in a hot plasma, waves in the presence of an external magnetic field. Kinetic approach: collisionless absorption of electrostatic waves, Landau damping. Physical interpretation of the resonant wave-plasma interaction.

Emission of electromagnetic radiation in a plasma I. Results of the general theory of the radiation emission by moving charged particles. EM emission in a plasma: Cyclotron and Bremsstrahlung radiation.

Controlled thermonuclear fusion. Introduction. Nuclear fusion reactions, thermonuclear plasmas.

PLASMA PHYSICS II

Waves in a Plasma II. General aspects of the kinetic study of collective modes in a plasma. Waves in the presence of an external magnetic field in the kinetic approach: Cyclotron resonances, their physical interpretation and main properties. Introduction to the study of collective modes in a nonlinear plasma: relativistic plasma models, wave propagation of arbitrary amplitude in the cold plasma approximation.

Laser-plasma interaction. Introduction. Interaction between electromagnetic waves and underdense/overdense plasmas. Ponderomotive force, excitation of waves in plasmas, wave-breaking. Parametric instabilities. Applications of the superintense laser-plasma interaction.

Physics of magnetically confined plasmas. Dynamics of charged particles in toroidal and “Tokamak” magnetic configurations: consequences on the system’s physical behavior. 1D MHD equilibrium and stability: theta-pinch, Z-pinch, screw-pinch. 2D MHD equilibria and stability: balance of toroidal forces, Grad-Shafranov equation, Solove'v equilibria, stability criteria. Fundamental properties of the plasma edge region in magnetically confined systems: limiters, divertor, scrape-off layer.

Emission of electromagnetic radiation in a plasma II. General theory of the radiation emission by charged particles in motion and emission of EM radiation in a plasma: Cyclotron and Bremsstrahlung emission.

Collisions in a plasma. General properties of the collisional term in the kinetic description. Coulomb collisions. Characteristic collision times. Collisional transmission of energy between electrons and ions. Descriptions of the collision integral: Balescu-Lenard, Landau and  Fokker-Planck equations.

Controlled thermonuclear fusion. Introduction. Lawson criteria and ignition conditions. Approaches to fusion: magnetic (MCF) and inertial (ICF) confinement. General scheme of a fusion power plant. Energy balances. Fundamental physical properties of magnetically/intertially confined thermonuclear plasmas. Main scientific and technological issues of fusion systems. Current state of research in MCF and ICF.

The topics of the 8-cfu course “Plasma Physics” will be agreed with the students, by removing one of the above mentioned topics also according to their interests and background.

To attend the course a knowledge, at least at an elementary level, of classical mechanics, electromagnetism and calculus is required. To attend Plasma physics II a knowledge of the subjects contained in the programme of Plasma physics I is assumed.

The evaluation consists in an oral examination. It aims at verifying the knowledge of the course topics, with particular reference to the ability in interpreting the physical meaning of the adopted mathematical methods, applied to develop the description of: main plasma quantities, theoretical plasma models, small amplitude collective modes (plasma physics I); non-linear waves in plasmas, laser-plasma interaction, magnetically confined plasmas, thermonuclear fusion (plasma physics II). The knowledge of the systems of units, the value of the fundamentals physical quantities in plasma physics and the ability to develop simple numerical estimates and derivations is addressed as well.