Master 2 courses in Physics - Physics of Plasmas and Fusion track

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This module is an introduction dedicated to fulfill two objectives: (i) to introduce the basic concepts of the "plasma state" and (ii) to present the different theoretical approaches related to the multi-scale (time and space) aspect of thermonuclear, cold and/or space fusion plasmas. This course remains at a basic level as far as the applications are concerned and focuses on giving the most precise general view of the tools used in plasma physics.
Indeed, plasma - or the fourth state of matter - constitutes 99% of the visible matter in the Universe and is essentially formed of ionized gas. This "plasma state" is thus characterized by a set of charged particles influenced by long-range electric and magnetic fields, and by their feedback on these fields. Plasmas are thus the result of two contradictory tendencies, a tendency to disorder due to thermal agitation and a tendency to organization due to the Coulombian interaction.
These two opposite behaviors between charged particles and electromagnetic fields makes the determination and calculation of the different space-time scales present within the plasma essential in order to understand both the dynamics of the plasma itself, but also and above all, the use of different theories and models used in plasma physics. Thus, among the different possible perimeters for this module, we have opted for a division according to these scales and their associated models in order to show the coherence and continuity of these different theoretical approaches.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The objective is to present the fluid approach of the generalized Magnetohydrodynamics (MHD) theory in which the corpuscular aspect (electrons, ions) is no longer essential to describe the linear and nonlinear physical processes in magnetized plasmas. Four main parts will be discussed: (I) Theoretical foundations of MHD; (II) Invariants and equilibria; (III) Instabilities and magnetic containment; (IV) MHD turbulence. The articulation between these parts will be facilitated by examples from astrophysical plasmas and magnetic thermonuclear fusion.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This course is divided into three parts.
I.  Kinetic theory : the foundations
This course aims to lay the basis of the kinetic theory of plasmas. It focuses on classical, non relativistic and fully ionized plasmas.
II. Application to magnetic fusion plasmas : transport and relaxation in tokamak plasmas
The objective of the course is to study the phenomena of reorganisation of the distribution function of plasma particles, undergoing for example heating, in velocity space (relaxation) or in position space (transport). In particular, hot, low collisional, and especially fully ionised plasmas are studied here. Such plasmas are encountered in thermonuclear fusion, but also in the universe.
III. Application to cold plasmas : Introduction to the kinetic theory of discharges
In cold plasmas, most of the electrical power is absorbed by the electrons which dissipate this energy by elastic and inelastic collisions with neutrals. Due to the low ionization rates observed in cold plasmas, electron-electron collisions are rare and the electron distribution function deviates significantly from a Maxwellian equilibrium distribution. This non-equilibrium character of electrons is the main reason for a kinetic description of the heating and transport of electrons in the cold plasmas studied in this course.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This course is divided into three parts.
I. Waves and instabilities in plasmas : the basics
This part aims at presenting in a very general way the theory of waves in plasmas in the framework of the fluid theory and the kinetic theory. The dispersion relations and the characteristics of the different wave solutions are calculated in the linear approximation. Several examples of nonlinear phenomena are then presented. The theory of linear instabilities is presented in non-magnetized media.
II. Application to astrophysical plasmas : waves and instabilities
This course presents different examples of waves and instabilities in astrophysical plasmas, using the fluid and kinetic formalisms.
III. Application to the laser-plasma interaction at ultra-high intensity (UHI).

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The objective of this course, both theoretical and applied, is twofold: (i) to train students in the methods and algorithms of numerical simulation by introducing them to the different mathematical models used in fluid dynamics and plasma physics, and (ii) to initiate them to numerical simulation by using specific computational codes, in order to study complex phenomena in plasma physics, which are described by fluid and/or kinetic models and which are dealt with in the different teaching units of the Master.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The objective of the course is to introduce students to the techniques of characterization, diagnosis and analysis of plasmas used in physics research laboratories. They can thus benefit from the expertise of internationally recognized researchers, professors, engineers and astronomers, who welcome them in their laboratories for several days of "Practical Work" organized within their research team.
The subjects proposed by the laboratories concern all types of plasmas (cold process plasmas, thermonuclear magnetic fusion plasmas, inertial fusion plasmas, natural and astrophysical plasmas). The practical work is very varied: instrumentation, experimental measurements on a research device, analysis of space data from a satellite, numerical modeling, use of calculation codes, etc...
Before these practical works, a theoretical course of 18 hours is given on the techniques of instrumentation, diagnosis and analysis of plasmas. Particular emphasis is placed on vacuum and gas flow techniques, but also on electrical diagnostics (Langmuir probes, ...), spectrometry diagnostics (OES, MS) and laser diagnostics (LIF, TALIF, ...).

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This module has two parts. The first one  recalls the quantum bases of atomic and molecular physics, and then presents the concepts of atomic and molecular ionization state distributions. The second part establishes the links with statistical physics to present the foundations of the dynamic physics of plasmas, then introduces the elements necessary for the modeling of chemical kinetics in plasmas, and finally presents the concepts of radiation and atomic and molecular spectroscopy. The course includes tutorials on the application of these concepts to different types of plasmas (hot fusion plasmas, cold process plasmas, natural plasmas).

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This unit provides an in-depths study of processes underlying the dynamics of the core of a magnetic fusion plasma, with an emphasis on turbulence, anomalous transport, heating and current drive, and the current state of research. We aim at understanding the overall physics of confinementof thermal particles, of impurities, and of energetic particles (produced by NBI-type heating, and by fusion reactions).

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The aim is to present the different methods of characterisation of Tokamak plasmas, from the core to the wall, by linking the outstanding observations to physical phenomena. Starting from remarkable experimental observations, the approach first consists in understanding the physics underlying the diagnostics used (radiation, wave probing, particles...). Then, by extending the « Tronc Commun » lessons, to understand the physical interpretations proposed.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The teaching unit presents the environment of magnetized stars. The concepts are presented mainly for the Earth and the planets of the Solar System - these environments, studied in-situ, are the best known. However, these concepts are applicable to more distant plasmas.
The "space" plasma closest to us is located at an altitude of about 70 km, where the ionization of the upper atmosphere by solar UV radiation produces a resistive and magnetized layer of plasma, called the ionosphere.
Much further away, the interplanetary medium is traversed by a supersonic expanding plasma (300 to 800 km/second), coming from the Sun which is called the Solar Wind.
Between the two regions, there is a zone controlled by the Earth's magnetic field called the magnetosphere. The plasma in this region is collisionless, continuously out of thermodynamic equilibrium and subject to irregular reconfigurations of its magnetic topology.
From an astrophysical point of view, these regions represent a model that can be used to better understand other objects for which in-situ exploration is rare (magnetospheres of the planets Jupiter, Saturn, Uranus, Neptune) or even impossible (exoplanets, stellar corona, environments of magnetized stars such as young stars, pulsars, supersonic / super magnetosonic jets), etc.
From the point of view of plasma physics, the magnetosphere and the solar wind are excellent laboratories for the study of collisionless plasmas, very interesting for the understanding of transport processes in systems without resistivity or viscosity, turbulence, wave-plasma interactions, acceleration phenomena, etc.
The course is mainly devoted to basic concepts, illustrated with examples of applications in space physics and astrophysics.  It is divided into 4 independent sections.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

Stars concentrate the overwhelming majority of visible matter in the universe in the form of hot plasmas. In this course, we focus on the high energy density plasmas that are involved in the formation and evolution of stars.
The objective of this module is to explain the macroscopic physical phenomena that structure stellar plasmas and dictate their thermodynamic conditions, as well as the microscopic physics that locally determine their properties.
After an introduction, we qualitatively address the star formation process. We study the dynamics of the accretion disks and astrophysical jets that occur at the beginning of the star's existence. We study their internal functioning during the main sequence, the longest phase of their existence. We look at the heat production within the star and the transport of this heat to its surface, leading to the equations of the stellar structure. We also discuss some modeling elements that allow us to calculate properties useful for modeling stars: the equations of state and opacities. We also discuss the evolution and end of life of stars, supernovae and cosmic ray acceleration. Finally, we discuss recent works that aim at reproducing some astrophysical phenomena in the laboratory, using high power lasers or magnetic pinch machines (z-pinch).

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This module focuses on the production of low-pressure plasmas, their maintenance, the physical mechanisms involved during their operation, but also on the interaction of plasma species with surfaces - a phenomenon that is very important for the establishment of the steady state, but also for many applications. Discharge plasmas are intrinsically sources of species, charged or not, but also of photons. Without being exhaustive, this course presents different configurations of plasmas used as sources of charged particles for accelerators or synchrotron, space ion thrusters, ion beams (positive and negative as in the FIB - Focus Ion Beam or additional heating of tokamaks), reactive ion etching reactors, etc. The 'cold' reaction kinetics of heavy species in low-pressure plasmas is also addressed - a major issue in microelectronics, thin film deposition, but also light sources (gas lasers, specific and low consumption lamps, ...), environmental applications (isotope separation, destruction of pollutants, ...), biology and medicine, etc.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The TU "High Pressure Cold Plasmas" aims to describe the basic concepts associated with high pressure non-equilibrium plasmas. Non-equilibrium plasmas are plasmas where an imbalance is created between the electronic population capable of acquiring energies as high as ten eV and other species (atomic and/or molecular, neutral or ionized, in their ground or excited states) which are maintained at temperatures below a few thousands Kelvin. This imbalance is most of the time generated as soon as the plasma is created by the application of a strong anisotropic electric field to which the electrons are mainly sensitive. The specificity of "high pressure" plasmas lies in the importance of collisions between species (electrons / neutrals, ions / ions, neutrals / neutrals, etc.) and their effects on the characteristics of the plasmas considered.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The inception of ultrahigh-intensity lasers, delivering pulses of duration ranging from a few femtosecond to a few picoseconds and intensity exceeding 10!"Wcm#$, unlocked the exploration of relativistic light-matter interactions, whereby the target electrons, accelerated to near-speed-oflight velocities, trigger a wealth of collective, radiative or nuclear processes. This research field has seen a boom in the past two decades due to the unprecedentedly extreme conditions that ultraintense lasers can achieve, the unrivalled properties (brevity, energy density, etc.) of the generated particle and photon sources, and the growing number of applications of the latter in physics and beyond. The coming into operation of a new breed of multipetawatt laser facilities in Europe (e.g. Apollon in France) and Asia will further multiply the already many spin-offs of relativistic laserplasma interactions. The purpose of this course is to provide the student with an in-depth review of the main concepts and phenomena underpinning this research field.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This module consists of two parts. The first one is devoted to laser-plasma interaction. It discusses the non-linear wave mixing mechanisms inherent in the propagation of a large wave in a plasma and the resulting resonant couplings. The ponderomotive force is described as well as its effects on plasma as self-focalization. Thomson scattering is also presented as a powerful method for plasma diagnosis and various parametric instabilities such as stimulated Raman scattering.  Finally various applications are presented.
The second part outlines the general concepts of inertial confinement fusion: compression, heating, ignition, gain. The fundamental concepts of nuclear physics, thermonuclear fusion and the principle of confinement are recalled. Post's temperature concepts and Lawson's criteria are introduced. Various gain fusion schemes are presented, such as isobaric ignition, fast ignition and shock ignition. The hydrodynamics of laser-created plasmas provide an opportunity to address the notions of self-similar flow or shocks. The modes of transport of thermal energy within the target are detailed.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 2nd Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The lecture goes deeper into astrophysical plasmas as the interstellar medium. Some of the classic processes and equations are derived and further discussed. Particular importance is given to the processes important in the context of structure formation. A particular emphasis is put on the dissipative and transport processes.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 2nd Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

Numerical simulation is an investigation tool shared by many specialties in plasma physics. This aim of this course is to expose students to handling this tool. More specifically, students will achieve a preliminary practical training followed by one long project in computational fluid dynamics (CFD).
All the proposed projects imply the magnetohydrodynamic (MHD) modeling in two dimensions of some physical processes involved in the Sun’s activity, being associated with magneto-convection at the interface between the star’s internal and external layers.
The goal of this course is not to do programming and code development – even if some lines will have to be typed and some parameters will have to be varied depending on the project. Instead, the principle is to use an operational code written in FORTRAN as well as a distinct visualization tool with GDL, so as to fine-tune, to test, and to conduct numerical experiments aiming at characterizing, understanding, and quantifying some physical mechanisms.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 2nd Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

Additional information on inertial confinement fusion is provided, as well as an introduction to the use of a hydrodynamic code for the simulation of laser implosions. The module is completed by experimental work on a power laser.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 2nd Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

Some notions on power lasers are given. The example of the LIL, LMJ and PETAL chains is presented. The module ends with pratical works on lasers.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 2nd Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The ambition of this module is to give students an integrated vision of the tokamak, to make tangible the interdependence of plasma physics, plasma-wall interaction, materials and superconductors in the definition of the characteristics of a fusion reactor.
The method consists in answering the following question: how to "size a tokamak" given the objectives assigned to it, mainly in terms of fusion power and energy efficiency? The work is done in small groups supervised by CEA/IRFM researchers.
The first two days are devoted to lectures that explain the topics studied during the following stages and the working methods (in particular the scaling laws, the operational regimes and the plasma-wall interaction).
In the first step of the group work, fusion performance goals and some constraints are given to all groups. Each group determines the best "engineering" parameters of the tokamak (torus radius, plasma current, magnetic field...) that allows to reach the objectives. For this, we use the scaling laws that relate the performance of a tokamak (for example the energy confinement time in the plasma) to the "engineering" parameters of the tokamak.
In the second stage, each group is tasked with examining a question of particular engineering or physical importance: the means of heating the plasma, magnetohydrodynamic equilibrium and turbulence, impurities and radiation, particle and heat fluxes on the enclosure components, sizing of the superconducting coils, etc. Each group is supervised by a subject expert.
During all the group work, the supervisors are present and available. During the two weeks, the students are encouraged to interact with the other groups and to interview all the CEA/IRFM researchers who can help them in their work.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 2nd Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

Students work in pairs on practical work supervised by IRFM physicists and engineers, on the facilities those use for their own research.
Each student performs two experiments from the list below, one of which (if possible) concerns work on data from a tokamak (COMPASS, GOLEM, WEST).

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 2nd Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The objective is to understand the principles and physical models of cold plasmas based on application examples in the fields of energy and aerospace. Recent advances and scientific and technical challenges are presented. The course alternates between a review of the basic principles and models and practical examples.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)

2nd year Master - 2nd Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The objective is to present the physical principles, advances and technological barriers of the application of low- and high-pressure non-equilibrium plasmas to materials, environment, biomedicine and agriculture. Students will discover innovative applications of cold plasmas, and benefit from the expertise of researchers and professors recognized internationally for their scientific expertise.

Prerequisites

First year of MSc in Physics or Engineering Schools.

Contact

Philippe Savoini  (philippe.savoini@sorbonne-universite.fr)