### Aims

The course aims at providing the students with an introduction to plasma physics and thermonuclear fusion.

### Contents

Introduction to plasma physics, charge particle motion in a magnetic field, introduction to collisional processes in plasmas, introduction to the collisional kinetic theory, basics of nuclear fusion in tokamak devices, physics principles of selected diagnostic techniques for tokamak plasmas.

### Detailed program

**Chapter 1: Introduction to plasma physics**

Introduction, general properties of a plasma and main plasma parameters. Quasi neutrality. Debye length. Coulomb collisions in plasmas. Rutherford cross section. Large and small angle collisions. Neutral particle collision cross section. Collision frequencies. Simple transport phenomena in plasmas: resistivity and ambipolar diffusion. Current in a vacuum tube. Arc discharge.

**Chapter 2: Particle motion in magnetic and electric fields**

Drift formalism of the particle motion in electric and magnetic fields. Magnetic moment invariance and its applications to mirror machines. Lagrangian formalism and exact constants of motion: rotational invariance and its application to tokamak confinement. Adiabatic invariants: adiabatic invariant of a pendulum; the action integral as an adiabatic invariant. Second and third adiabatic invariant for the motion of a charged particle in a magnetic field. Toroidal confinement configurations: tokamaks and stellarators. Magnetic surfaces, rotational transform and safety factor of a tokamak. Passing and trapped particles in a tokamak. Guiding centre motion of a passing and trapped particle in a tokamak.

**Chapter 3: Collisions, ionization, charge exchange and emission of radiation from a plasma**

Coronal equilibrium and ionization. Penetration of neutrals in a plasma. Molecular and atomic collisions, ionization, charge exchange. Bremsstrahlung radiation from a plasma. Radiative losses. Emission of cyclotron radiation from a plasma. Radiation transport. Recombination radiation from a plasma. Propagation of electromagnetic radiation in a plasma: cut-off and resonances.

**Chapter 4: Coulomb collisions in plasmas and charged particle slowing down**

Main properties of collisions in fully ionized plasmas. Formal derivation of the Fokker-Planck equation. Isotropy and friction terms in the Fokker-Planck equation for small angle Coulomb collisions. Slowing down equation for the average particle velocity. Slowing down of a charged particle in a plasma: resistive and runaway regimes. Slowing down of a charged particle having a velocity between the thermal ion and electron velocities. Calculation of the plasma resistivity and of the Dreicer electric field for runaway electron production starting from the Fokker-Planck equation. Calculation of the steady state alpha particle slowing down distribution from the Fokker-Planck equation.

**Chapter 5: Collisional transport**

Diffusion due to charged particle collisions: random walk model, diffusion equation, diffusion coefficients in magnetized and non magnetized plasmas. General properties of diffusion in weakly ionized plasmas. Two fluid model for weakly ionized plasmas without magnetic field: calculation of the ambipolar electric field and diffusion coefficient. Introduction to diffusion in fully ionized plasmas: role of like and unlike particle collisions. Particle diffusion due to electron-ion collisions in fully ionized plasmas: calculation of the diffusion coefficient and comparison with experimental data. Diffusion of energy in fully ionized plasmas: role of ion-ion, electron-electron and ion-electron collisions and their thermal diffusivities. Comparison between theory and experiment. Introduction to neoclassical transport: contribution of passing and trapped charges to particle and energy transport in toroidal geometry. Bootstrap current. Brief introduction to some experimental aspects of turbulent transport.

**Chapter 6: Introduction to controlled thermonuclear fusion**

Main reactions of interest for controlled thermonuclear fusion, role of alpha particles and neutrons in the deuterium-tritium reaction, classical and quantum reaction cross section. Calculation of the reactivity and of the reaction rate, processes that contribute to plasma heating and plasma cooling. Energy confinement time, Lawson criterion, thermonuclear reactor regimes: ideal ignition, ignition and power amplification. Thermal and electric gain factor Q.

### Semester

1st year, Master degree, First semester