Fusion energy and plasma physics - WPMEDPC9

Goal(s)

Provide the basic theoretical elements needed to understand plasmas using different approaches (kinetic, fluid), as well as some data concerning TOKAMAKs and the conditions for stable controlled thermonuclear fusion.
The basic elements of MHD will be provided, as well as the conceptual tools for modeling fluid instabilities. Resonant wave-particle interaction will be briefly discussed in the case of electrostatic kinetic waves.

Content(s)

1. Introduction to Hot Plasma Physics
1.1. Characteristic Lengths and Times
1.2. Introduction to Controlled Nuclear Fusion

2. Particle Trajectories in a Strong Magnetic Field
2.1. Adiabatic Limit
2.2. Guide-Center Motion
2.2.1. Secular Drifts: Electric and Curvature
2.2.2. Invariance of the Magnetic Moment
2.2.3. Parallel Dynamics
2.3. Applications: Magnetic Mirror; E-B Motion and Hamiltonian Dynamics

3. Kinetic Theory and Collective Phenomena
3.1. The Vlasov Equation
3.1.1. Derivation
3.1.2. Conservation Properties
3.1.3. Landau Damping
3.2. Collisions and the Landau Operator
3.2.1. Review of Weak Collisions
3.2.2. Derivation of the Landau Operator
3.2.3. Theorem H

4. Fluid Theory
4.1. Advantages and Weaknesses
4.2. Conservation Equations of Matter, Momentum, etc.
4.3. Drift Velocities in the Adiabatic Limit
4.4. Example of a Non-Collisional Closure

5. Main Drift Wave Instabilities
5.1. In a Homogeneous B Field
5.1.1. Physical Mechanism
5.1.2. Derivation and Study of the Hasegawa-Wakatani Model
5.2. In an Inhomogeneous B Field (Interchange)
5.2.1. Physical Mechanism
5.2.2. Extension of the Hasegawa-Wakatani Model with Curvature
5.2.3. Analogy with Rayleigh-Bénard
5.3. Kinetic and Reactive Instabilities

6. Turbulence and Nonlinear Saturation
6.1. Feedback of Fluctuations on Equilibrium
6.2. Nonlinear Couplings
6.2.1. Nonlinear Invariants and Energy Cascades (Kolmogorov)
6.2.2. Application to Hasegawa-Mima Turbulence
6.3. Concepts of Turbulence Self-Organization

7. From Turbulence to Transport
7.1. Case of Test Particles
7.2. Importance of Phase
7.3. Wave-Particle Resonance and Quasilinear Transport
7.4. Transition from Weak Turbulence to Developed Turbulence
7.5. Application to the Vlasov-Landau Model

• Courses in fluid mechanics (Navier-Stokes), electromagnetism, and classical statistical physics are essential prerequisites.
• Having taken a course in analytical mechanics, as well as basic elements of plasmas (content from the 2A / M1 course “Introduction to Plasmas”) are useful prerequisites.

Test

Written exam (2h). No notes/documents or calculator are permitted
Same for the second session.

Additional Information

Bibliography

See description in the GEN 3A stream / voir fiche filière GEN 3A