Nonlinear dynamics, Hydrodynamics and Magnetohydrodynamics

Contents:

• Introduction to nonlinear science
• Conservation laws
• Waves and instabilities in classical fluids
• Two-fluid an one-fluid models
• MHD equations  ideal MHD
• bParameter
• magnetic number
• magnetic diffusion
• Alfven number
• MHD equilibria in cylindrical and plane geometry
• magnetic Helicity
• Force free equilibrium
• Woltjer theorem
• 2D equilibrium
• Grad-Shafranov equation
• Tokamak equilibrium
• the MHD energy principle
• Interchange, flutes, Rayleigh-Taylor instabilities
• Sausages and kink instabilities.