Fundamental parameters in plasmas. Particles orbit theory. Kinetic theory: Vlasov and Boltzmann equations. Moments equation and fluid descriptions. One fluid models and magnetohydrodynamic equations (MHD). MHD equilibria and instabilities. MHD and plasma waves and shock waves. Vlasov linear theory and wave-particle interaction. Magnetic reconnection and resistive instabilities. Introduction to plasma turbulence.
C Chiuderi and M. Velli, Fisica del plasma:Fondamenti ed applicazioni astrofisiche,Springer
T. J. M Boyd and J. J. Sanderson, The physics of plasmas, Cambridge University Press
D. R. Nicholson, Introduction to plasma physics, Wiley and sons, NY
S. Galtièr, Introduction to modern magnetohydrodynamics, Cambridge Univerisity Press
Learning Objectives
The course aims to provide the student interested in the study of astrophysical, heliophysical and geophysical processes, the fundamental concepts of plasma physics: characteristic quantities, fluid and kinetic models, waves, instabilities, dissipation. These concepts are the basis of many phenomena that characterize the distant universe, the circumterrestrial environment and the heliosphere. The course also introduces several concepts of non-linear physics which can be useful also for a student more interested on theoretical physics.
Prerequisites
None
Teaching Methods
frontal branch
Further information
Contacts:
simone.landi@unifi.it
Type of Assessment
Oral interview on topics of the program
Course program
Definition of plasma and fundamental quantities: Definition of plasma, Debye length, plasma frequency, collision frequency and mean-free path lenght, plasma parameter.
Theory of orbits: orbits in homogeneous electric and magnetic fields, in slowly varying in time and space. Adiabitic particle's invariants and magnetic bottling.
Kinetic theory: Liouville theorem, statistical equilibrium, ensemble avrage, Vlasov and Boltzmann equations. Fundamental properties of the Vlasov equation; Boltzmann equation and thermodynamic equilibrium.
From the kinetic theory to the fluid description: moments of the Boltzmann equation and closure for the hydrodynamic case: Euler and Navier-Stokes equations. Moment system equations for the electromagnetic case and two-fluid plasma model. One fluid model, generalized Ohm's law and magnetohydrodynamic equations (MHD) in the non-relativistic limit. General theory of MHD equilibrium: force-free and current-free equilibrium, Grad-Shafranov equation. Equilibria in cylindrical geometry (Tokamak and coronal loops). Magnetic hydrodynamic instabilities: general theory. The case of Kelvin-Helmholtz, Reyleigh-Taylor and floatation instabilities (supernova shocks, jets and loops emergence in star's surfaces). MHD waves and plasma waves: Alfven waves, magnetoacoustic waves, ion cyclotron and whistler (waves from the sun and in the magnetospheres). High frequency waves: Langmuir and electron-cyclotron. General theory of the linear Vlasov equation. The concept of resonance and application to the Langmuir wave case. The Landau damping. Basic concepts of magnetic diffusion and fundamental parameters. Steady state reconnection. Tearing and plasmoid instabilities. Fast magnetic reconnection in MHD. Introduction to plasma turbulence: standard phenomenological observations and models (Kolmogorv and Iroshnikov-Kraichnan); phenomenological models for electromagnetic fluctuations at ionic and electronic kinetic scales.