Advanced
Topics
in Applied math
Introduction
to
Plasma Physics – Syllabus
Instructor:
Professor
Jeff Freidberg
Prerequisites:
UG electromagnetic theory,
fluid dynamics, and partial differential equations
Lecture
1: Definition of a plasma
Basic
properties of an
un-magnetized plasma; DC Debye shielding; quasi-neutrality; AC
shielding;
collective effects; properties of a magnetized plasma
Lecture 2: Single particle motion I
Constant
B, E =
0 (gyro motion);
constant E, B = 0; constant B and E (E
x B drift); constant external force; grad-B drift; curvature drift
Lecture 3: Single particle motion II
Polarization
drift; effect of a
non-uniform electric field; conservation of magnetic moment;
magnetic mirroring
Lecture 4: Coulomb collisions – theory
Heuristic
derivation of the
Coulomb collision cross section; rigorous derivation of the
Coulomb collision
cross section; conservation laws
Lecture 5: Coulomb collisions – applications
Reaction
rate concept; momentum
relaxation; energy relaxation; pitch angle scattering
Lecture 6: Two fluid and single fluid (MHD)
models of a plasma
Properties
of a fluid model;
heuristic derivation of the two fluid model of a plasma,
conservation laws
reduction to the single fluid MHD model
Lecture 7: MHD equilibrium
Equilibrium
in a straight
cylinder; radial pressure balance;
Lecture 8: Alfven waves and MHD stability
MHD
waves in a homogeneous
plasma; shear Alfven wave and fast and slow magneto-sonic waves;
MHD stability
in a cylinder; m = 0 sausage instability; m = 1 helical
instability; toroidal
effects of curvature and toroidal current; stabilizing MHD
instabilities
Lecture 9: Plasma transport in a cylinder
Velocity
space and physical
space transport; random walk approximation; particle transport;
ambipolar
diffusion; magnetic field diffusion; energy transport
Lecture 10: Plasma transport in
multi-dimensional geometries
Transport
in a multi-dimensional
geometry (neoclassical transport); banana orbits; ohmic heating
Lecture 11: Plasma waves – theory
General
principles of electromagnetic
wave propagation; the dielectric tensor; the dispersion
relation; cutoffs and
resonances; wave polarization; reflection, transmission,
absorption, and mode
conversion; accessibility
Lecture 12: Plasma waves – applications
Cold
plasma dielectric tensor;
cold plasma dispersion relation; principle resonances; electron
cyclotron
heating; ion cyclotron heating
Lecture 13: Kinetic model of a plasma
Derivation
of the Boltzmann
equation; conservation of particles in 6-D phase space; the
Vlasov equation;
the Boltzmann collision operator, the Fokker-Planck collision
operator; the
Krook collision operator; fluid equations from kinetic equations
Lecture 14: Landau damping
Wave
damping
in a collisionless plasma (Landau damping); mathematical
derivation of Landau
damping; physical derivation of Landau damping