Asymptotic methods, Dominant balance, ODEs: initial and Boundary value problems, Wronskian, Green's functions, Complex Variables: Cauchy's theorem, Taylor and Laurent expansions, Approximate Solution of Differential Equations, singularity type, Series expansions. Asymptotic Expansions. Stationary Phase, Saddle Points, Stokes phenomena. WKB Theory: Stokes constants, Airy function, Derivation of Heading's rules, bound states, barrier transmission. Asymptotic evaluation of integrals, Laplace's method, Stirling approximation, Integral representations, Gamma function, Riemann zeta function. Boundary Layer problems, Multiple Scale Analysis
Analytical Techniques in Differential Equations
Instructors: Jong-Kyu Park
Fusion Plasmas & Plasma Diagnostics
Introduction to experimental plasma physics, with emphasis on high-temperature plasmas for fusion. Requirements for fusion plasmas: confinement, beta, power and particle exhaust. Discussion of tokamak fusion and alternative magnetic and inertial confinement systems. Status of experimental understanding: what we know and how we know it. Key plasma diagnostic techniques: magnetic measurements, Langmuir probes, microwave techniques, spectroscopic techniques, electron cyclotron emission, Thomson scattering.
Instructors: Philip Charles Efthimion, Richard P. Majeski
General Plasma Physics I
An introductory course to plasma physics, with sample applications in fusion, space and astrophysics, semiconductor etching, microwave generation, plasma propulsion, high power laser propagation in plasma; characterization of the plasma state, Debye shielding, plasma and cyclotron frequencies, collision rates and mean-free paths, atomic processes, adiabatic invariance, orbit theory, magnetic confinement of single-charged particles, two-fluid description, magnetohydrodynamic waves and instabilities, heat flow, diffusion, kinetic description, and Landau damping. The course may be taken by undergraduates with permission of the instructor.
Instructors: Nathaniel J. Fisch, Hong Qin
Plasma Waves and Instabilities
Hydrodynamic and kinetic models of nonmagnetized and magnetized plasma dispersion; basic plasma waves and their applications; basic instabilities; mechanisms of collisionless dissipation; geometrics-optics approximation, including ray tracing, field-theoretical description of continuous waves, and ponderomotive effects; conservation laws and transport equations for the wave action, energy, and momentum; mode conversion; quasilinear theory.
Instructors: Ilya Yevgenyevich Dodin
Seminar in Plasma Physics
Advances in experimental and theoretical studies or laboratory and naturally-occurring high-termperature plasmas, including stability and transport, nonlinear dynamics and turbulence, magnetic reconnection, selfheating of "burning" plasmas, and innovative concepts for advanced fusion systems. Advances in plasma applications, including laser-plasma interactions, nonneutral plasmas, high-intensity accelerators, plasma propulsion, plasma processing, and coherent electromagnetic wave generation.
Instructors: Samuel A. Cohen, Allan H. Reiman
Software Engineering for Scientific Computing
The goal of this course is to teach basic tools and principles of writing good code, in the context of scientific computing. Specific topics include an overview of relevant compiled and interpreted languages, build tools and source managers, design patterns, design of interfaces, debugging and testing, profiling and improving performance, portability, and an introduction to parallel computing in both shared memory and distributed memory environments. The focus is on writing code that is easy to maintain and share with others. Students will develop these skills through a series of programming assignments and a group project.
Instructors: James McLellan Stone
General Plasma Physics II
This is an introductory graduate course in plasma physics, focusing on magnetohydrodynamics (MHD) and its extension to weakly collisional or collisionless plasmas. Topics to be covered include: the equations of MHD and extended MHD, the structure of magnetic fields, static and rotating MHD equilibria and their stability, magnetic reconnection, MHD turbulence, and the dynamo effect. Applications are drawn from fusion, heliophysical, and astrophysical plasmas.
Instructors: Hantao Ji
Introduction to Classical and Neoclassical Transport and Confinement
The first half of this course intends to provide students with a systematic development of the fundamentals of gyrokinetic (GK) theory, and the second half provides students with an introduction to transport and confinement in magnetically confined plasmas.
Instructors: Hong Qin, William Ming-Wu Tang
Irreversible Processes in Plasmas
Introduction to theory of fluctuations and transport in plasma. Origins of irreversibility. Random walks, Brownian motion, and diffusion; Langevin and Fokker-Planck theory. Fluctuation-dissipation theorem; test-particle superposition principle. Statistical closure problem. Derivation of kinetic equations from BBGKY hierarchy and Klimontovich formalism; properties of plasma collision operators. Classical transport coefficients in magnetized plasmas; Onsager symmetry. Introduction to plasma turbulence, including quasilinear theory. Applications to current problems in plasma research.
Instructors: Gregory Wayne Hammett
Laboratory in Plasma Physics
Develop skills, knowledge, and understanding of basic and advanced laboratory techniques used to measure the properties and behavior of plasmas. Representative experiments are: cold-cathode plasma formation and architecture; ambipolar diffusion in afterglow plasmas; Langmuir probe measurements of electron temperature and plasma density; period doubling and transitions to chaos in glow discharges; optical spectroscopy for species identification; microwave interferometry and cavity resonances for plasma density determination; and momentum generated by a plasma thruster.
Instructors: Samuel A. Cohen
Nonlinear Processes in Fluids and Plasmas
A comprehensive introduction to the theory of nonlinear phenomena in fluids and plasmas, with emphasis on turbulence and transport. Experimental phenomenology; fundamental equations, including Navier-Stokes, Vlasov, and gyrokinetic; numerical simulation techniques, including pseudo-spectral and particle-in-cell methods; coherent structures; transition to turbulence; statistical closures, including the wave kinetic equation and direct-interaction approximation; PDF methods and intermittency; variational techniques. Applications from neutral fluids, fusion plasmas, and astrophysics.
Instructors: John Albert Krommes
Physics of Plasma Propulsion
Focus of this course is on fundamental processes in plasma thrusters for spacecraft propulsion with emphasis on recent research findings. Start with a review of the fundamentals of mass, momentum & energy transport in collisional plasmas, wall effects, & collective (wave) effects, & derive a generalized Ohm's law useful for discussing various plasma thruster concepts. Move to detailed discussions of the acceleration & dissipation mechanisms in Hall thrusters, magnetoplasmadynamic thrusters, pulsed plasma thrusters, & inductive plasma thrusters, & derive expressions for the propulsive efficiencies of each of these concepts.
Instructors: Edgar Yazid Choueiri
Seminar in Plasma Physics
Advances in experimental and theoretical studies or laboratory and naturally-occurring high-temperature plasmas, including stability and transport, nonlinear dynamics and turbulence, magnetic reconnection, selfheating of "burning" plasmas, and innovative concepts for advanced fusion systems. Advances in plasma applications, including laser-plasma interactions, nonneutral plasmas, high-intensity accelerators, plasma propulsion, plasma processing, and coherent electromagnetic wave generation.
Instructors: Allan H. Reiman, William Ming-Wu Tang