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
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.
Hydrodynamic and kinetic models of nonmagnetized and magnetized plasma dispersion; basic plasma waves and their applications; basic instabilities; mechanisms of collisionless dissipation; geometrical-optics approximation; conservation laws and transport equations for the wave action, energy, and momentum; mode conversion; quasilinear theory.
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.
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.
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.
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.
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.
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.
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.