Graduate Certificate in Plasma Science and Engineering

Advisory Prerequisite: AEROSP 335, senior standing. Enforced Prerequisite: None. (3 credits) Introduction to electric propulsion with an overview of electricity and magnetism, atomic physics, non-equilibrium flows and electrothermal, electromagnetic and electrostatic electric propulsion systems.

Advisory Prerequisite: MATH 216 and PHYSICS 240. Enforced Prerequisite: None. (4 credits) Introduction to solar terrestrial relations with an overview of solar radiation and its variability on all time-scales. The effects of this variability on the near-Earth space environment and upper atmosphere are considered, as well as effects on the lower and middle atmosphere with connections to weather and climate. Subjects are approached through extensive data analysis, including weekly computer lab sessions.

Advisory Prerequisite: None. Enforced Prerequisite: SPACE 370. Minimum grade requirement of “C” for enforced prerequisites. (4 credits) An introduction to a variety of models of the space environment, including models of the sun, magnetosphere, ring current, ionosphere, thermosphere and ionospheric electrodynamics. Students will learn the origins of different models, what each represents, to run the models and become familiar with the output.

Prerequisite: None. (4 credits) Basic physical and chemical processes important in controlling the upper/middle atmosphere and ionosphere: photochemistry, convection, diffusion, wave activity, ionization, heating and cooling. The terrestrial, as well as planetary atmospheres and ionospheres are to be considered.

Advisory Prerequisite: MATH 450, PHYSICS 405 and PHYSICS 406. Enforced Prerequisite: None. (3 credits) Fundamental tools and discoveries of high-energy density physics, where pressures are above a million atmospheres. Fundamental physical models, equations of state, hydrodynamics including shocks and instabilities, radiation transport, radiation hydrodynamics, experimental technique, inertial fusion, experimental astrophysics and relativistic systems.

Advisory Prerequisite: SPACE 310 or SPACE 370. (4 credits) Identify, define, and practice the way to get from a science question to a set of measurements necessary to answer the question. Phases are: 1) highlight the relevant scientific themes, 2) practice with the simulation tools available, and 3) carry out 4 hardware experiments in the lab.

Advisory and Enforced Prerequisite: None. (4 credits) A graduate level introduction to physical and aeronomical processes in the space environment. Discussion of theoretical tools, the Sun, solar wind, heliosphere, magnetosphere, ionosphere and the upper atmosphere. Spacecraft interaction with radiation, spacecraft-plasma interactions.

Advisory Prerequisite: Graduate standing. Enforced Prerequisite: None. (3 credits) General principles of magnetohydrodynamics; theory of the expanding atmosphere; properties of solar wind, interaction of solar wind with the magnetosphere of the Earth and other planets; bow shock and magnetotail, trapped particles, auroras.

Prerequisite: Senior-level statistical physics course. (3 credits) Basic plasma concepts, Boltzmann equation, higher order moments equations, MHD equations, double adiabatic theory. Plasma expansion to vacuum, transonic flows, solar wind, polar wind. Collisionless shocks, propagating and planetary shocks. Fokker-Planck equation, quasilinear theory, velocity diffusion, cosmic ray transport, shock acceleration. Spacecraft charging, mass loading.

Advisory Prerequisite: SPACE 574 and PHYSICS 505 or equivalent. Enforced Prerequisite: None. (3 credits) A complete description of the physical processes that govern the behavior of the Sun and the heliosphere with emphasis on recent theoretical and observational results.

Prerequisite: Senior undergraduate or graduate standing. (4 credits) Basic principles and hands-on experience with semiconductor micro/nano-fabrication technologies. Students will perform computer simulations of fabrication steps, and will practice some of the key processing steps used in fabricating different devices in modern IC manufacturing. Students will test and/or analyze electrical properties of various devices and compare results to theory.

Prerequisite: EECS 311 or EECS 312 or EECS 414 or graduate standing. (4 credits) Development of a complete integrated microsystem, from functional definition to final test. MEMS-based transducer design and electrical, mechanical and thermal limits. Design of MOS interface circuits. MEMS and MOS chip fabrication. Mask making, pattern transfer, oxidation, ion implantation and metallization. Packaging and testing challenges. Students work in interdisciplinary teams. Projects are overseen/graded by faculty and may also involve mentoring by representatives from external organizations.

Prerequisite: ECE 517, permission of instructor, or graduate standing. (3 credits) Focuses on the plasma chemistry and plasma-surface interactions occurring in low temperature plasmas as used in, for example, materials processing, chemical conversion, biotechnology, environmental remediation, and photon sources. Emphasis is on the atomic and molecular processes that produce chemically reactive species by electron and ion-molecule collisions, neutral-neutral reactions; and reactions with inorganic, organic and liquid surfaces. Plasma-surface interactions will be addressed that result in deposition, etching and sputtering. Radiation transport producing photoionization and photodissociation, and trapping will be discussed.

Advisory Prerequisite: (PHYSICS 240 or PHYSICS 260) and (MATH 216 or MATH 286 or MATH 296). Enforced Prerequisite: None. (3 credits) Addresses the science and technology of low temperature, partially ionized, non-equilibrium plasmas as used for materials processing, biotechnology/medicine, environment/energy, lasers, displays and lighting. The course topics include the fundamentals of electron-atom/molecule collisions, electron and ion transport; and electrostatic, magnetostatic and electromagnetic interactions with plasmas. Fundamental aspects of the kinetics of plasmas, electron energy distributions and diagnostics are addressed. Applications of these fundamentals to electrical discharges and plasma sources are discussed.

Prerequisite: EECS 421 and EECS 423. (3 credits) Theoretical analysis of the chemistry and physics of process technologies used in micro-electronics fabrication. Topics include: semiconductor growth, material characterization, lithography tools, photo-resist models, thin film deposition, chemical etching, plasma etching, electrical contact formation, micro-structure processing and process modeling.

Prerequisites: senior or graduate standing. I (3 credits) Application of lasers in materials processing and manufacturing. Laser principles and optics. Fundamental concepts of laser/material interaction. Laser welding, cutting, surface modification, forming, and rapid prototyping. Modeling of processes, microstructure and mechanical properties of processed materials. Transport phenomena. Process monitoring.

Prerequisite: NERS 312. (4 credits) Applications of radiation interaction with matter using various forms (neutrons, ions, electrons, photons) of radiation, including activation analysis, neutron radiography, nuclear reaction analysis, Rutherford backscattering analysis, proton-induced x-ray emission, plasma-solid interactions and wave-solid interactions. Lectures and laboratory.

Prerequisite: preceded or accompanied by Physics 240 or 260. (3 credits) Single particle orbits in electric and magnetic fields, moments of Boltzmann equation and introduction to fluid theory. Wave phenomena in plasmas. Diffusion of plasma in electric and magnetic fields. Analysis of laboratory plasmas and magnetic confinement devices and applications, including fusion. Introduction to plasma kinetic theory.

Prerequisite: NERS 471. (3 credits) Study of technological topics relevant to the engineering feasibility of fusion reactors as power sources. Basic magnetic fusion and inertial fusion reactor design. Problems of plasma confinement. Energy and particle balances in fusion reactors, neutronics and tritium breeding, and environmental aspects. Engineering considerations for ITER and NIF.

Prerequisite: NERS 471 or Physics 405. (3 credits) Single particle motion, collision and transport; plasma stability from orbital considerations; Vlasov and Liouville equations; Landau damping; kinetic modes and their reconstruction from fluid description; electrostatic and electromagnetic waves, cutoff and resonance.

Prerequisite: NERS 571. (3 credits) Waves in non-uniform plasmas, magnetic shear; absorption, reflection and tunneling gradient-driven micro-instabilities; BGK mode and nonlinear Landau damping; macroscopic instabilities and their stabilization; non-ideal MHD effects.

Prerequisite: NERS 471 or graduate standing. (3 credits) This course covers the theory and application of plasma concepts relevant to plasma engineering problems encountered in the workplace. Focus areas addressed include plasma propulsion, semiconductor processing, lighting, and environmental mitigation. Students will accumulate over the term a toolbox of concepts and techniques directly applicable to real world situations.

Prerequisite: NERS 471 or 571. Minimum grade of a “B” required for enforced prerequisites. (3 credits) An introduction to plasma simulation techniques, including fluid and Vlasov descriptions. Stability analysis. Finite difference and volume methods. The particle-in-cell method. Boundary conditions. Field solvers. Students will develop an understanding in the relationship between the hierarchy of kinetic models describing plasmas and their numerical equivalents. A series of short projects will demonstrate numerical modeling of plasma phenomena.

Prerequisite: preceded or accompanied by a course covering electromagnetism. (4 credits) Laboratory techniques for plasma ionization and diagnosis relevant to plasma processing, propulsion, vacuum electronics, and fusion. Plasma generation techniques includes: high voltage-DC, radio frequency, and e-beam discharges. Diagnostics include: Langmuir probes, microwave cavity perturbation, microwave interferometry, laser schlieren and optical emission spectroscopy. Plasma parameters measured are: electron/ion density and electron temperature.

Prerequisite: Physics 240 or 260; or EECS 230. (3 credits) Principles of electrostatic and electrodynamic charged particle accelerators, magnetic and electrostatic focusing, transient analysis of pulsed accelerators. Generation of intense electron and ion beams. Dynamics, stability, and beam transport in vacuum, neutral and ionized gases. Intense beams as drivers of coherent radiation generation. Novel accelerations using plasma and dielectric materials.

Prerequisite: introductory courses in plasma and quantum mechanics. (3 credits) Basic theory of atomic and molecular spectroscopy and its application to plasma diagnostics. Atomic structure and resulting spectra, electronic (including vibrational and rotational) structure of molecules and the resulting spectra, the absorption and emission of radiation and the shape and width of spectral lines. Use of atomic and molecular spectra as a means of diagnosing temperatures, densities and the chemistry of plasmas.

Advisory Prerequisite: (PHYSICS 240 or PHYSICS 260) and (MATH 216 or MATH 286 or MATH 296). Enforced Prerequisite: None. (3 credits) Addresses the science and technology of low temperature, partially ionized, non-equilibrium plasmas as used for materials processing, biotechnology/medicine, environment/energy, lasers, displays and lighting. The course topics include the fundamentals of electron-atom/molecule collisions, electron and ion transport; and electrostatic, magnetostatic and electromagnetic interactions with plasmas. Fundamental aspects of the kinetics of plasmas, electron energy distributions and diagnostics are addressed. Applications of these fundamentals to electrical discharges and plasma sources are discussed.

Prerequisite: NERS 572 advised. (3 credits) Study of the equilibrium, stability and transport of plasma in controlled fusion devices. Topics include MHD equilibrium for circular and non-circular cross section plasmas; magneto-hydrodynamic and micro-instabilities; classical and anomalous diffusion of particles and energy and scaling laws.

Prerequisite: None. Advisory Prerequisite: MATH 450, PHYSICS 405 & PHYSICS 406. (3 credits) Fundamental tools and discoveries of high-energy density physics, where pressures are above a million atmospheres. Fundamental physical models, equations of state, hydrodynamics including shocks and instabilities, radiation transport, radiation hydrodynamics, experimental technique, inertial fusion, experimental astrophysics and relativistic systems.

Prerequisite: NERS 471 or Physics 405. (3 credits) Collective interactions between electrons and surrounding structure studied. Emphasis given to generation of high power coherent microwave and millimeter waves. Devices include: cyclotron resonance maser, free electron laser, peniotron, orbitron, relativistic klystron and crossed-field geometry. Interactions between electron beam and wakefields analyzed.

Prerequisite: NERS 471, NERS 571 or permission of instructor. (3 credits) Coupling of intense electromagnetic radiation to electrons and collective modes in time-dependent and equilibrium plasmas, ranging from underdense to solid-density. Theory, numerical models and experiments in laser fusion, x-ray lasers, novel electron accelerators and nonlinear optics.

Prerequisite: ECE 517, permission of instructor, or graduate standing. (3 credits) Focuses on the plasma chemistry and plasma-surface interactions occurring in low temperature plasmas as used in, for example, materials processing, chemical conversion, biotechnology, environmental remediation, and photon sources. Emphasis is on the atomic and molecular processes that produce chemically reactive species by electron and ion-molecule collisions, neutral-neutral reactions; and reactions with inorganic, organic and liquid surfaces. Plasma-surface interactions will be addressed that result in deposition, etching and sputtering. Radiation transport producing photoionization and photodissociation, and trapping will be discussed.

Advisory Prerequisite: AEROSP 325 or preceded or accompanied by MECHENG 520. Enforced Prerequisite: None. (3 credits) Physical and mathematical foundations of computational fluid mechanics with emphasis on applications. Solution methods for model equations and the Euler and the Navier-Stokes equations. The finite volume formulation of the equations. Classification of partial differential equations and solution techniques. Truncation errors, stability, conservation, and monotonicity.

Advisory Prerequisite: Permission of instructor. Enforced Prerequisite: None. (3 credits) Analysis of basic gas properties at the molecular level. Kinetic theory: molecular collisions, the Boltzmann equation. Maxwellian distribution function. Quantum mechanics: the Schrodinger equation, quantum energy states for translation, rotation, vibration, and electronic models of atoms and molecules. Statistical mechanics: the Boltzmann relation, the Boltzmann energy distribution, partition functions. These ideas are combined for the analysis of a chemically reacting gas at the molecular level.

Advisory Prerequisite: AEROSP 225. Enforced Prerequisite: None. (3 credits) This course covers the fundamentals of combustion systems and fire and explosion phenomena. Topics covered include thermochemistry, chemical kinetics, laminar flame propagation, detonations and explosions, flammability and ignition, spray combustion and the use of computer techniques in combustion problems.

Advisory and Enforced Prerequisite: None. (3 credits) An introduction to the science of space and space exploration. Topics covered include history of spaceflight, rockets, orbits, the space environment, satellites, remote sensing and the future human presence in space. The mathematics will be at the level of algebra and trigonometry.

Advisory Prerequisite: CHEM 130, MATH 216. Enforced Prerequisite: None. (4 credits) Thermochemistry, photochemistry and chemical kinetics of the atmosphere; geochemical cycles, generation of atmospheric layers and effects of pollutants are discussed.

Advisory Prerequisite: Graduate standing. Enforced Prerequisite: None. (4 credits) Solar system formation; giant planets and origin of their atmospheres; biogeochemical evolution of terrestrial planet atmospheres; radiative transfer, internal energy and thermal structure; thermochemical cloud formation; radiative and charged particle energetic processes for neutrals and ions; origin of satellite atmospheres; extrasolar planets; life in the universe; planetary exploration.

Advisory Prerequisite: CHEM 461 or CLIMATE 479 or permission of instructor. Enforced Prerequisite: None. (3 credits) A general course in chemical kinetics, useful for any branch of chemistry where reaction rates and mechanisms are important. Scope of subject matter: practical analysis of chemical reaction rates and mechanisms, theoretical concepts relating to gas and solution phase reactions.

Advisory Prerequisites: Calculus and Physics at the high school or university level are strongly recommended. Students should expect a level of math equivalent to MATH 115 (Calculus I). (4 credits; NS, BS, QR/1) Discover the extraordinary nature of astronomy, e.g. stars, black holes, galaxies, dark matter, and the universe. This course uncovers the astrophysics behind the most important and common astronomical phenomena in our universe. A major topic is stars and their lives, which can end violently through supernova explosions, leaving behind black holes or neutron stars. This is followed by the study of the Milky Way and its content, other galaxies, and how unseen "dark" matter shapes the universe we see today. We conclude with the origin of the universe and the limitations of looking back in time. Three lectures and two hours of laboratory work weekly; The course requires after-dark observing with telescopes on Angel Hall at least once during the semester, at a time TBD based on weather conditions.

Enforced Prerequisites: MATH 215, 255 or 285, and prior or concurrent enrollment in PHYSICS 340 or PHYSICS 360, or graduate standing. Advisory Prerequisites: MATH 216, 256 or 286 and ASTRO 201. (3 credits; BS) This course examines the appearance, structure, and evolution of stars. We examine the basic physical processes that cause stars to have their observed structures; a study of the energy generation through nucleosynthesis; the basic physical laws that lead to the structure of stars; the transfer of radiation through the outer parts of the star; how spectroscopic information informs us as to the composition and motion of stars; and an in-depth look at the late stages of stellar evolution and stellar death.

Prerequisite: EECS 330 (“C” or better) or graduate standing. (4 credits) Fundamentals of electromagnetic radiation and propagation (near earth, troposphere, ionosphere, indoor and urban); antenna parameters; practical antennas; link analysis; system noise; fading and multipath interference; applications. Course includes informative labs and a team project in practical wireless system design. Projects are overseen/graded by faculty and may also involve mentoring by representatives from external organizations.

Prerequisite: EECS 330. (3 credits) Introduction to numerical methods in electromagnetics including finite difference, finite element and integral equation methods for static, harmonic and time dependent fields; use of commercial software for analysis and design purposes; applications to open and shielded transmission lines, antennas, cavity resonances and scattering.

Prerequisite: EECS 330 or Physics 438. (3 credits) Maxwell's equations, constitutive relations and boundary conditions. Potentials and the representation of electromagnetic fields. Uniqueness, duality, equivalence, reciprocity and Babinet's theorems. Plane, cylindrical, and spherical waves. Waveguides and elementary antennas. The limiting case of electro- and magneto-statics.

Prerequisite: ECE 537 and ECE 538 and Graduate Standing. (3 credits) Complete study of laser operation: the atom-field interaction; homogeneous and inhomogeneous broadening mechanisms; atomic rate equations; gain and saturation; laser oscillation; laser resonators, modes, and cavity equations; cavity modes; laser dynamics, Q-switching and modelocking. Special topics such as femto-seconds lasers and ultrahigh power lasers.

Prerequisite: EECS 281 and graduate standing. (4 credits) The development of programs for parallel computers. Basic concepts such as speedup, load balancing, latency, system taxonomies. Design of algorithms for idealized models. Programming on parallel systems such as shared or distributed memory machines, networks. Grid Computing. Performance analysis. Course includes a substantial term project.

Prerequisite: EECS 530. (3 credits) Numerical techniques for antennas and scattering; integral representation: solutions of integral equations: method of moments, Galerkin's technique, conjugate gradient FFT; finite element methods for 2-D and 3-D simulations; hybrid finite element/boundary integral methods; applications: wire, patch and planar arrays; scattering composite structures.

Prerequisite: MATH 214, 217, 417, 419, or 420; and one of MATH 450, 451, or 454 (3 credits) Numerical linear algebra is at the core of much of scientific computing, and is a fundamental skill for anyone with any interest in numerical/computational mathematics; the course is a core course for the AIM program. We will cover robust, accurate, and efficient methods for finding (1) solutions of linear systems of equations, (2) eigenvalues and eigenvectors of matrices, and (3) solution of least squares problems. These standard problems arise in all venues of science and engineering.

Topics will include: (1) Orthogonal matrices, vector and matrix norms, singular value decomposition (SVD). (2) QR factorization, Householder triangularization, least squares problems. (3) Stability: Condition numbers, floating point arithmetic, backward error analysis. (4) Direct methods: Gaussian elimination, pivoting, LU and Cholesky factorizations. (5) Eigenvalues and eigenvectors: Reduction to Hessenberg or tridiagonal form, Rayleigh quotient, inverse iteration, the QR algorithm, computing the SVD. (6) Iterativ e methods: Classical methods (Jacobi, Gauss-Seidel, SOR), Krylov subspace methods, conjugate gradients, Arnoldi iteration, GMRES, preconditioning

Prerequisite: MATH 214, 217, 417, 419, or 420; and one of MATH 450, 451, or 454 (3 credits) Computer simulation is routinely used in science and engineering, and increasingly also in other fields such as finance and medicine. Accurate and efficient computer simulations can be challenging; using a faster computer is no guarantee of success; sometimes a better algorithm is needed. Math 572 is an introduction to numerical methods for differential equations. The course focuses on finite-difference schemes for initial value problems involving ordinary and partial differential equations. Theory and practical computing issues will be covered

Prerequisite: AEROSP 325 or preceded or accompanied by MECHENG 520. (3 credits) Physical and mathematical foundations of computational fluid mechanics with emphasis on applications. Solution methods for model equations and the Euler and the Navier-Stokes equations. The finite volume formulation of the equations. Classification of partial differential equations and solution techniques. Truncation errors, stability, conservation and monotonicity. Computer projects and homework.

Prerequisite: NERS 511. (3 credits) Classical and quantum-mechanical analysis of the processes by which radiation interacts with matter. Review of nuclear structure and properties. Nuclear models. Nuclei as sources of radiation. Interaction of electromagnetic radiation with matter. Interaction of charged particles with matter. Radiative collisions and theory of Bremsstrahlung. Interaction of neutrons with matter. Interaction mechanisms and cross sections are developed.

Advisory Prerequisite: MATH 371 or MATH 471. Enforced Prerequisite: ENGR 101 or 151 or EECS 183 AND MATH 216 or 256 or 286; or Graduate Status. Minimum grade of “C” required for enforced prerequisite. (4 credits) Designed for graduate students developing the methods and using the tools of scientific computing. Students learn how to use HPC clusters, and utilize community tools and software engineering best practices to develop their own codes. Students are expected to have had some introduction to programming, linear algebra, and differential equations.

Advisory pre-requisite: PHYSICS 340 or 360 and 351 and one of MATH 216, 256, 286, or 316. (3 credits) This course provides a rigorous introduction to electricity and magnetism, suitable for junior year physics majors or engineering students. Subjects include static electric fields in vacuum, in matter and in vacuum and matter. Also includes time-dependent phenomena, electromagnetic induction and Maxwell's equations.

Advisory pre-requisite: PHYSICS 340 or PHYSICS 360 and PHYSICS 351 (3 credits) Introduction to thermal processes including the classical laws of thermodynamics and their statistical foundations: basic probability concepts; statistical description of systems of particles; thermal interaction; microscopic basis of macroscopic concepts such as temperature and entropy; the laws of thermodynamics; and the elementary kinetic theory of transport processes.

Advisory pre-requisite: Graduate Standing. (3 credits) Electrostatics, magnetostatics, quasi-static fields, electromagnetic waves.

Advisory pre-requisite: PHYSICS 505 or equivalent (3 credits) Scattering and diffraction, wave guides, radiation theory, covariant formulation of electrodynamics.

Advisory pre-requisite: PHYSICS 505 or equivalent (3 credits) Review of thermodynamics. Statistical basis of the second law of thermodynamics, entropy and irreversibility, equipartition, the Gibbs paradox. Quantum statistics, ideal Fermi gas, ideal Bose-Einstein condensation, phase equilibrium, phase transitions, fluctuations, and transport theory.