Prerequisite: preceded by AEROSP 225 and MATH 216. I, II (4 credits) Airbreathing propulsion, rocket propulsion and an introduction to modern advanced propulsion concepts. Includes thermodynamic cycles as related to propulsion and the chemistry and thermodynamics of combustion. Students analyze turbojets, turbofans and other air-breathing propulsion systems. Introduces liquid- and solid-propellant rockets and advanced propulsion concepts such as Hall thrusters and pulsed plasma thrusters. Students also learn about the environmental impact of propulsion systems and work in teams to design a jet engine.

# Graduate Certificate in Plasma Science and Engineering

MIPSE is administering the graduate certificate in Plasma Science and Engineering (PSE). The graduate certificate provides an opportunity for students conducting research in the fundamentals or applications of PSE to both broaden and deepen that experience. The components of the graduate program include:

- Coursework in the fundamentals and applications of PSE:
- Plasma courses
- Supporting courses
- Download a list of courses (PDF)

- Participation in the MIPSE Graduate Research Symposium.
- Research on a topic related to PSE.
- Opportunity to use internship experiences for laboratory credit.

#### Information for students interested in pursuing the graduate certificate in PSE

### Plasma Courses

#### Aerospace Engineering

Prerequisite: AEROSP 335, senior standing. I (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.

#### Climate and Space Sciences and Engineering

Prerequisite: MATH 216, Physics 240. (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.

Prerequisite: MATH 216. (4 credits) The fundamentals of electricity, magnetism and electrodynamics in the context of the Earth. The first segment will cover electrostatics, the electric structure and circuit of the Earth, electricity in clouds and lightning. The second segment will cover magnetostatics, currents, the magnetic field and magnetic dynamo of the Earth, and the Earth's magnetosphere. The third segment will cover electrodynamics, electromagnetic waves, radiation in the Earth environment, waveguides and radiation from sources.

Prerequisite: SPACE 370. (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.

Prerequisite: MATH 450, Physics 405 & Physics 406. (3 credits) Introduces students to fundamental tools and discoveries of high-energy density physics, where pressures are above a million atmospheres. Discusses 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: Senior or graduate standing. (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.

Prerequisite: Graduate standing. (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.

Prerequisite: SPACE 574 & Physics 505 or equivalent. (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.

#### Electrical Engineering and Computer Science

Prerequisite: EECS 320 or graduate standing. (4 credits) Semiconductor material and device fabrication and evaluation: diodes, bipolar and field-effect transistors, passive components. Semiconductor processing techniques: oxidation, diffusion, deposition, etching, photolithography. Lecture and laboratory. Projects to design and simulate device fabrication sequence.

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.

Prerequisite: EECS 330. (3 credits) Plasma physics applied to electrical gas discharges used for material processing. Gas kinetics; atomic collisions; transport coefficients; drift and diffusion; sheaths; Boltzmann distribution function calculation; plasma simulation; plasma diagnostics by particle probes, spectroscopy and electromagnetic waves; analysis of commonly used plasma tools for materials processing.

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.

Prerequisite: EECS 537 or permission of instructor.

Prerequisite: permission of instructor.

#### Mechanical Engineering

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.

#### Nuclear Engineering and Radiological Sciences

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 equivalent. (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. 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 320 or MATH 454, NERS 471, NERS 571 or an electricity and magnetism course. (3 credits) Develop understanding in the relationship between the hierarchy of kinetic models describing plasmas and numerical equivalents. Short projects will develop simple codes and demonstrate numerical modeling of plasma phenomena. Students will develop their own projects involving original numerical research with a final report in a style appropriate for an academic journal.

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 EECS 331. (3 credits) Principles and technology of electrostatic and electrodynamic 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 for inertial confinement and for high power coherent radiation.

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.

Prerequisites: EECS 330. (3 credits) Plasma physics applied to electrical gas discharges used for material processing. Gas kinetics; atomic collisions; transport coefficients; drift and diffusion; sheaths; Boltzmann distribution function calculation; plasma simulation; plasma diagnostics by particle probes, spectroscopy, and electromagnetic waves; analysis of commonly used plasma tools for materials processing.

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: 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.

### Supporting Courses

#### Aerospace Engineering

Prerequisite: permission of instructor. (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.

Prerequisite: AEROSP 225. (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.

#### Climate and Space Sciences and Engineering

Prerequisite: CHEM 130, MATH 216. (4 credits) Thermochemistry, photochemistry and chemical kinetics of the atmosphere; geochemical cycles, generation of atmospheric layers and effects of pollutants are discussed.

Prerequisite: CLIMATE 464. (3 credits) Physical, chemical and dynamical properties of the atmosphere between the tropopause and the turbopause. Among the topics covered are the heat and radiation budgets, atmospheric ozone, stratospheric warmings, the biennial stratospheric oscillation, airglow.

Advised prerequisite: Graduate standing. (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.

Prerequisite: CHEM 461 or CLIMATE 479 (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.

#### Astronomy

(3 credits) This course covers the assembly of stars and their protoplanetary disks from cold gas dust in the interstellar medium. Specific topics include fragmentation, disk dynamics, and jets. Radiative transfer in stellar atmospheres and envelopes, essential to interpreting observations of stars and their environs, is addressed in the second part.

#### Electrical Engineering and Computer Science

Prerequisite: EECS 330. (4 credits) Fundamentals of electromagnetic propagation and radiation; radiowave propagation in different environments (near Earth, troposphere, ionosphere, indoor and urban); antenna parameters; practical antennas; link analysis; system noise; fading and multipath interference. Course includes lectures, labs and a project in which student teams develop and implement practical wireless systems.

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: EECS 537 and EECS 538. (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.

#### Mathematics

Prerequisite: MATH 214, 217, 417, 419, or 420; and one of MATH 450, 451, or 454 (3 credits) This course is a rigorous introduction to numerical linear algebra with applications to 2-point boundary value problems and the Laplace equation in two dimensions. Both theoretical and computational aspects of the subject are discussed. Some of the homework problems require computer programming. Students should have a strong background in linear algebra and calculus, and some programming experience. This course is a core course for the Applied and Interdisciplinary Mathematics (AIM) graduate program. Content: The topics covered usually include direct and iterative methods for solving systems of linear equations: Gaussian elimination, Cholesky decomposition, Jacobi iteration, Gauss-Seidel iteration, the SOR method, an introduction to the multigrid method, conjugate gradient method; finite element and difference discretizations of boundary value problems for the Poisson equation in one and two dimensions; numerical methods for computing eigenvalues and eigenvectors.

Prerequisite: MATH 214, 217, 417, 419, or 420; and one of MATH 450, 451, or 454 (3 credits) This is one of the basic courses for students beginning study towards the Ph.D. degree in mathematics. Graduate students from engineering and science departments and strong undergraduates are also welcome. The course is an introduction to numerical methods for solving ordinary differential equations and hyperbolic and parabolic partial differential equations. Fundamental concepts and methods of analysis are emphasized. Students should have a strong background in linear algebra and analysis, and some experience with computer programming. This course is a core course for the Applied and Interdisciplinary Mathematics (AIM) graduate program. Content: Content varies somewhat with the instructor. Numerical methods for ordinary differential equations; Lax's equivalence theorem; finite difference and spectral methods for linear time dependent PDEs: diffusion equations, scalar first order hyperbolic equations, symmetric hyberbolic systems.

#### Materials Science and Engineering

Prerequisites: MATSCIE 330 and MATSCIE 335. (3 credits) The design of production and refining systems for engineering materials. Design of problems for the extraction and refining of metals, production and processing of ceramics, polymeric materials and electronic materials. Written and oral presentation of solutions to processing design problems.

#### Mechanical Engineering

(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.

#### Physics

PHYSICS 340 or 360, and one of: MATH 216, 256, 286, 296 or 316; or graduate standing (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.

PHYSICS 390 or graduate standing (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.

(3 credits) Electrostatics, magnetostatics, quasi-static fields, electromagnetic waves.

(3 credits) Scattering and diffraction, wave guides, radiation theory, covariant formulation of electrodynamics.

(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.