Graduate Programs and Preliminary Exams

Major Fields of Study

Minor Fields of Study

Applied Mathematics (syllabus)

A student who  elects Applied Mathematics as a minor field wm be held responsible for the body of knowledge contained in a coherent croup or courses to be approved in advance by the Field Committee. The program must comprise at least 12 quarter units in J1ldulte work. Committee approval or any proposed course work group will depend on such factors as the student’s major field interests, and the breadth of his or her prior mathematical course work record.

A student may satisfy the filed requirements by examination or achieving satisfactory grades in a group of courses selected as follows:

1. One course from the following list (offered by SEAS):

EE M208A/MAE M291A, EE
M208B/MAE M291B, EE 208C, MAE 291C

2. Any two additional courses from 1, or Graduate courses offered by the Mathematics Department

Students formally enrolled in an approved program of courses u outlined above, and who achieve grades or B or better in all courses, and at least one A, will be deemed to have completed the minor field requirement.

A transfer student may petition the Field Committee for permission to list one course taken at another institution in his or her approved
course group, provided the course was taken by the student in graduate status.

Examination for the Minor Field

See General Information Bulletin. EGS.32.

Syllabus for the Minor Field

I. 
Prerequisite Material
(see “Outline of Normal Prerequisite Coverage” below).

           
II.     
Topics in Applied Mathematics
corresponding to approved selections u described
in “Minimum Preparation” above.

Outline of Normal Prerequisite Coverage       
I.     
Linear Algebra

Fundamentals or linear
algebra (including finite-dimensional vector space, linear transformations,
matrices) as covered in contemporary Sophomore level calculus
sequences (Mathematics 12A or 13BC).

           
II.     
Differential Equations

Ordinary differential equations
and applications (vibrations, circuits, etc.), including transform methods
of solutions for linear systems; some basic partial differential equations
of engineering interest and simple boundary value problems, as covered
in Junior and Senior level courses in Mathematics (presently 140 series
of courses and in Engineering Mathematics 191A, 192 series).

         
III.     
Vector Calculus

Scalar and vector fields,
gradient, divergence, curl, line integrals, surface integrals, integral
theorems (as covered in Sophomore-level calculus sequences and undergraduate
core-curriculum Engineering& courses, including E81ineerin&
1008).

          
IV.     
Functions of a Complex
Variable

Analytic functions, series
expansions, contour integrals, conformal mapping covered in part in
Mathematics and Engineering courses in the undergraduate core-curriculum,
and in Mathematics 132 (Introduction to Complex Analysis), and Engineering
191A.

            
V.     
Advanced Calculus (Introductory
Real Analysis)

Functions, limits, derivatives,
integrals, etc., emphasizing the axiomatic approach with complete proofs
of theorems; e.g. Mathematics 131 (Analysis) or the equivalent.

References

Textbooks
currently used in pertinent undergraduate Engineering and Mathematics
courses.

Applied Plasma Physics (syllabus)

Applied Plasma Physics and Fusion Engineering

The field of Applied Plasma Physics and Fusion Engineering, as partial preparation for the degree of Doctor of Philosophy in Engineering, covers the subject matter described below.

Minimum Preparation for Major Field Students Examination

The Major Field Examination is an eight hour examination covering material from the syllabus. Part of the examination will cover material in the core; all students are responsible for this pan. The remainder of the examination will cover material from the elective sections of the syllabus.
In advance of the examination, each student shall inform his adviser of the core elective topics on which he wishes to be tested.

Syllabus for the Major Field Core Topics

I.       
Fundamentals of plasma
physics (MAE M185)

A.      
Particle motion in
electromagnetic field; adiabatic invariants

B.      
Fluid equations and
diamagnetic drifts

C.      
Debye shielding; plasma
sheaths

D.      
Maxwell’s equations
in the plasma; the equivalent dielectric tensor

E.      
Electrostatic and electromagnetic
plasma waves at principal angles to a magnetic field; cutoffs and resonances

F.      
Diffusion in partially
ionized gases

G.      
Resistivity and diffusion
in fully ionized gases; In A. factor; magnetic viscosity

H.      
Magnetohydrodynamic
{MHD) theory

1.      
Single-fluid equations

2.      
Hydromagnetic equilibrium
in confinement geometries

3.      
Basic types of instabilities

I.       
Kinetic theory; Vlasov
equation and Landau damping

J.       
Anomalous transport
processes K. Basic diagnostic techniques

II.     
Fundamentals of fusion
engineering (MAE 137)

A.      
Fusion reactions and
fuel cycles; thermonuclear conditions; Lawson and ignition criteria

B.      
Magnetic mirror confinement:
tandem mirrors, energy and particle flows, power balance

C.      
Toroidal magnetic confinement:
tokamak, stellarator, reversed-field pinch

D.      
Start-up and burning-plasma
analysis

E.      
Inertial confinement
laser and particle beam drivers; concepts of compression, central ignition,
and burn-wave propagation

F.      
Fusion blanket design
and nuclear analysis; tritium breeding: induced radioactivity

G.      
Fission-fusion hybrids

H.      
Tritium: inventor,
methods of recovery

I.       
Magnets: superconductivity;
structural design

J.       
Radiation damage to
materials: influence on design

K.      
Designs of fusion reactors

Elective Topics

III.   
Linear waves in uniform
plasmas (EE28SA)

A.      
Waves in cold and warm
plasmas: CMA diagram; phase velocity surfaces; polarization and particle
orbits; Fredericks and Stringer diagrams for low-frequency
waves

B.      
Electromagnetic waves:
ordinary and extraordinary waves, Appleton-Hartree formula, microwave
diagnostics. Alfven waves whistlers, e.m., cyclotron waves

C.      
Electrostatic waves:
Bohm-Gross waves, ion acoustic waves. two-ion hybrid waves, e.g. cyclotron
waves

D.      
Wave packets and group
velocity in anisotropic media; resonance cones

E.      
Waves in hot plasmas:
Bernstein modes. cyclotron harmonics, Landau and cyclotron damping

F.      
Damping and excitation
of waves: resistivity. viscosity, neutral collisions, resonant particles;
grids, coils

G.      
Waves in bounded plasmas;
Trivelpiece-Gould modes

H.      
Accessibility and tunneling

I.       
R. F. heating of plasmas

J.       
Tonks-Dattner resonances

IV.    
Waves and instabilities
in non-uniform plasmas (EE28SB)

A.      
Beam-plasma interactions;
convective and absolute instabilities

B.      
Streaming instabilities;
Penrose criterion; current-driven instabilities

C.      
Energy and momentum
of waves; positive and negative energy waves

D.      
Drift waves and universal
instabilities

E.      
Kelvin-Helmholtz instabilities

F.      
Instabilities in partially
ionized gases (Simon-Hoh. Kadomtsev-Nedospasov)

G.      
Wave propagation in
inhomogeneous plasmas: Budden tunneling, resonance absorption

H.      
Ponderomotive force.
optical mixing, parametric decay and OTS, stimulated Brillouin and Raman
scattering, filamentation, two-plasmon decay; saturation mechanisms

I.       
Nonlinear waves; Kortweg-deVries
and nonlinear Schrödinger equations; shock waves, solitons

J.       
Quasilinear diffusion

V.      
Magnetic confinement
of plasmas (EE286’MAE237 A)

A.      
MHD equilibrium: simple
axisymmetric configurations, virial theorem, force-free fields, rotational
transform and toroidal equilibrium; Grad-Shafranov equation

B.      
MHD stability: energy
principle. interchange and kink instabilities, Suydam criterion, Kroskal
limit, shear, and min-B stabilization. finite Larmor radius stabilization

C.      
Microinstabilities:
drift, ballooning, tearing, and trapped particle modes

D.      
Toroidal confinement

1.      
Tokamaks: banana orbits,
q and Q, islands, sawteeth, Mirnov oscillations, disruptions, impurity
diffusion, runaway electrons, Alcator and Murakami scaling, elongated
cross sections, flux conservation, profile consistency

2.      
Neoclassical and Pfirsch-Schlüter
diffusion

3.      
Convective and poloidal
Bohm diffusion

4.      
Minimum-B devices:
multipoles, spherators, levitrons

E.      
Mirror confinement

1.      
Ioffe bars, min-K principle

2.      
Velocity space diffusion
and electron drag

3.      
The DCLC instability
and its control

4.      
Tandem mirrors, axisymmetric
plugs, thermal barriers

5.      
Field reversal; compact
torus

F.      
Plasma heating; ohmic
heating, neutral beam injection, rf heating and current drive, magnetic
pumping

VI.    
Plasma diagnostics
(Phys. 180E. EE282B. EE289S)

A.      
Faraday rotation, microwave
interferometry and scattering

B.      
Langmuir probes

C.      
Neutral and ion beam
probes

D.      
Magnetic probes, Rogowski
coils. diamagnetic loops

E.      
Optical and uv spectroscopy

F.      
Soft x-ray diagnostics

G.      
Synchrotron radiation

H.      
Particle detectors
and velocity analyzers

I.       
Laser diagnostics:
Thomson scattering and holography in the far-IR, IR, and visible

VII.  
Fusion plasma physics
and analysis (MAE237B/EE287)

A.      
Plasma energy and particle
balance

B.      
Radiation processes:
bremsstrahlung, synchrotron and recombination radiation

C.      
Atomic processes in
plasmas; impurities

D.      
Fokker-Planck equation;
equilibrium and slowing down rates

E.      
Plasma heating; neutral
beam injection

F.      
Plasma burn modes;
burn kinetics and thermal stability; Q calculation of driven plama reactors

G.      
Mirror reactor physics;
tandem mirror burn dynamics

H.      
Tokamak reactor physics;
β limits, transport, start-up and burn dynamics

VIII.
Plasma engineering and technology (MAE237B/EE287,
MAE237C/EE288)

A.      
Plasma-surface interactions

B.      
Physics and technology
of limiters, divertors, and direct converters

C.      
Plasma fueling

D.      
Technology of plasma
heating: neutral beams. rf. lasers, pulsed power, heavy ion accelerators

IX.
Fusion engineering and reactor design (MAE237C/EE288)

A.      
Fusion reactor concepts
and designs)

B.      
Neutronics: nuclear
responses, nuclear heating, radioactivity

C.      
Fuel cycle: function,
description, analysis

D.      
Blanket function and
design

E.      
Self-cooled liquid
metal blankets

F.      
Solid breeder blankets

G.      
In-vessel components;
first wall, limiter, divertor

H.      
Radiation shielding:
design and analysis

I.       
Magnet systems: normal
and superconducting magnet design, cryogenic stability, radiation effects

X.      
Nuclear fuel element
behavior (MAE236A)

A.      
Fuel swelling due to
fission gases

B.      
Pore migration and
fuel restructuring kinetics

C.      
Fission gas release

D.      
Mechanical properties
of fuel materials

E.      
Structural behavior
of fuel elements and assemblies

XI.    
Radiation damage in
reactor materials (MAE236B)

A.      
Ion transport in solids

B.      
Theory of collision
cascades

C.      
Ion ranges

D.      
Damage and ion distributions

E.      
Backscattering and
reflection

F.      
Sputtering and blistering

G.      
Displacement damage

H.      
Microstructure evolution
and kinetic behavior

I.       
Relationship to mechanical
properties

J.       
Embrittlement, swelling,
irradiation creep

XII.  
Nuclear reactor theory
(MAE235A)

A.      
Physics and mathematics
of fission reactor core design

B.      
Diffusion theory

C.      
Reactor kinetics

D.      
Slowing down and thermalization

E.      
Multigroup method

F.      
Cell calculations for
heterogeneous core lattices

XIII.
Kinetic theory of plasmas and particle
transport (MAE235B)

A.      
Transport phenomena

B.      
Liouville equation,
Boltzmann collision integral and H-theorem

C.      
Fokker-Planck, neutron
and radiation transport equations

D.      
Fluid moment equations

E.      
Dispersion relations

F.      
Space and time relaxation
phenomena

XIV. 
Reactor thermal hydraulic design (MAE136)

A.      
Thermal hydraulic design
of various nuclear power reactor concepts

B.      
Power cycles

C.      
Power generation and
heat removal

D.      
Thermal and hydraulic
and component design

E.      
Overall plant design

F.      
Startup, steady-state,
and transient operation

XV.   
Convective heat transfer
(MAE231A)

A.      
Conservation equations
for mass, momentum, and energy

B.      
Similarity in forced
and free convection

C.      
Laminar boundary layer
equations

D.      
Similarity solutions
for constant property two-dimensional boundary layer

E.      
Laminar flow in ducts

F.      
Transport in turbulent
flows

G.      
Turbulent forced convection
external boundary layers

H.      
Turbulent flow in ducts

I.       
Laminar and turbulent
free convection boundary layers

XVI. 
Numerical methods for engineering applications
(MAE192C)

A.      
Matrix algebra

B.      
Lagrange interpolation
and quadrature methods

C.      
Numerical solutions
for ordinary differential equations

1.      
Initial value problems

2.      
Boundary value problems

D.      
Numerical solutions
for partial differential equations

1.      
Parabolic

2.      
Elliptic

3.      
Hyperbolic

E.      
Integral equations

Minimum Preparation for Major Field
Students

The body of knowledge in Sections I and II, in two of Sections
III through XIII, and in two others of Sections III through XVI.

Recommended Course Preparation

Major Field

Students
selecting Applied Plasma Physics and Fusion Engineering as their major
field are responsible for the core sections I and II comprising material
contained in EE185 and MAE137. In addition to this core material, students
are to choose four elective sections from those numbered ill through
XVI. The material described in sections ill through XVI is contained
in one or more appropriate courses, as indicated in the syllabus for
each section. Those students who wish to emphasize applied plasma physics
in the Ph.D. dissertation research should select the majority of their
four electives from sections III-IX. Students wishing to emphasize fusion
engineering in their PhD. dissertation research should select the majority
of their four electives from Sections VIII-XVI. Thesis students should
be familiar with the current literature in their chosen field of research
and become acquainted with recent developments in plasma physics and
fusion engineering by attending the various seminars, colloquia. and
tutorials offered by the faculty, staff, and visitors working in the
field.

Minor Field

Students
electing Applied Plasma Physics and Fusion Engineering as a minor field
can satisfy the minor requirement by taking EE185 or MAE135D and two
courses from the following list:

EE285A, 2858, 286 (MAE237A),
Phys. 180E, 222A, MAE2378 (EE287), M237C (EE288), 236B, 235B

References

The
following books can be helpful to students emphasizing applied plasma
physics:

1.      
F. Chen, “Introduction
to Plasma Physics,” 2nd ed., Plenum, 1983. (EE185)

2.      
Schmidt, “Physics
of High Temperature Plasmas,” Academic Press, 1979. (EE286/MAE237A,
Phys. 222)

3.      
N. Krall and A. W.
Trivelpiece, “Principles of Plasma Physics,” McGraw-Hill,
1973. (Phys. 222)

4.      
T. H. Stix, “Theory
of Plasma Waves,’. McGraw-Hill, 1962. (EE285AB)

5.      
L. Spitzer, Jr., “Physics
of Fully Ionized Gases,” 2nd ed., Wiley, 1962. (EE185, 285A, EE2861MAE237
A)

6.      
V. L. Ginzburg, “The
Propagation of Electromagnetic Waves in Plasmas,” Pergamon Press,
1964. (EE2858)

7.      
R. Huddlestone and
S. Leonard, e&., “Plasma Diagnostic
Techniques,” Academic Press, 1965. (MAE2378/EE287)

8.      
K. Nishikawa and C.
S. Liu, “Parametric Instabilities in Plasma” in Advances
in Plasma Physics
, Vol. 6, ed. by A. Simon and W. B. Thompson,
Wiley-Interscience, 1976. (EE2858)

9.      
B. Milhailovsky, “Theory
of Plasma Instabilities,” Vols. 1 and 2, Consultants Bureau, 1974.

10.   
E. Keen, ed., “Plasma
Physics,” Institute of Physics, London, 1974.

11.   
E. Sindoni and C. Wharton,
eds., “Diagnostics for Fusion Experiments,” Pergamon Press,
1979.

12.   
W. Lochte-Holtgreven,
ed., “Plasma Diagnostics,” North Holland, 1968.

13.   
N. C. Luhmann, Jr.,
“Instrumentation and Techniques for Plasma Diagnostics: An Overview,”
in Infrared and Millimeter Waves, ed. by K. J. Button, Vol. II,
Academic Press, 1979.

14.   
“Review Modem
Fusion Diagnostics,” to be published in Review of Scientific Instruments

(a)    
N. C. Luhmann and W.
A. Peebles -Magnetic Confinement Diagnostics

(b)    
M. Campbell -Inertial
Confinement Diagnostics

15.   
“Nonlinear Wave
Effects in Laboratory Plasmas: A Comparison Between Theory and Experiment,”
M. Porkolab and R. P. H. Chang, Review of Mod. Phys. ~ 745 (1978).

16.   
“Waves and Microinstabilities
in Plasmas,”

(a)    
Linear Effects: J.E.
Allen and A. D. R. Phelps, Rep. Prog. Phys. 40, 1305

(b)    
Nonlinear Effects:
R. N. Franklin, Rep. Prog. Phys. 40 1369 (1977).

The
following books can be helpful to students emphasizing fusion physics
and engineering:

1.      
R. A. Gross, “Fusion
Energy,” Wiley & Sons, 1982. (MAE137)

2.      
R. W. Conn, “Magnetic
Fusion Reactors,” in ~ ed. by E. Teller, Vol. IB, pp. 193-410,
Academic Press, 1981. (MAE137)

3.      
T. J. Dolan, “Fusion
Research,” Vols. 1-3, Pergamon Press, 1982. (MAEI37)

4.      
W. M. Stacey, Jr.,
“Fusion Plasma Analysis,” Wiley, 1981. (EE286/MAE237A, MAE237B/EE287)

5.      
P. Shkarofsky, T. W.
Johnston and M. P. Bachynski, “The Particle Kinetics of Plasmas,”
Addison- Wesley, 1966. (EE287/MAE237B)

6.      
J. Duderstadt and G.
A. Moses, “Inertial Confinement Fusion,” Wiley 1982. (MAE237B/EE287)

7.      
J. Rose and M. Clark,
“Plasmas and Controlled Fusion,” M.I.T. Press, 1961. (EE286’MAE237
A, MAE237B/EE287, MAE237C/EE288)

8.      
B. Davison, “Neutron
Transport Theory,” Oxford University Press, 1958. (MAE235A)

9.      
Bell and S. Glasstone, “Nuclear Reactor
Theory,” Van Nostrand, 1970. (MAE235A)

10.   
J. J. Duderstadt and
W. R. Martin, “Transport Theory,” Wiley, 1979. (MAE235A)

11.   
Clark and K. Hans en,
“Numerical Methods of Reactor Analysis,” Academic Press, 1964.
(MAE235C)

12.   
Greenspan, C. N. Kleber,
and D. Okrent, “Computing Methods in Reactor Physics,” Gordon
and Breach, 1968. (MAE235C)

13.   
R. W. Varga, “Matrix
Interactive Analysis,” Prentice-Hall, 1962). (MAE235C)

14.   
R. D. Richtmyer and
K. W. Morton, “Difference Methods for Initial-Value Problems,”
2J1d Ed., Wiley-Interscience, 1967.  (MAE235C)

15.   
D. R. Orlander, “Fundamental
Aspects of Nuclear Reactor Fuel Elements,’” Technical Information Center, Dept of Energy, 1976. (MAE136C, 236B)

16.   
Y. Y. Hsu and R. W.
Graham, “Transport Processes in Boiling and Two-Phase Systems,”
McGraw- Hill, 1976. (MAE231C)

17.   
R. T. Lahey and F.
J. Moody, “Thermal Hydraulics of Boiling Water Reactors,”
American Nuclear Society, 1977. (MAE231C)

18.   
M. EI-Wakil, “Nuclear
Power Engineering,” McGraw-Hill, 1962 (MAE136B)

19.   
W. Thompson, “Defects
and Radiation Damage in Metals,” Cambridge University Press, 1969. (MAE236B )

20.   
L. T. Chadderton, “Radiation
Damage in Crystals,” Methaen and Co., 1965. (MAE236B)

Literature: Pertinent Journals and
Serial Publications

Nuclear
Fusion

Physical
Review Letters

Applied
Physics Letters

Physics
of Fluids

Plasma
Physics and Controlled Fusion

Soviet
Journal of Plasma Physics

IEEE
Trans. on Plasma Science Journal of Fusion Energy

Nuclear
Technology

Fusion
Technology

Nuclear
Science and Engineering

Nuclear
Engineering and Design/Fusion

Journal
of Nuclear Materials

Journal
of Heat Transfer

Comments
on Plasma Physics and Controlled Fusion

Transactions
of the American Nuclear Society

Plasma
Physics and Controlled Nuclear Fusion Research:

1961, 1965, 1968, 1971,
1974, 1976, 1978, 1980, 1982, 1984

Published every other year
by the International Atomic Energy Agency, Vienna

SIAM J. of Computational Physics

J.
of Vacuum Science and Technology

Inter.
Journal of Infrared and Millimeter Waves

Review
of Scientific Instruments

MAJORS

DESIGN, ROBOTICS, AND MANUFACTURING
Rajit Gadh, Dennis Hong, Jonathan Hopkins, Xiaochun Li, Jacob Rosen (Chair), Veronica Santos
The program is developed around an integrated approach to manufacturing and mechanical product design. It includes research on material behavior (physical and mechanical) in manufacturing processes and design; design of mechanical systems (for example, power, micro-electro-mechanical systems and transportation); design methodology; automation, robotics and unmanned machinery; manufacturing and mechanical systems(reliability, safety, and optimization); CAD/CAM theory and applications; computational geometry and geometrical modeling, composite structure; beam and plasma assisted manufacturing.

FLUID MECHANICS
Jeff Eldredge, Ann Karagozian, Pirouz Kavehpour, John Kim, Mitchell Spearrin, Richard Wirz (Chair), Xiaolin Zhong
This program includes experimental, numerical, and theoretical studies related to topics on fluid mechanics such as stratified and rotating flows, thermal convection, interfacial phenomena, acoustically driven combustion flows, high-speed combustion, hazardous waste incineration, laser diagnostics, aerodynamic noise production, unsteady aerodynamics of fixed and rotary wings, flow instabilities and transition, turbulence, flow control, and micro-scale fluid mechanics.

MICRO-NANO ENGINEERING
Yong Chen, Pei-Yu Chiou, Vijay Gupta, Yongjie Hu, Lihua Jin, Sungtaek Ju, Chang-Jin Kim (Chair), Laurent Pilon
The Micro-Nano Engineering program focuses on the integration of science, engineering, and technology in the length scale of micrometers and nanometers. The study topics include science, fabrication technologies, devices, systems, material processing, intelligent material systems, flow phenomena, heat transfer, and biotechnologies at the micron/nano scales. The program is highly interdisciplinary in nature.

STRUCTURAL AND SOLID MECHANICS
Greg Carman, Nasr Ghoniem, Vijay Gupta (Chair), Christopher Lynch, Ajit Mal
The solid mechanics program features theoretical, numerical and experimental studies, including fracture mechanics and damage tolerance, micromechanics with emphasis on technical applications, wave propagation and nondestructive evaluation, mechanics of composite materials, mechanics of thin films and interfaces, and investigation into coupled electro-magneto-thermo-mechanical material systems. The structural mechanics program includes structural dynamics with applications to aircraft and spacecraft, fixed-wing and rotary-wing aeroelasticity, fluid structure interaction, computational transonic aeroelasticity, structural optimization, finite element methods and related computational techniques, structural mechanics of composite material components, and analysis of adaptive structures.

SYSTEMS AND CONTROL
Steven Gibson, Jonathan Hopkins, Tetsuya Iwasaki, Robert M’Closkey, Jacob Rosen, Veronica Santos, Jason Speyer, Tsu-Chin Tsao (Chair)
This program features systems engineering principles and applied mathematical methods of modeling, analysis, and design of continuous and discrete-time control systems. Emphasis is on computational methods, simulation, and modern applications in engineering, system concepts, applied optimal control, differential games, and computer process control. This field covers a broad spectrum of topics, emphasizing primarily aerospace and mechanical engineering applications.

THERMAL SCIENCE AND ENGINEERING (TSE)
Mohamed Abdou, Vijay Dhir, Tim Fisher, Yongjie Hu, Sungtaek Ju, Pirouz Kavehpour, Adrienne Lavine, Jayathi Murthy, Laurent Pilon (Chair)
This program includes studies of convection, radiation, conduction, evaporation, condensation, boiling, two-phase flow, chemically reacting and radiating flow, instability and turbulent flow, and reactive flows in porous media.

MINORS

APPLIED MATHEMATICS
Jason Speyer, Chair
Students opting for Applied Mathematics as a minor field are responsible for the body of knowledge contained in a coherent group of courses offered by the School of Engineering and/or the Mathematics Department. The program must consist of at least twelve quarter units of graduate study. In addition to the graduate course work, students in this minor field are expected to be familiar with the basic material in linear algebra, differential equations, vector calculus, functions of complex variables, and advanced calculus.

APPLIED PLASMA PHYSICS
Mohamed Abdou, Chair
Research in Applied Plasma Physics and Fusion Engineering is an appropriate advanced extension of traditional research and multi-disciplinary graduate-oriented field. The program emphasizes fusion as an important future option for energy production, conversion, and utilization. Research explores challenging applications of structural and solid mechanics, fluid mechanics, heat transfer, plasma-material interactions, and particle transport. The minor field offers education and training in plasma and fusion engineering to supplement the education received via one of the traditional major fields offered by the Department.


UCLA Samueli Mechanical and Aerospace Engineering

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