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

# Courses

For a more comprehensive list of all courses offered at Princeton University, go to the Office of the Registrar and check out Course Offerings for classes offered.

Please note that the following list includes all Astrophysics graduate courses. The designated Plasma Physics courses are course numbers AST 551 and above.

### Fall 2020

Analytical Techniques in Differential Equations

**Instructors:**Steven Charles Cowley, Jong-Kyu Park

Diffuse Matter in Space

Subject of course is the astrophysics of the interstellar medium: theory and observations of the gas, dust, plasma, energetic particles, magnetic field, and electromagnetic radiation in interstellar space. Emphasis will be on theory, including elements of: fluid dynamics; excitation of atoms, molecules and ions; radiative processes; radiative transfer; simple interstellar chemistry; and physical properties of dust grains.The theory will be applied to phenomena including; interstellar clouds (both diffuse atomic clouds and dense molecular clouds); HII regions; shock waves; supernova remnants; cosmic rays; interstellar dust; and star formation.

**Instructors:**Bruce T. Draine

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, William Randolph Fox II, Yevgeny Raitses

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

Introduction to Plasma Astrophysics

Introductory course to plasma physics, as it applies to space and astrophysical systems. Fundamental concepts are developed with mathematical rigor, and application to the physics of a wide variety of astrophysical systems are made. Topics include magnetohydrodynamics, kinetic theory, waves, instabilities, and turbulence. Applications to the physics of the solar wind and corona, the intracluster medium of galaxy clusters, the interstellar medium of galaxies, and a wide variety of accretion flows are given.

**Instructors:**Matthew Walter Kunz, Eve Charis Ostriker

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

Seminar in Theoretical Astrophysics

Designed to stimulate students in the pursuit of research. Participants in this seminar discuss critically papers given by seminar members. Ordinarily, several staff members also participate. Often topics are drawn from published data that present unsolved puzzles of interpretation.

**Instructors:**Adam S. Burrows

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:**Gabriel Perez-Giz

Topics in Statistics and Machine Learning: Statistical Data Analysis

The course provides an introduction to modern data analysis and data science. It addresses the central question, "what should I do if these are my data and this is what I want to know"? The course covers basic and advanced statistical descriptions of data. It also introduces the computational means and software packages to explore data and infer underlying structural parameters from them. The topics are exemplified by real-world applications. Prerequisites are linear algebra, multi-variate analysis, and a familiarity with basic statistics and programming (ideally in python).

## Pages

### Spring 2021

Computational Methods in Plasma Physics

Analysis of methods for the numerical solution of the partial differential equations of plasma physics, including those of elliptic, parabolic, hyperbolic, and eigenvalue type. Topics include finite difference, finite element, spectral, particle-in-cell, Monte Carlo, moving grid, and multiple-time-scale techniques, applied to the problems of plasma equilibrium, transport and stability. Basic parallel programming concepts are discussed.

**Instructors:**Hong Qin

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:**Amitava Bhattacharjee, Hantao Ji

High Energy Astrophysics

Selected astrophysical applications of electrodynamics, special and general relativity, nuclear and particle physics. Topics may include synchrotron radiation, comptonization, orbits and accretion in black-hole metrics, radio sources, cosmic rays, and neutrino astropysics.

**Instructors:**Anatoly Spitkovsky

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:**Matthew Walter Kunz

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

Modern Statistics

The course provides an introduction to modern statistics and data analysis. It addresses the question, "What should I do if these are my data and this is what I want to know"? The course adopts a model based, largely Bayesian, approach. It introduces the computational means and software packages to explore data and infer underlying parameters from them. An emphasis will be put on streamlining model specification and evaluation by leveraging probabilistic programming frameworks. The topics are exemplified by real-world applications drawn from across the sciences.

**Instructors:**Peter Michael Melchior

Numerical Algorithms for Scientific Computing

A broad introduction to numerical algorithms used in scientific computing. The course begins with a review of the basic principles of numerical analysis, including sources of error, stability, and convergence. The theory and implementation of techniques for linear and nonlinear systems of equations and ordinary and partial differential equations are covered in detail. Examples of the application of these methods to problems in engineering and the sciences permeate the course material. Issues related to the implementation of efficient algorithms on modern high-performance computing systems are discussed.

**Instructors:**Gregory Wayne Hammett

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 Observational Astrophysics: Current Research Topics in Astrophysics

Students improve their ability to give effective professional presentations, through lessons and opportunities to communicate their own research.

**Instructors:**Eliot Quataert, Joshua Nathan Winn

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:**Stewart C. Prager, Allan H. Reiman