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Senior Research Seminar. Offered in any two consecutive terms, by arrangement with HPS faculty. Under the guidance of an HPS faculty member, students will research and write a focused research paper of 15, words approximately 50 pages. In the second term, students will draft and revise their paper. L abc. Elementary French. The course uses a multimedia program, and emphasizes the acquisition of fundamental skills: oral ability, comprehension, writing, and reading.

The course is mainly designed for students with no previous knowledge of French. Students who have had French in secondary school or college must consult with the instructor before registering. Instructor: Orcel. Selected Topics in Philosophy. Ae ab. Aerospace Control Systems. Part a: Optimization-based design of control systems, including optimal control and receding horizon control.

Introductory random processes and optimal estimation. Kalman filtering and nonlinear filtering methods for autonomous systems. Part b: Nonlinear control design for aerospace systems, flight dynamics, and attitude dynamics. Guidance, navigation, and control of autonomous aerospace systems. Instructor: Fragoso. Introduction to Data Analysis in the Biological Sciences. Prerequisites: Bi 1, Bi 1x, Bi 8, or equivalent; or instructor's permission.

This course covers tools needed to analyze quantitative data in biological systems. Students learn basic programming topics, data organization and wrangling, data display and presentation, basic image processing, and resampling-based statistical inference. Students analyze real data in class and in homework. Instructors: Bois, Phillips. Statistical Inference in the Biological Sciences. This course introduces students to statistical modeling and inference, primarily taking a Bayesian approach.

Topics include generative modeling, parameter estimation, model comparison, hierarchical modeling, Markov chain Monte Carlo, graphical display of inference results, and principled workflows. Other topics may also be included.

All techniques are applied to real biological data sets in class and in homework. Instructor: Bois. Introduction to Finance. Prerequisites: Ec 11 required; Ma 1 abc recommended to be familiar with calculus and linear algebra. Finance, or financial economics, covers two main areas: asset pricing and corporate finance. For asset pricing, a field that studies how investors value securities and make investment decisions, we will discuss topics like prices, risk, and return, portfolio choice, CAPM, market efficiency and bubbles, interest rates and bonds, and futures and options.

For corporate finance, a field that studies how firms make financing decisions, we will discuss topics like security issuance, capital structure, and firm investment decisions the net present value approach, and mergers and acquisitions. In addition, if time permits, we will cover some topics in behavioral finance and household finance such as limits to arbitrage and investor behavior.

Instructor: Jin. ChE abc. Transport Phenomena. A rigorous development of the basic differential equations of conservation of momentum, energy, and mass in fluid systems. Solution of problems involving fluid flow, heat transfer, and mass transfer. Reading in Computer Science. Management of Technology. A course intended for students interested in learning how rapidly evolving technologies are harnessed to produce useful products or fertile new area for research.

Students will work through Harvard Business School case studies, supplemented by lectures to elucidate the key issues. There will be a term project where students predict the future evolution of an exciting technology. The course is team-based and designed for students considering choosing an exciting research area, working in companies any size, including start-ups or eventually going to business school. Topics include technology as a growth agent, financial fundamentals, integration into other business processes, product development pipeline and portfolio management, learning curves, risk assessment, technology trend methodologies scenarios, projections , motivation, rewards and recognition.

Industries considered will include electronics hardware and software , aerospace, medical, biotech, etc. Students will perform both primary and secondary research and through analysis present defensible projections. En Introduction to Medieval British Literature. This course offers a tour of major as well as some minor genres and works written in Britain prior to Far from a literary "dark age," the Middle Ages fostered dramatic experiments in narrative form, bequeathing to modern literature some of its best-loved genres and texts.

We will practice reading in Middle English-the language of Chaucer and his contemporaries-while we concentrate on the following questions: how did these texts circulate among readers? How do they establish their authority? What kinds of historical and cultural currents to they engage? Texts may include the lives of saints, the confessions of sinners, dranma, lyrics, romances, selections from Chaucer's Canterbury Tales, and Malory's Morte Darthur.

Readings will be in Middle and modern English. Earth's Biogeochemical Cycles. Global cycles of carbon, nitrogen and sulfur. Photosynthesis, respiration and net primary production. Soil formation, erosion, and carbon storage. Ecosystem processes, metrics, and function. Nutrient supply and limitation. Microbial processes underlying weathering, decomposition, and carbon remineralization.

Stable isotope tracers in the carbon and hydrologic cycles. The human footprint on the Earth. Instructor: Frankenberg. Introduction to the Solar System. Formation and evolution of the solar system. Interiors, surfaces, and atmospheres. Orbital dynamics, chaos, and tidal friction. Comets and asteroids. Extrasolar planetary systems. Instructor: Ingersoll. HPS Public Lecture Series. Student attend four lectures, featuring speakers from outside Caltech, on topics in the history and philosophy of science.

Students may choose from a variety of regularly scheduled HPS lectures, including HPS seminars, Harris lectures, and Munro seminars history or philosophy of science only. Graded on attendance. Not available for credit toward the humanities-social science requirement.

Instructor: Visiting lecturers. Intermediate French. Prerequisites: L abc or equivalent. The first two terms feature an extensive grammar review and group activities that promote self- expression. Op-Ed articles and a series of literary texts provide a basis for classroom discussion and vocabulary expansion. Several short written compositions are required.

The third term is designed to further develop an active command of the language. A variety of 19th- and 20th-century short stories are discussed in class to improve comprehension and oral proficiency. Students are expected to do an oral presentation, to write four short compositions, and a final paper. Instructors: Merrill, Orcel. Applied Linear Algebra. ACM 11 is desired. This is an intermediate linear algebra course aimed at a diverse group of students, including junior and senior majors in applied mathematics, sciences and engineering.

The focus is on applications. Matrix factorizations play a central role. Topics covered include linear systems, vector spaces and bases, inner products, norms, minimization, the Cholesky factorization, least squares approximation, data fitting, interpolation, orthogonality, the QR factorization, ill-conditioned systems, discrete Fourier series and the fast Fourier transform, eigenvalues and eigenvectors, the spectral theorem, optimization principles for eigenvalues, singular value decomposition, condition number, principal component analysis, the Schur decomposition, methods for computing eigenvalues, non-negative matrices, graphs, networks, random walks, the Perron-Frobenius theorem, PageRank algorithm.

Instructor: Zuev. Experimental Methods. Lectures on experiment design and implementation. Measurement methods, transducer fundamentals, instrumentation, optical systems, signal processing, noise theory, analog and digital electronic fundamentals, with data acquisition and processing systems. Experiments second and third terms in solid and fluid mechanics with emphasis on current research methods. Relativistic Astrophysics. Prerequisites: Ph 1, Ph 2 ab.

This course is designed primarily for junior and senior undergraduates in astrophysics and physics. Prerequisites: Ec 11, BEM , some familiarity with statistics. Examines the theory of financial decision making and statistical techniques useful in analyzing financial data. Topics include portfolio selection, equilibrium security pricing, empirical analysis of equity securities, fixed-income markets, market efficiency, and risk management.

Instructor: Roll. Intermediate Organic Chemistry. Prerequisites: Ch 41 abc. A survey of selected topics beyond introductory organic chemistry, including reaction mechanisms and catalysis. Instructor: Fu. Imagining the Medieval in the Nineteenth Century. Following the Enlightenment and amidst the Industrial Revolution, the late-eighteenth and nineteenth centuries saw a surging interest in the literature, lives, art, and architecture of the Middle Ages.

In this course, we will explore how authors represented, invoked, and often idealized the medieval past-with its knights, peasants, saints, and monsters-as a way to think through the challenges-social, literary, political, aesthetic-of their own time. Requirements for the course will include weekly response papers and two essays.

Current Problems in Environmental Science and Engineering. Discussion of current research by ESE graduate students, faculty, and staff. Introduction to Geobiology. Lectures about the interaction and coevolution of life and Earth surface environments. We will cover essential concepts and major outstanding questions in the field of geobiology, and introduce common approaches to solving these problems. Topics will include biological fractionation of stable isotopes; history and operation of the carbon and sulfur cycles; evolution of oxygenic photosynthesis; biomineralization; mass extinctions; analyzing biodiversity data; constructing simple mathematical models constrained by isotope mass balance; working with public databases of genetic information; phlyogenetic techniques; microbial and molecular evolution.

Instructors: Fischer, Kirschvink. L French Cinema. A critical survey of major directors, genres, and movements in French cinema. Particular attention is devoted to the development of film theory and criticism in France and their relation to film production. The course may also focus on problems of transposition from literature to cinema. Students are expected to write three 5-page critical papers. Conducted in French. Students who write papers in English may enroll in this class as VC , which satisfies the advanced humanities requirement.

VC ACM Applied Real and Functional Analysis. This course is about the fundamental concepts in real and functional analysis that are vital for many topics and applications in mathematics, physics, computing and engineering. The aim of this course is to provide a working knowledge of functional analysis with an eye especially for aspects that lend themselves to applications.

The course gives an overview of the interplay between different functional spaces and focuses on the following three key concepts: Hahn-Banach theorem, open mapping and closed graph theorem, uniform boundedness principle. More advanced topics include: spectral theory, compact operators, theory of distributions generalized functions , Fourier analysis, calculus of variations, Sobolev spaces with applications to PDEs, weak solvability theory of boundary value problems.

Ae abc. Space Engineering. Prerequisites: ME 11 abc and ME 12 abc or equivalent. Part a: Design of space missions based on astrodynamics. Topics include conic orbits with perturbations J2, drag, and solar radiation pressure , Lambert's Theorem, periodic orbits and ground tracks, invariant manifolds, and the variational equation with mission applications to planetary flybys, constellation, formation flying, and low energy planetary capture and landing.

Part b: Introduction to spacecraft systems and subsystems, mission design, rocket mechanics, launch vehicles, and space environments; spacecraft mechanical, structural, and thermal design; communication and power systems; preliminary discussion and setup for team project leading to system requirements review. Part c: Team project leading to preliminary design review and critical design review Instructor: Chung.

States of Matter. Prerequisites: APh 17 abc or equivalent. Thermodynamics and statistical mechanics, with emphasis on gases, liquids, materials, and condensed matter. Effects of heat, pressure, and fields on states of matter are presented with both classical thermodynamics and with statistical mechanics.

Conditions of equilibrium in systems with multiple degrees of freedom. Applications include ordered states of matter and phase transitions. The three terms cover, approximately, thermodynamics, statistical mechanics, and phase transitions. Optical Astronomy Instrumentation Lab. Prerequisites: Ay An opportunity for astronomy and physics undergraduates juniors and seniors to gain firsthand experience with the basic instrumentation tools of modern optical and infrared astronomy. The 10 weekly lab experiments include radiometry measurements, geometrical optics, polarization, optical aberrations, spectroscopy, CCD characterization, vacuum and cryogenic technology, infrared detector technology, adaptive optics wavefront sensors, deformable mirrors, closed loop control and a coronography tuturial.

Instructors: Mawet, Hillenbrand. An introduction to option pricing theory and risk management in the discrete-time, bi-nomial tree model, and the continuous time Black-Scholes-Merton framework. Both the partial differential equations approach and the martingale approach risk-neutral pricing by expected values will be developed.

The course will cover the basics of Stochastic, Ito Calculus. Since , the course is offered in the flipped format: the students are required to watch lectures online, while problem solving and case and paper presentations are done in class. Instructor: Cvitanic. Prerequisites: Completion of Core Curriculum Courses. Maximum enrollment: 15, by application only.

The theory of evolution is arguably biology's greatest idea and serves as the overarching framework for thinking about the diversity and relationships between organisms. This course will present a broad picture of evolution starting with discussions of the insights of the great naturalists, the study of the genetic basis of variation, and an introduction to the key driving forces of evolution.

Following these foundations, we will then focus on a number of case studies including the following: evolution of oxygenic photosynthesis, origin of eukaryotes, multicellularity, influence of symbiosis, the emergence of life from the water i. A specific focus for considering these issues will be the island biogeography of the Galapagos. Given in alternate years; not offered Instructors: Phillips, Orphan. Dynamics and Control of Chemical Systems. Prerequisites: ACM 95 ab or concurrent registration, or instructor's permission.

Analysis of linear dynamic systems. Feedback control. Stability of closed-loop control systems. Root locus, Frequency response, and Nyquist analysis. Feedforward, cascade, and multivariable control systems. Instructor: Seinfeld. Design for Freedom from Disability. Students visit the Center to define products based upon actual stated and observed needs. Designs and testing are done in collaboration with Rancho associates.

Speakers include people with assistive needs, therapists and researchers. Classes teach normative design methodologies as adapted for this special area. Firms, Competition, and Industrial Organization. Prerequisites: Ec 11 or equivalent. A study of how technology affects issues of market structure and how market structure affects observable economic outcomes, such as prices, profits, advertising, and research and development expenditures.

Emphasis will be on how the analytic tools developed in the course can be used to examine particular industries-especially those related to internet commerce-in detail. Each student is expected to write one substantial paper. Instructor: Shum. EE abc. Electrical Engineering Seminar. All candidates for the M. Instructor: Emami. Old English Literature. This course will introduce students to Old English: the earliest form of the English language, spoken in England from roughly the years to In studying the language, we will turn to its diverse and exciting body of literature, including one poem commemorating the brutal defeat by a Viking army and another based on the biblical story of Judith, who tricks the evil king Holofernes into sleeping with her-but not before slicing off his drunken head.

We will also read a variety of shorter texts: laws, medical recipes, humorously obscene riddles. Successful completion of the course will give students a richer sense not only of the earliest period of English literature, but also of the English language as it is written and spoken today. No prior experience with Old or Middle English is necessary for this course. Hum ab. Topics in French Culture and Literature.

Prerequisites: L abc or equivalent.. Offered concurrently with L ab. Hum a and Hum b taught in alternate years. Part a: 20th-century French literature. Part b: Contemporary France. Students who write papers in French may enroll in this class as L ab. Part a not offered L ab. Offered concurrently with Hum ab. L a and L b taught in alternate years. Students who write papers in English may enroll in this class as Hum ab, which satisfies the advanced humanities requirement.

Analog Electronics for Physicists. Prerequisites: Ph 1 abc, Ma 2, or equivalent.. A laboratory course intended for graduate students, it covers the design, construction, and testing of simple, practical analog and interface circuits useful for signal conditioning and experiment control in the laboratory.

No prior experience with electronics is required. Students will use operational amplifiers, analog multipliers, diodes, bipolar transistors, and passive circuit elements. The course culminates in a two-week project of the student's choosing.

Frontiers in Neuroeconomics. The new discipline of Neuroeconomics seeks to understand the mechanisms underlying human choice behavior, born out of a confluence of approaches derived from Psychology, Neuroscience and Economics. This seminar will consider a variety of emerging themes in this new field. Some of the topics we will address include the neural bases of reward and motivation, the neural representation of utility and risk, neural systems for inter-temporal choice, goals vs habits, and strategic interactions.

We will also spend time evaluating various forms of computational and theoretical models that underpin the field such as reinforcement-learning, Bayesian models and race to barrier models. Introductory Methods of Computational Mathematics. The sequence covers the introductory methods in both theory and implementation of numerical linear algebra, approximation theory, ordinary differential equations, and partial differential equations.

The linear algebra parts covers basic methods such as direct and iterative solution of large linear systems, including LU decomposition, splitting method Jacobi iteration, Gauss-Seidel iteration ; eigenvalue and vector computations including the power method, QR iteration and Lanczos iteration; nonlinear algebraic solvers.

The approximation theory includes data fitting; interpolation using Fourier transform, orthogonal polynomials and splines; least square method, and numerical quadrature. The ODE parts include initial and boundary value problems. Stability analysis will be covered with numerical PDE. Programming is a significant part of the course. Instructor: Hou. Comparative Biomechanics. Have you ever wondered how a penguin swims or why a maple seed spins to the ground?

How a flea can jump as high as a kangaroo? If spider silk is really stronger than steel? This class will offer answers to these and other questions related to the physical design of plants and animals. The course will provide a basic introduction to how engineering principles from the fields of solid and fluid mechanics may be applied to the study of biological systems.

The course emphasizes the organismal level of complexity, although topics will relate to molecular, cell, and tissue mechanics. The class is explicitly comparative in nature and will not cover medically-related biomechanics. Topics include the physical properties of biological materials, viscoelasticity, muscle mechanics, biological pumps, and animal locomotion. Offered Instructor: Dickinson.

Poetry and the Project of Justice. This course explores how contemporary poets grapple with the most urgent questions of our moment: identity, equality, environmental crisis, and justice. In this class, students will gain confidence in reading, discussing, and writing about contemporary poems and will encounter recent and more distant traditions of protest poetry.

We will ask how poetic language articulates questions of embodiment, community, law, and memory. The syllabus will focus in particular on writers of color, including queer and indigenous poets, and will include opportunities to attend local poetry readings. Instructor: Jahner. Research in Environmental Science and Engineering. Units by arrangement: any term.

Exploratory research for first-year graduate students and qualified undergraduates. Introduction to Structural Geology. Prerequisites: Ge 11 ab. Description and origin of main classes of deformational structures. Introduction to continuum mechanics and its application to rock deformation. Interpretation of the record of deformation of the earth's crust and upper mantle on microscopic, mesoscopic, and megascopic scales.

Introduction to the tectonics of mountain belts. Instructor: Avouac. Elementary Japanese. Prerequisites: Section a is required for sections b and c. Emphasis on oral-aural skills, and understanding of basic grammar.

Immediate introduction of the native script-hiragana, katakana-and gradual introduction to to characters. Instructor: Fujio. Ph abc. Topics in Classical Physics. Prerequisites: Ph 2 ab or Ph 12 abc, Ma 2. An intermediate course in the application of basic principles of classical physics to a wide variety of subjects. Ph a will be devoted to mechanics, including Lagrangian and Hamiltonian formulations of mechanics, small oscillations and normal modes, central forces, and rigid-body motion.

Ph b will be devoted to fundamentals of electrostatics, magnetostatics, and electrodynamics, including boundary-value problems, multipole expansions, electromagnetic waves, and radiation. It will also cover special relativity. Ph c will cover advanced topics in electromagnetism and an introduction to classical optics. Instructors: Fuller, Golwala, Hutzler. Introduction to Astronomical Observation.

Prerequisites: CS 1 or equivalent coding experience recommended. This hands-on, project-based course covers the design, proposal, and execution of astronomical observations, the basics of data reduction and analysis, and interacting with astronomical survey catalogs. In the first module, students will learn to use small, portable telescopes and find and image objects of interest using finder charts. In the second module, students will use Palomar Observatory to propose and execute their own research projects focused on astrophysical or planetary topics.

In the third module, students will query and work with data from on-line archives and catalogs. The scope of the course includes imaging and spectroscopic observational techniques at optical and infrared wavelengths. The format centers on projects and practical skills but also includes a lecture and problem set component to establish the theoretical underpinnings of the practical work. The course meets once a week in the evening, and there are required field trips to Palomar Observatory.

Instructors: Hillenbrand, de Kleer. BE Students will formulate and implement an engineering project designed to explore a biological principle or property that is exhibited in nature. Students will work in small teams in which they build a hardware platform that is motivated by a biological example in which a given approach or architecture is used to implement a given behavior.

Alternatively, the team will construct new experimental instruments in order to test for the presence of an engineering principle in a biological system. Each project will involve proposing a specific mechanism to be explored, designing an engineering system that can be used to demonstrate and evaluate the mechanism, and building a computer-controlled, electro-mechanical system in the lab that implements or characterizes the proposed mechanism, behavior or architecture. Instructors: Dickinson, Murray.

Corporate Finance. Prerequisites: BEM The main objective of the course is to develop insight into the process by which firms can create value for their shareholders. We will study major corporate decisions from the perspective of the firm with an emphasis on the interaction of the firm with financial markets: quantitative project evaluation for investment, choice between borrowing and issuing stock, dividend policy, organizational form for example, mergers and acquisitions.

Theory, empirical evidence, and case analysis all play significant roles in the course. Topics include discounted cash flow models, risk and return, capital asset pricing model, capital market efficiency, capital structure and the cost of capital and dividend policy. Instructor: Ewens. Social Media for Scientists. An introduction to the use of social media for scientific communication.

Social media platforms are discussed in the context of their use to professionally engage scientific communities and general audiences. Topics will include ethics, privacy, reputation management, ownership and the law, and will focus on the use and impact of social media for personal and professional career development. Lectures will include presentations by invited experts in various specialties, a number of whom will have worldwide recognition.

Linear Analysis with Applications. Covers the basic algebraic, geometric, and topological properties of normed linear spaces, inner-product spaces, and linear maps. Emphasis is placed both on rigorous mathematical development and on applications to control theory, data analysis and partial differential equations.

Instructor: Stuart. Medieval Romance. The medieval term romanz designated both a language, French, and a genre, romance, dedicated to the adventures of knights and ladies and the villains, monsters, magic, and miles that stood in their way. This course explores key examples from the twelfth through the fifteenth centuries, while also examining evolutions in the form.

We will consider how romances figured love and desire as well as negotiated questions of law, territory, and cultural difference. Graduate Writing Seminar. This course provides guided instruction in academic writing in STEM fields. More specifically, it teaches graduate students about composing texts in scientific English for expert audiences.

It helps familiarize writers with academic STEM discourse, and it teaches writers about the style and genres of U. From here, students learn to review the literature in their fields and situate their own research goals within that context. This course is designed for non-native speakers of English, but it covers topics that are relevant to native English speakers. Intermediate Japanese. Continued instruction and practice in conversation, building up vocabulary, and understanding complex sentence patterns.

The emphasis, however, will be on developing reading skills. Recognition of approximately 1, characters. Instructor: Hirai. Mathematical Models in Fintech. Prerequisites: Some knowledge of game theory and optimization is helpful, BEM Introduction to Finance is recommended, and a calculus-based course in probability is required. In this course we will go over recent works on topics broadly contained in the newly emerging field of Fintech.

In particular, the topics include mathematical modeling of strategic actions of agents interacting via a blockchain technology, via crowdfunding platforms, and via online investment platforms "robo-advisors". Computational Mechanics. Numerical methods and techniques for solving initial boundary value problems in continuum mechanics from heat conduction to statics and dynamics of solids and structures. Finite difference methods, direct methods, variational methods, finite elements in small strains and at finite deformation for applications in structural mechanics and solid mechanics.

Solution of the partial differential equations of heat transfer, solid and structural mechanics, and fluid mechanics. Transient and nonlinear problems. Computational aspects and development and use of finite element code. Long before torrents of lava cascaded down Los Angeles streets in the film Volcano, volcanic disaster narratives erupted across 19th-century British pages, stages, and screens.

This class will examine the enduring fascination with volcanoes in literary and visual culture and the socio-political tensions that disaster narratives expose. Students will analyze Mary Shelley's Frankenstein and Tambora's infamous eruption, James Pain's s pyrotechnic adaptation of Vesuvius's 79AD eruption, and paintings of global sunsets after Krakatoa's eruption. Instructor: Sullivan.

Intermediate Graduate Writing Seminar. This course focuses on strategies for composing an academic journal article in a STEM field. The rhetorical purpose and form of each section of the journal article will be considered in depth. The course is intended for graduate students who are prepared to be a lead author on a manuscript.

While the course will cover strategies for collaborative writing, students will be asked to draft sections of an original journal article based upon their own research. The course will also provide instruction on selecting a target journal, preparing a manuscript for submission, and responding to feedback from peer reviewers. Clarity in scientific writing and creating effective figures will also be discussed. Course enrollment is limited to 15 students. Applications of Physics to the Earth Sciences.

Prerequisites: Ph 2 and Ma 2 or equivalent. An intermediate course in the application of the basic principles of classical physics to the earth sciences. Topics will be selected from: mechanics of rotating bodies, the two-body problem, tidal theory, oscillations and normal modes, diffusion and heat transfer, wave propagation, electro- and magneto-statics, Maxwell's equations, and elements of statistical and fluid mechanics. Instructor: Brown. H a.

The Early Middle Ages. This course is designed to introduce students to the formative period of Western medieval history, roughly from the fourth through the tenth centuries. It will emphasize the development of a new civilization from the fusion of Roman, Germanic, and Christian traditions, with a focus on the Frankish world. The course focuses on the reading, analysis, and discussion of primary sources. H b. The High Middle Ages. This course is designed to introduce students to European history between and It will provide a topical as well as chronological examination of the economic, social, political, and religious evolution of western Europe during this period, with a focus on France, Italy, England, and Germany.

The course emphasizes the reading, analysis, and discussion of primary sources. Advanced Japanese. Developing overall language skills. Literary and newspaper readings. Technical and scientific translation. Improvement of listening and speaking ability so as to communicate with Japanese people in real situations. Recognition of the 1, general-use characters. Ma abc. Classical Analysis. Prerequisites: Ma 1 or equivalent, or instructor's permission.

May be taken concurrently with Ma Second term: brief introduction to ordinary differential equations; Lebesgue integration and an introduction to Fourier analysis. Third term: the theory of functions of one complex variable. Instructors: Dunn, Karpukhin, Demirel-Frank. Mathematical Modelling. This course gives an overview of different mathematical models used to describe a variety of phenomena arising in the biological, engineering, physical and social sciences.

Emphasis will be placed on the principles used to develop these models, and on the unity and cross-cutting nature of the mathematical and computational tools used to study them. Applications will include quantum, atomistic and continuum modeling of materials; epidemics, reacting-diffusing systems; crowd modeling and opinion formation.

Mathematical tools will include ordinary, partial and stochastic differential equations, as well as Markov chains and other stochastic processes. Introduction to techniques of micro-and nanofabrication, including solid-state, optical, and microfluidic devices.

Students will be trained to use fabrication and characterization equipment available in the applied physics micro- and nanofabrication lab. Topics include Schottky diodes, MOS capacitors, light-emitting diodes, microlenses, microfluidic valves and pumps, atomic force microscopy, scanning electron microscopy, and electron-beam writing.

Instructors: Troian, Ghaffari. Frontiers in Behavioral Economics. Prerequisites: Ec This course will study topics in behavioral economics demonstrating departures from the classic economics assumptions of rationality and pure self-interest. We will study evidence of these departures, models that have been designed to capture these preferences, and applications of these models to important economic questions.

Topics will include biases and heuristics, risk preferences, self-control, strategic uncertainty, and social preferences, among others. The course will be based in readings from both classic and modern research. Methodologically, the course will combine both theoretical and empirical evidence of the mentioned above topics.

Instructor: Nielsen. Madness and Reason. Madness threatens to dissolve boundaries of the most various kinds: between the human and the inhumane, reality and fantasy, sickness and health. One of the tasks of a literary text is to subdue and contain madness through the construction of rational frameworks. How does a literary text accomplish this? Which strategies, such as the use of irony and humor, are the most effective?

What role do insane characters play in literary texts? And when - if ever - should we consider an excess of reason as a kind of madness in its own right? Instructor: Holland. Oral Presentation. Units to be arranged:. Practice in the effective organization and the delivery of oral presentation of scientific results before groups. Units and scheduling are done by the individual options. H Medieval Knighthood.

This course tells the story of the knight from his beginnings in the early Middle Ages, through his zenith in the 11th, 12th, and 13th centuries, to his decline and transformation in the late medieval and early modern periods. The course treats the knight not simply as a military phenomenon but also as a social, political, religious, and cultural figure who personified many of the elements that set the Middle Ages apart.

This course will introduce students to the artistic style and the social, historical, and political content of French films, starting with Melies and the Lumiere brothers and working through surrealism and impressionism, s poetic realism, the Occupation, the New Wave, the Cinema du look, and the contemporary cinema.

The class will teach students to look at film as a medium with its own techniques and formal principles. Conducted in English. Introduction to Geometry and Topology. Prerequisites: Ma 2 or equivalent, and Ma must be taken previously or concurrently. First term: aspects of point set topology, and an introduction to geometric and algebraic methods in topology. Second term: the differential geometry of curves and surfaces in two- and three-dimensional Euclidean space.

Third term: an introduction to differentiable manifolds. Transversality, differential forms, and further related topics. Instructors: Smillie, Park. Wr Topics in Applied Physics. A seminar course designed to acquaint advanced undergraduates and first-year graduate students with the various research areas represented in the option. Lecture each week given by a different member of the APh faculty, who will review his or her field of research. Instructor: Bellan. Venture Capital.

Prerequisites: BEM , An introduction to the theory and practice of venture capital financing of start-ups. This course covers the underlying economic principles and theoretical models relevant to the venture investment process, as well as the standard practices used by industry and detailed examples. CDS Introduction to Feedback Control Systems.

An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. Design of feedback controllers in state space and frequency domain based on stability, performance and robustness specifications. Introduction to Biochemistry. Prerequisites: Ch 41 abc or instructor's permission.

Lectures and recitation introducing the molecular basis of life processes, with emphasis on the structure and function of proteins. Topics will include the derivation of protein structure from the information inherent in a genome, biological catalysis, and the intermediary metabolism that provides energy to an organism. Instructor: Clemons. This graduate course examines the research on university-level STEM science, technology, engineering, and mathematics teaching and learning, which has been used to inform a well-established body of evidence-based teaching practices.

Weekly interactive meetings will provide focused overviews and guided application of key pedagogical research, such as prior knowledge and misconceptions, novice-expert differences, and cognitive development as applied to university teaching. We will explore the roles of active learning, student engagement, and inclusive teaching practices in designing classes where all students have an equal opportunity to be successful and feel a sense of belonging, both in the course and as scientists.

Readings will inform in-class work and students will apply principles to a project of their choice. Instructors: Horii, Weaver. Embedded Systems Design Laboratory. The student will design, build, and program a specified microprocessor-based embedded system. This structured laboratory is organized to familiarize the student with large-scale digital and embedded system design, electronic circuit construction techniques, modern development facilities, and embedded systems programming.

The lectures cover topics in embedded system design such as display technologies, interfacing to analog signals, communication protocols, PCB design, and programming in high-level and assembly languages. Given in alternate years; c Offered ; ab Not offered Instructor: George. Sinners, Saints, and Sexuality in Premodern Literature.

What made the difference between saint and sinner in medieval and Renaissance literature? This class takes up this question by focusing on the unruly problems of embodiment. We will read across a wide range of literatures, including early medical texts, saints' lives, poetry and romance, as we examine how earlier periods understood gender and sexual difference. Questions we may consider include the following: how did writers construct the "naturalness" or "unnaturalness" of particular bodies and bodily acts?

How did individuals assert control over their own bodies and those of others? In what ways did writing authorize, scrutinize, or police the boundaries of the licit and illicit? Finally, how have modern critics framed these questions? Instructor: Not offered ESE abc. Seminar in Environmental Science and Engineering.

Seminar on current developments and research in environmental science and engineering. Instructor: Callies. Causation and Explanation. An examination of theories of causation and explanation in philosophy and neighboring disciplines. Topics discussed may include probabilistic and counterfactual treatments of causation, the role of statistical evidence and experimentation in causal inference, and the deductive-nomological model of explanation.

The treatment of these topics by important figures from the history of philosophy such as Aristotle, Descartes, and Hume may also be considered. Instructor: Eberhardt. Elementary Spanish. Grammar fundamentals and their use in understanding, speaking, reading, and writing Spanish. Exclusively for students with no previous knowledge of Spanish. Instructors: Arjona, Garcia. Prerequisites: Ma or previous exposure to metric space topology, Lebesgue measure. Second term: basic complex analysis: analytic functions, conformal maps and fractional linear transformations, idea of Riemann surfaces, elementary and some special functions, infinite sums and products, entire and meromorphic functions, elliptic functions.

Third term: harmonic analysis; operator theory. Operator theory: compact operators, trace and determinant on a Hilbert space, orthogonal polynomials, the spectral theorem for bounded operators. If time allows, the theory of commutative Banach algebras. Instructors: Karpukhin, Rains, Angelopoulos. Special Laboratory Work in Mechanical Engineering. Special laboratory work or experimental research projects may be arranged by members of the faculty to meet the needs of individual students as appropriate.

A written report is required for each term of work. MS abc. Materials Research Lectures. A seminar course designed to introduce advanced undergraduates and graduate students to modern research in materials science. Instructors: Fultz, Faber, Bernardi. Ay ab. Introduction to Current Astrophysics Research. This course is intended primarily for first-year Ay graduate students, although participation is open and encouraged.

Students are required to attend seminar-style lectures given by astrophysics faculty members, describing their research, to attend the weekly astronomy colloquia, and to follow these with additional readings on the subject. At the end of each term, students are required to summarize in oral or written form at the discretion of the instructor , one of the covered subjects that is of most interest to them. Instructors: Hallinan, Hopkins. Quantitative Risk and Portfolio Management.

An introduction to financial risk management. Concepts of Knightian risk and uncertainty; coherent risk; and commonly used metrics for risk. Techniques for estimating equity risk; volatility; correlation; interest rate risk; and credit risk are described. Discussions of fat-tailed leptokurtic risk, scenario analysis, and regime-switching methods provide an introduction to methods for dealing with risk in extreme environments.

Instructor: Winston. Biochemistry of Gene Expression. Lectures and recitation on the molecular basis of biological structure and function. Emphasizes the storage, transmission, and expression of genetic information in cells. Specific topics include DNA replication, recombination, repair and mutagenesis, transcription, RNA processing, and protein synthesis. Instructors: Campbell, Parker. Sustainable Chemical Engineering.

Begins with the Earth's resources including fresh water, nitrogen, carbon and other biogeochemical cycles that set the global context for chemical engineering; examines regional and local systems using chemical engineering thermodynamics, reaction analysis and transport phenomena to model the effects of human activities on air, water and soil; concludes with examples of computational models guiding public policy.

Instructor: Kornfield. Injecting enough water propellant to bring the temperature down to 3, to 3, K will lower the I sp to to seconds. Doing the same with liquid hydrogen will lower the I sp to 1, to 1, seconds.

Spin-polarized triplet helium. Two electrons in a helium atom are aligned in a metastable state one electron each in the 1s and 2s atomic orbitals with both electrons having parallel spins, the so-called "triplet spin state", if you want the details. When it reverts to normal state it releases 0. Making the stuff is easy. The trouble is that it tends to decay spontaneously, with a lifetime of a mere 2. And it will decay even quicker if something bangs on the fuel tank. Or if the ship is jostled by hostile weapons fire.

To say the fuel is touchy is putting it mildly. The fuel is stored in a resonant waveguide to magnetically lock the atoms in their metastable state but that doesn't help much. There were some experiments to stablize it with circularly polarized light, but I have not found any results about that. Meta-helium would be such a worthwhile propulsion system that scientists have been trying real hard to get the stuff to stop decaying after a miserable 2.

One approach is to see if metastable helium can be formed into a room-temperature solid if bonded with diatomic helium molecules, made from one ground state atom and one excited state atom. This is called diatomic metastable helium. The solid should be stable, and it can be ignited by heating it. Theoretically He IV-A would be stable for 8 years, have a density of 0.

The density is a plus, liquid hydrogen's annoying low density causes all sorts of problems. Robert Forward in his novel Saturn Rukh suggested bonding 64 metastable helium atoms to a single excited nitrogen atom, forming a stable super-molecule called Meta.

Whether or not this is actually possible is anybody's guess. In theory it would have a specific impulse of seconds. Metastable helium is the electronically excited state of the helium atom, easily formed by a 24 keV electron beam in liquid helium.

Spin-aligned solid metastable helium could be a useful, if touchy, high thrust chemical fuel with a theoretical specific impulse of 3. Robert Forward. All of these propulsion systems require huge amounts of electricity for their operation.

Most have the advantage of very good specific impulse and exhaust velocity. This gives the spacecraft more delta-V and lower fuel mass requirements. On the disadvantage side, they require lots of electricity and their thrust is very very low. You can often measure the thrust in humming-bird powers. What the joke is saying is that electric drives are power hogs.

Solar power is relatively lightweight but the energy is so dilute you need huge arrays. Nuclear power can supply megawatts of power but reactors have a mass measured in tons , which drastically reduces the spacecraft thrust-to-weight ratio and the acceleration. Meaning the spacecraft might take a couple of years just to break out of Terra's orbit and enter Trans-Martian Insertion.

But the joke is on the wag. Turns out there is such a thing as "an extension cord long enough", it is called beamed power. This is where the spacecraft has a relatively lightweight power receptor. While back at home is a massive orbiting power satellite which beams torrents of power to the spacecraft via microwaves or laser. The beam becomes the "extension cord", meaning the remote power satellite adds zero mass to the spacecraft.

This improves the thrust-to-weight ratio something wonderful and brings its acceleration up to useful levels. Of course the spacecraft is at the mercy of whoever is controlling the powersat, but you can't have everything. I'm going to pull up a military chestnut and coin a maxim:. A long-standing pet peeve of mine is the breathless popular science articles on the latest over-hyped electric rocket.

Electric propulsion of course is not a new idea — mentioned in passing by Tsiolkovsky, seriously championed by Ernst Stuhlinger, and now used routinely in geostationary satellites for stationkeeping and in some deep space missions. On the face of it, it seems attractive. Electric propulsion systems come in a bewildering array of flavors — gridded ion thrusters, hall effect thrusters, magnetoplasmadynamic systems, hot plasma expelled through a magnetic nozzle, and so on.

In every case, either they use higher temperatures than combustion reactions, or they use non-thermal processes to push the expelled reaction mass to higher velocities than chemical rockets can achieve. After all, everyone has an electric thruster in their house that has an exhaust velocity of the speed of light — we call it a flashlight. If we want to get to Mars in a month 2. Peak acceleration would then have to be about.

To get that acceleration, then, at that I sp , Psp has to be 0. Another factor of two or so improvement is possible based on things in the laboratory. What about nuclear sources? The one nuclear reactor the U. After many years, NASA is now nearing maturity on a more modern design, Kilopower or KRUSTY , which uses Stirling cycle power to get more electricity from the reactor, and hopes to reach W in a kg package which still needs shielding mass added.

There are designs for extremely high temperature reactors. These designs tend to use gas-cores, running at temperatures so high that solid reactor elements would melt. No such reactor has ever been tested with fission fuel even in a laboratory some pieces of it, like power conversion machinery, have been tested with electric heaters. Those processes side-step the temperature limits discussed above or, if you prefer, are using the fact that a process running at volts has an effective temperature of about 1.

I think this is an encouraging route to a high Psp power supply — but there are practical challenges. For fusion, we have the ongoing problem that making a fusion reaction happen at all in a net-energy producing way remains a technological stretch unless we want to accept a very large reaction happening quickly, vaporizing the apparatus in the process a fusion bomb.

Ironically, the old joke about the long extension cord is probably the most promising route. Today we can see how to build beams — lasers, microwave beams, particle beams, and so on — which can beam power a long way. There is some work going on at NASA for mission designs using laser beams to power high-intensity solar arrays and drive an electric thruster — presently just to accelerate because of the limited range of the beam.

But we already have thrusters that are better by far than our power supplies can effectively use. What we need is a better power supply! Nuclear electric propulsion NEP systems convert heat from the fission reactor to electrical power, much like nuclear power plants on Earth. This electrical power is then used to produce thrust through the acceleration of an ionized propellant. An NEP system can be defined in terms of six subsystems, which are depicted in Figure 3. NEP system performance is governed by the total system mass required to produce the required power level i.

System design trades focus on maximizing the power conversion subsystem efficiency, the waste heat rejection temperature, and the efficiency and specific impulse I sp of the EP subsystem while achieving the mission lifetime and reliability requirements. An integrated technology development program aimed specifically toward a NEP system operating at more than 1 MWe has not been undertaken.

Developing an NEP system for the baseline mission will likely involve the use of multiple NEP modules which, in the aggregate, will provide the total propulsive power. This would increase system complexity, especially since the NEP system design includes six major subsystems on each NEP module , and the spacecraft would also need to incorporate a chemical in-space propulsion system.

No reactor has been developed that is representative of that needed for NEP applications. Extensive development has occurred for proposed HEU fuels and cladding for NEP reactors, including irradiations up to NEP-relevant lifetime fuel burnup levels for numerous fuel elements. Overall, there is a sound technical basis regarding the fuel and cladding temperatures and fuel burnup levels that are needed for NEP fuel systems.

However, significant technology recapture activities would be needed to reestablish robust UN or UC fuel fabrication capabilities. Beryllium and BeO reflectors and control rods have been recently manufactured for the Kilopower program. In the Prometheus program, simulation of reactor and plant interactions were used to determine overall stability of the system.

For any spacecraft with a source of nuclear radiation, the dose rate is managed by a combination of 1 distance between the reactor or other source and the payload and 2 attenuation by the shield. State-of-the-art shielding materials include 1 Be, LiH, and B4C to moderate and absorb neutrons and tungsten to attenuate gamma rays; these were tested in the SP program and were planned for use in the Prometheus system as well.

Shielding designs incorporated cooling of the LiH, and designs allowed passage of coolant and control lines without radiation leakage. Shield modeling performed in the Prometheus program was deemed mature enough for design, and it was used to verify that coolant and electrical paths could successfully be integrated into the shadow shield. Power conversion technologies relevant to space power systems have been identified in a myriad of system studies and development programs at a range of power levels over decades.

The most relevant power conversion technologies are as follows:. The level of development and the potential performance of these technologies varies widely, and none have been tested to the power levels required for a MWe-class NEP system in an appropriate operating environment, even if multiple power conversion units are used to meet total power and system reliability requirements. Thermoelectric converters have a long history in space nuclear fission systems, particularly with the SNAP program and the SP program.

Thermoelectric and thermionic converters, however, do not scale well to megawatt electric-power levels. As noted above, the SP program would have shifted from static to dynamic power conversion technology to achieve MWe-class performance. Brayton power conversion has had the greatest development effort, with NEP relevant development conducted most recently for the Prometheus and Fission Surface Power FSP programs, both of which use superalloys, unlike the SNAP system that relied on refractory materials.

A design schematic for the kWe Prometheus system design is shown in Figure 3. The Prometheus project development yielded a test of a state-of-the-art 2 kWe Brayton power conversion system directly coupled to a 2. The Brayton system was operated for h. The Thermionic Fuel Element TFE Verification Program focused on life testing of single fuel elements, each with multiple thermionic converters surrounding a UO 2 fuel element in a relevant thermal and neutronic environment.

Prior to the end of the program in , a single fuel element was operated up to 18 months. The TFE, however, required fuel temperatures on the order of K, which introduced additional structural material concerns for the reactor. The characteristics of the most recent power conversion technology tests relevant to space power systems are shown in Table 3. As shown, the demonstrated power levels for the different options vary widely, as they were not intended for use in high power, low specific mass systems.

The Rankine cycle concept has been tested at kWe. The other three concepts have been tested at power levels that are far below the level needed for a MWe-class NEP system. The tested values for maximum temperatures, power per converter, and the assumed materials to be used are described. The state of the art shown is for actual tested components.

Much of the power conversion subsystem estimates used in projections for MWe NEP systems are based on designing existing concepts for operation at higher temperatures and scaling them to higher powers. Scaling to higher power is required, rather than simply using greater numbers of existing components to keep NEP system complexity manageable. Different power conversion technologies have different waste heat rejection needs.

Brayton and Stirling power conversion subsystems, which use gaseous working fluids, reject heat over a range of temperatures as the gases cool while passing through a heat exchanger. A Rankine system uses the energy released by a reactor to boil a working fluid, which is subsequently condensed at a constant temperature the boiling point of the working fluid. Thermoelectric and thermionic converters are cooled either by 1 radiation from the cold side of the converter or 2 a coolant that transfers waste heat to a radiator.

Radiator operating temperature and size is determined by various system design considerations. The transport of heat from the power conversion subsystem to the radiator is generally done either by 1 coolant that is pumped through an array of pipes attached to radiator panels or 2 heat pipes, which are essentially self-contained heat transfer systems that create high thermal conductivity through an internal phase change flow in each heat pipe.

Because a significant portion of the reactor power is rejected as waste heat, radiator panel area and mass can dominate an NEP system. In addition, the structural considerations for launch and deployment as well as the large-scale heat pipes required will present significant challenges. Multiple heat pipes on a single representative panel were tested in vacuum in The projected specific mass of the heat rejection subsystem for this kWe system was Power management and distribution PMAD technology is dependent on both the power source and load electronics.

The JIMO design assumed a direct-drive approach, where the power was delivered to thrusters at the voltage needed for thrust generation. This approach was demonstrated at a very low power with a test of a 1. The power output of approximately 55 volts AC from the Brayton system was rectified and converted to V of direct current DC and transferred to the ion thruster to provide beam power to generate thrust.

The efficiency of this approach was 91 percent. While this was a successful demonstration of the overall direct-drive NEP concept, it was at a very low power for a very short period of time. This test did not incorporate flight-like components for the direct drive, and it did not address many aspects of fault tolerance or system transients. EP systems have been used for spaceflight for decades, but to date the available power level has been limited to kilowatt-electric, not megawatt electric, and the source of power has been solar panels.

Of the various thruster types that have been used, the two most likely to provide the required performance and lifetime capabilities for Mars missions at the required power levels are ion thrusters and Hall thrusters. Both of these types of thrusters have extensive flight heritage at power levels below 5 kWe. Ion thrusters use two or more parallel grids with a voltage applied to each to extract and accelerate ions created in a discharge chamber upstream of the grids see Figure 3.

Because ions are extracted and accelerated through the grids, a cathode neutralizer is needed to emit electrons to prevent a charge imbalance from forming. Charge separation in the grid assembly limits the maximum thrust density of ion thrusters, meaning that kWe class ion thrusters are likely quite large. With Hall thrusters see Figure 3.

A voltage difference is applied between the anode, which usually serves as the propellant injector at the upstream end of the channel, and a downstream hollow cathode that supplies the electrons to the channel. The mixture of electrons and ions in the acceleration zone means that the thruster does not have the thrust density limitation associated with ion thrusters, although other lifetime considerations limit the achievable thrust densities.

This introduces uncertainty into current predictions of in-space performance and lifetime for high-power Hall thrusters. Table 3. This table includes the following four flight systems:. All flight thrusters also have flight PPU and PMS subsystems, although they are designed to interface with a solar photovoltaic power system, not a nuclear power source. Current flight EP thrusters have a maximum power of 6. Several thrusters have undergone laboratory tests for tens of hours at 50 kWe and above, including two of the Hall thrusters listed in Table 3.

MPD thrusters see Figure 3. The applied magnetic field from an electromagnet may be used to enhance the acceleration process. MPD thrusters have among the highest thrust and power densities of any EP thruster. While they can operate on a number of propellants, lithium appears to be most promising for NEP applications.

The status of these more immature, but higher power concepts is given in Table 3. Neither thruster has undergone significant life testing in recent years. The state-of-the art PPU for Hall thrusters is arguably the one associated with the 4. This PPU has an input power conversion efficiency of at least 92 percent with an input voltage of 70 V DC, and it has a mass of The As noted above, all of these PPUs are designed for use with photovoltaic arrays, not nuclear power sources.

The baseline mission requires an NEP system whose performance far exceeds that of existing flight systems in terms of power, specific mass, and reliability, though limited subscale demonstrations of several relevant technologies have been completed. Existing thruster concepts such as Hall thrusters and ion thrusters can meet I sp and efficiency requirements, but thruster power levels must increase by an order of magnitude compared to current and near-term solar electric propulsion SEP flight systems.

System lifetimes and reliability are poorly understood at megawatt electric power levels. EP propellant management will essentially be a relatively straightforward scaling of current flight practice and design for systems that use propellants stored as a gas or liquid. A feed system for MPD thrusters that use lithium propellant stored as a solid would require further development. In either case, as discussed in Chapter 1, a 1 MWe-class NEP system capable of executing the baseline mission also requires augmentation by a chemical propulsion system using cryogenic propellants and assumes minimal boiloff using cryocooler technology.

This technology will have to be matured in parallel with NEP development. The NEP system is a complex system, with performance requirements for power level, specific mass, I sp , efficiency, lifetime, and reliability propagating throughout the subsystems in terms of temperature and power density requirements.

The multiple subsystems of an NEP system must demonstrate adequate performance and reliable operation of interconnected subsystems across all phases of mission operations as well as unexpected transients during abnormal operating conditions.

The NEP system relies on a wide spectrum of physics and engineering: neutronics, thermal hydraulics, high-temperature materials, fluid mechanics, turbomachinery, power electronics, electromagnetism, and plasma physics. While this will require definitions of interfaces throughout the development of the subsystems, such a process has been successfully demonstrated for the significantly lower power levels associated with SEP robotic missions in Earth orbit and interplanetary space.

Demonstrating Prometheus-level technology at the power level and scale required for the baseline mission while meeting goals for specific mass is a considerable challenge. For the baseline mission, such a system would experience reactor fuel burnup of about 4 percent over a period of about 4 years. These parameters are within the envelope of irradiation tests performed on fuel systems in prior space reactor programs.

Key reactor concept decisions to be finalized include fuel enrichment HEU versus HALEU and neutron spectrum fast versus moderated , which in turn will drive the selection of specific fuel, cladding, and structural materials for the reactor. Available reactivity control materials are sufficient to produce a highly reliable reactor system. Technology recapture activities will be needed for the manufacturing of legacy materials and reactor components.

A variety of feasible radiation shield options are available that would enable suitable shielding for the crew and sensitive electronic components at distances of about 50 to m from the reactor over a 4-year life. As noted previously, shielding consists of layers of low atomic number materials e.

Most of these shields work best at temperatures between about and K, so cooling below the reactor operating temperature is desirable; most hydride shield materials rapidly lose hydrogen at higher temperatures. Power conversion subsystems couple with the reactor at maximum temperatures comparable to the reactor coolant outlet temperature. For dynamic power conversion, this requires turbine material temperatures of to K, requiring at least superalloy materials or refractory metals if temperatures higher than K are necessary.

For the targeted power level of 1 to 2 MWe, individual converter output power levels of kWe would be needed, with the specific selection depending on component and system level performance, lifetime, and reliability trade studies. Power conversion subsystem lifetimes less than that required for the entire mission 2 to 4 years depending on mission assembly and operation requirements would require duplicate components or subsystems to ensure mission success. Operating temperatures for the power conversion subsystems tested to date are at the minimum acceptable level to meet NEP needs.

Brayton energy conversion technologies are more advanced than other types, but they introduce new types of risks, and demonstrated power levels for space-qualified systems are orders of magnitude below that required for a 1 to 2 MWe system. A Rankine power conversion system, although used extensively in terrestrial systems, would pose additional risks associated with handling a two-phase flow in zero gravity. Liquid metal working fluids adopted for some power conversion options would also likely introduce the need for refractory metals in the power conversion sections.

Advanced NEP systems will likely be able to convert perhaps 20 to 35 percent of the thermal energy from the reactor coolant into electrical power. Temperatures of at least K are necessary for radiators to reject heat in a mass efficient manner. At these temperatures, a total radiating area on the order of m 2 to m 2 single sided would be required for a 1 to 2 MWe NEP system.

These radiators must also provide high thermal conductivity and operate reliably for the entire reactor and power system operating time 2 to 4 years depending on mission design. Initial studies for the NEP module used carbon composite structure and water-filled heat pipes in conjunction with a pumped sodium-potassium alloy NaK liquid metal loop to reach an area specific mass of about 7. A reduction in specific mass for this subsystem is possible by using higher temperature panels, but that would propagate back throughout the NEP system to higher reactor and power conversion temperatures.

Another way to reduce the mass of this system is to use a constant-rejection temperature cycle such as the Rankine cycle in which the working fluid undergoes a phase change, instead of the Brayton cycle in which the working fluid decreases in temperature throughout the heat rejection portion of the cycle. This change would require additional development of the power conversion subsystem to address two-phase flow in zero gravity.

A third option for reducing the mass of the heat rejection subsystem is to develop lower-mass high-temperature materials. With such a large area, stowing, deploying, and on-orbit assembly of the heat rejection system will be significant challenges. To fit in the shroud of likely launch vehicles, the radiator panels and fluid transport systems for distributing heat to the heat pipes would need to be folded without breaching the seals for the coolant piping, and this complex assembly would need to survive launch environments.

There is limited flight heritage in this area. Higher voltage transmission could result in lower mass power distribution due to the reduced current requirements. For state-of-the-art silicon components, the low K operating temperature for these electronics implies large area requirements for heat rejection. In order to meet the specific mass requirements for the baseline mission including heat rejection , PMAD efficiencies of at least 90 to 95 percent will be needed to reduce waste heat.

Additionally, as was observed in the JIMO program, radiation hardening to protect electronics against radiation damage from both the NEP system and from the space environment will be required. PMAD designs will need to address reliability in terms of switching and power regulation for the 2- to 4- year life of the baseline mission.

The limited availability of highly reliable, radiation-hardened electronic components may limit the voltage and current options for the PMAD system. Further improvement in performance might be realized with higher temperature semiconductor materials, such as SiC or GaN. These have been considered in past MWe NEP studies, but performance and life demonstration are required to determine their actual efficacy for the baseline mission.

SiC can withstand higher operating temperatures of the power electronics for the PMAD subsystem and the PPU in the EP subsystem , thereby reducing the radiator area and mass, but performance and operational life at megawatt electric power levels would have to be demonstrated for a space relevant environment. Thruster performance requirements are to some extent dependent on power system specific mass and power levels.

As specified in Chapter 1, the I sp goal is 2, s or more, with thruster efficiencies greater than 50 percent in order to provide enough acceleration for the power levels, payloads, and trip times. Thruster power levels of kWe or more allow for a reduction in system complexity in terms of the numbers of thrusters, PPUs, and PMSs that must be integrated. Similarly, the baseline mission imposes a total system operating time of at least 2 years, which is approximately 20, h.

Lifetime must therefore be a minimum of 2 years, or, with the typical 50 percent margin required for space systems, 3 years or 30, h, or spare units will have to be included, with a commensurate mass penalty. In addition, the system must be available for the full mission life of about 4 years, which includes time for launch, in-space assembly, and the round trip to Mars.

Existing thrusters cannot meet all mission requirements. Flight qualified or demonstrated thrusters such as Hall and ion thrusters have operated at 4. All of these thrusters, however, are expected to meet the lifetime requirement of at least 20, h: the 4.

Testing plasma thrusters for extended periods at power levels greater than approximately 20 kWe poses facility challenges that have limited development at these power levels see below. Scaling thrusters to higher power levels at the required Isp represents a risk in terms of the increased power density or thruster size. In the case of ion thrusters, this represents an increase in grid area of an order of magnitude, while maintaining inter grid spacings within less than 1 mm.

In the case of Hall thrusters, either channel power density must be increased, which introduces heating and lifetime issues, or channel and thruster diameter must increase for the same reason as the ion thruster. Laboratory models have been tested to address this scaling, including the use of multiple concentric channels. For the ion thruster, the annular ion thruster mitigates grid spacing issues by providing a central support to the grids. For the Hall thruster, multiple, nested channels have been tested to kW power levels.

Both concepts have been tested only for short periods of time and further testing is needed. As a consequence, demonstrated performance and life testing are lacking. High-power thruster testing, in general, has not been prioritized because traditional spacecraft cannot provide the power levels necessary to operate them in space.

Lithium MPD thruster research to date has demonstrated promising results, there is little data on performance, electrode lifetime, and thermal response at power levels above kWe. Work to date has not demonstrated the physics of the magnetic nozzle used to accelerate the plasma, the life of the device, and the implementation of superconducting magnet coils, all of which are required to meet efficiency requirements.

If a standard PPU approach is needed, then the PPU architecture, requirements, and risks will be similar for those of other EP systems, albeit at a much higher power level. For a directdrive approach, the PPU is greatly simplified, but it still must provide power and control for cathode operation, magnet coils, thruster current control feedback to the PMS, thruster ignition and shutdown transients, thruster throttling if required , and any thruster-to-thruster interactions that might occur in a multi-thruster system where the plasma plumes interact.

Additionally, PPUs may be required to manage power during fast transients that occur normally during thruster operation and during component failures, which can induce large power transients in an integrated system and may be exacerbated for multi-thruster systems.

While a significant challenge, a potential advantageous factor may be the use of direct-drive PMAD, in which the power from the power conversion subsystem is already configured to match thruster beam requirements. This approach could substantially reduce PPU specific mass; however, only laboratory simulations of direct drive have been performed, with laboratory power supplies supplying the other low voltage and power components needed by a thruster, and without a full assessment of control during transients.

For instance, the simulated direct drive of an ion thruster by a Brayton conversion device was only for the V thruster beam power; other thruster components such as cathodes were operated using laboratory power supplies. Additionally, system reliability and fault protection requirements for flight systems will increase the PPU mass. The two most mature thruster concepts, ion and Hall thrusters, both use xenon propellant.

There is extensive flight experience with the storage and distribution of xenon for orbital and interplanetary missions. Xenon is stored at high pressure as a supercritical gas, with pressure and flow regulation to the thrusters. Of course, this is still orders of magnitude below the amount of propellant which may be around , kg that will be required for the baseline mission, and it is not clear how the propellant tank mass will scale for these very large propellant loads.

At a concept modeling and analysis level, NEP shows promise for the baseline mission. However, intermittent funding has resulted in very limited, if any, advance in its technology readiness since , and that work focused on kWe NEP systems, not the MWe-class system required for this application.

The need to extrapolate from those results to a 1 to 2 MWe system required for the baseline mission without increasing specific mass results in considerable uncertainty in feasibility of this path on a timeline consistent with the baseline mission. In particular, uncertainty in fuel system architecture and the significant scaling of thruster requirements and thermal and power management are considerable challenges. The reliability and lifetime requirements of such a system merit careful attention and the lack of any substantive integrated system test remains a challenge.

The present state of NEP technology and limited subsystem ground test facilities for reactors and high-power EP thrusters require near-term assessment. Advanced reactor test facilities are currently under development for terrestrial programs, but the extent to which those facilities would be able to contribute to the development of MWe-class NEP systems remains to be determined.

EP has benefited from gradual increases in power level for solar powered spacecraft. There are currently hundreds of kilowatt-electric-class spacecraft flying operationally and a 40 kWe SEP system, using multiple 13 kWe thrusters, is projected to launch in However, testing thrusters at power levels above 50 kWe, particularly for in-space performance and lifetime, will challenge existing vacuum facility capabilities.

Electromagnetic ion thrusters use the Lorentz force to move the propellant ions. Electrodeless Plasma Thruster. Helicon Double Layer Thruster. Magnetoplasmadynamic thruster , a travelling wave plasma accelerator. Propellant is potassium seeded helium. Impulsive electric rockets can accelerate propellant using magnetoplasmadynamic traveling waves MPD T-waves. In the design shown, superfluid magnetic helium-3 is accelerated using a megahertz pulsed system, in which a few hundred kiloamps of currents briefly develop extremely high electromagnetic forces.

The accelerator sequentially trips a column of distributed superconducting L-C circuits that shoves out the fluid with a magnetic piston. The propellant is micrograms of regolith dust entrained by the superfluid helium. Each J pulse requires a millifarad of total capacitance at a few hundred volts. Compared to ion drives, MPDs have good thrust densities and have no need for charge neutralization.

However, they run hot and have electrodes that will erode over time. Moreover, small amounts of an expensive superfluid medium are continually required. Pulsed inductive thruster. Pulsed plasma thruster. One of my mentors, Dr. Roger C. Jones of the University of Arizona, has worked out the physics of this. A plasmoid rocket creates a torus of ball lightning by directing a mega-amp of current onto the propellant.

Almost any sort of propellant will work. The plasmoid is expanded down a diverging electrically conducting nozzle. Magnetic and thermal energies are converted to directed kinetic energy by the interaction of the plasmoid with the image currents it generates in the nozzle. Unlike other electric rockets, a plasmoid thruster requires no electrodes which are susceptible to erosion and its power can be scaled up simply by increasing the pulse rate.

The design illustrated has a meter diameter structure that does quadruple duty as a nozzle, laser focuser, high gain antenna, and radiator. Laser power 60 MW from a remote laser power station is directed onto gap photovoltaics to charge the ultracapacitor bank used to generate the drive pulses.

This propulsion system has a combination of exhaust velocity and thrust which is unlike all the other propulsion systems. I guess this means there are some missions this engine would be optimal for. A new concept for generation of thrust for space propulsion is introduced. Energetic thrust is generated in the form of plasmoids confined plasma in closed magnetic loops when magnetic helicity linked magnetic field lines is injected into an annular channel.

Using a novel configuration of static electric and magnetic fields, the concept utilizes a current-sheet instability to spontaneously and continuously create plasmoids via magnetic reconnection. The generated low-temperature plasma is simulated in a global annular geometry using the extended magnetohydrodynamic model. Because the system-size plasmoid is an Alfvenic outflow from the reconnection site, its thrust is proportional to the square of the magnetic field strength and does not ideally depend on the mass of the ion species of the plasma.

Natural plasma engines such as the sun continuously generate enormous magnetic energy with complex field topology, and release this magnetic energy in other forms. In the solar corona region, the linkage and the complexity of field lines, magnetic helicity, is injected through twisting field lines via shear motion of their foot points. This build up of magnetic helicity is then released through the process of magnetic reconnection, i.

On the surface of the sun, the process of magnetic helicity injection provides the reconnection sites for oppositely-directed fields lines to come together to reconnect and energize. In this letter, we introduce a novel thruster concept, which takes advantage of a similar effect to convert magnetic energy to kinetic energy to produce thrust. In this concept, the reconnection sites are also generated via helicity injection, but by driving current along open field lines rather than twisting them via shear motion.

This concept is based on the combination of two key physical effects, I magnetic helicity injection and II axisymmetric magnetic reconnection. Significant thrust is generated in the form of plasmoids confined plasma objects in closed magnetic loops when helicity is injected into a cylindrical vessel to induce magnetic reconnection. This new concept, capable of reaching high and variable exhaust velocities could complement existing designs for such missions.

This is quantitatively expressed by the Tsiolkovsky rocket equation,. To surpass the exhaust velocity allowed by limited chemical energy density and reaction rates, electromagnetic propulsion can be used. Existing space-proven plasma thrusters can reach a specific impulse I sp of about a couple of thousands seconds i. High-thrust electromagnetic propulsion with I sp of tens of thousand of seconds is needed to explore the solar system beyond the Moon and Mars, as well as to rendevouz with asteroids, to deflect them if they are on a collision course with Earth, or to capture them for use as a source of water and construction materials to support human presence in space.

Here, we show that these high specific impulses could be achieved through continuous production of plasmoids to accelerate ions via a magnetic reconnection process. Magnetic reconnection, which is ubiquitous in natural plasmas, energizes many astrophysical settings throughout our solar system including corona solar flares , solar wind, planetary interiors and magnetospheres and references therein], as well as throughout our universe, such as flares from accretion disks around supermassive black holes.

Magnetic reconnection causes particle acceleration to high energies, heating, energy and momentum transport, and self-organization. The Parker Solar Probe also provides access to a new frontier for exploring and providing observational evidence of large-and small scale reconnecting structures in the solar corona. In laboratory fusion plasmas plasmoid mediated reconnection has shown to be important during plasma startup formation, nonlinear growth of an internal kink mode, as well as transient explosive events such as edge localized modes in tokamaks.

Here, we demonstrate a practical application of plasmoid mediated reconnection, namely for space propulsion. The new type of plasma thruster we are here proposing uses an innovative magnetic configuration to inject magnetic helicity using two annular electrodes biased by a voltage source, thereby inducing spontaneous reconnection via formation of a current sheet, which continuously breaks and generates plasmoids.

The concept of biasing open field lines to stretch lines of force and form "plasma rings" was first introduced in the so-called coaxial plasma gun accelerator experiments in Since then, coaxial annular plasma accelerators have been extensively used and evolved for various applications, including for fusion plasmas to form spheromaks and to fuel tokamaks with compact toroids.

The plasma accelerator has also been proposed as a magnetoplasmadynamic MPD thruster for propulsion applications and for generating high-velocity plasma jets. In our new concept the acceleration is instead due to magnetic reconnection. Unlike existing plasma accelerators, the thrust is generated from the acceleration of bulk fluid due to continuous formation of reconnecting plasmoids in the magnetohydrodynamic MHD regime.

Neither external pulsing nor rotating fields are required here for acceleration through reconnection. Axisymmetric reconnecting plasmoids are secondary magnetic islands, which are formed due to plasmoid instability. At high Lundquist number, the elongated current sheet becomes MHD unstable due to the plasmoid instability, an example of spontaneous reconnection. Our thruster concept is based on the formation of this elongated current sheet for triggering fast reconnection and plasmoid formation.

However, for thruster application we desire system-size MHD plasmoid formation with radius ranging from a few to tens of centimeters , where kinetic effects become subdominant for low-temperature plasma in the range of a few eV to a couple of tens of eV. Here, the MHD plasmoid mediated reconnection occurs at high Lundquist number about 10 4 and above , which is achieved at high magnetic field rather than low magnetic diffusivity or high temperature.

To form a single or multiple X-point reconnection site, oppositely-directed biased magnetic field in the range of G is injected through a narrow gap in an annular device. We find that the plasmoid structures demonstrated in resistive or extended MHD simulations produce high exhaust velocity and thrust that scale favorably with applied magnetic field. Figure 1 shows the main parts of the reconnecting plasmoid thruster in an annular configuration.

Magnetic-helicity injection starts with an initial injector poloidal field B P inj , in blue, with radial, R, and vertical, Z, components , connecting the inner and outer biased plates in the injector region. Gas is injected and partially ionized by applying an injector voltage V inj of a few hundred volts between the inner and outer plates indicated by numbers 1 and 2 , which also drives a current I inj along the open magnetic field lines.

The plasma formation through electron impact ionization has been widely used by plasma accelerators and other helicity injection experiments. The conventional Townsend avalanche breakdown theory is applicable for coaxial helicity injection experiments, a configuration similar to the thruster proposed here.

Up to this point the concept of magnetic helicity injection through the linkage of the injected poloidal field and injected azimuthal field from poloidal current along the open field lines is similar to the conventional annular accelerators. However, at this stage we introduce the new concept of plasmoid-mediated reconnection for generating thrust, i. To continuesly form a current sheet at the reconnection site, the detachment and shaping poloidal fields, B P D and B P S shown in Fig.

These coils can be effectively used to strongly and radially squeeze the injector poloidal field to cause oppositely directed field lines in the Z direction shown in blue arrows at the reconnection site to reconnect. To form this reconnection site, the currents in the detachment and shaping coils are in the opposite direction of the current in the injector coil, and the detachment-coil current is of equal or larger magnitude than the injector-coil current.

As a result, azimuthally symmetric system-sized plasmoid structures are detached and ejected to produce thrust. In general I inj could vary from a few to a few hundred kA. We have not yet performed a systematic optimization, but tentatively the optimal parameter range for this new thruster will be I SP specific impulse from 2, to 50, s, power from 0. It would thus occupy a complementary part of parameter space with little overlap with existing thrusters.

In helicity injection startup plasma experiments with an injection region similar to here , plasma has been efficiently produced, and both plasma and magnetic fields have been successfully injected via an injector gap. The fundamentals of plasma production and ionization for this concept are essentially the same as for an unmagnetized DC gas discharge.

As shown by, for keeping the operating voltage in a reasonable range of a few hundred volts for acceptable cathode sputtering and good ionization efficiency , the Paschen curve imposes a minimum gas pressure. Operating voltages from a few hundred up to a thousand volts have routinely been used for helicity injection experiments, including plasma accelerators as well as plasma startup for current-drive.

Significant cathode erosion from sputtering or arcing in the injector region has not been reported. For long-pulse operation, the cathode is sometimes coated with graphite or tungsten to minimize sputtering. Once the plasmoid has formed, the simulations show that it stays away from the walls and should therefore not contribute to wall erosion. In the simulations walls provide the necessary boundary conditions in the domain, however more evolved versions of this thruster might in fact be wall less.

The details of neutral dynamics also remain for future work. Here, we have presented a new concept for generation of thrust for space propulsion. With a low plasma temperature of only a few eV, the plasmoid objects, which could have diameters as large as several tens of centimeters, are generated in a fluid-like MHD and two-fluid Hall regime and move with the center of mass of plasma. The concept is explored via 3-D extended MHD simulations of reconnecting plasmoid formation during helicity injection into an annular channel.

Based on the simulations above, we find that there are fundamentally several advantages of this novel thruster, including:. The first qualitative experimental evidence of plasmoid formation demonstrated there was first predicted by global MHD simulations, later expanded for plasmoid-driven startup in spherical tokamaks. The extended MHD simulations presented here have been instrumental for exploring the fundamental physics of this new concept. However, more detailed physics for example neutral dynamics and multi-fluid effects could be numerically investigated in a future study to develop predictive capabilities for building a prototype device.

Some classify this as an electromagnetic plasma, some as an electrodeless electrothermal. The variable specific impulse magnetoplasma rocket is a plasma drive with the amusing ability to " shift gears. Three "gears" are shown on the table. There are more details here and here. A chemical rocket tug would require 60 metric tons of liquid oxygen - liquid hydrogen propellant. Granted the VASIMR tug would take six month transit time as opposed to the three days for the chemical, but there are always trade offs.

The variable-specific-impulse magnetoplasma rocket VASIMR has two unique features: the removal of the anode and cathode electrodes which greatly increases its lifetime compared to other electric rockets and the ability to throttle the engine, exchanging thrust for specific impulse. Propellant typically hydrogen, although many other volatiles can be used is first ionized by helicon waves and then transferred to a second magnetic chamber where it is accelerated to ten million degrees K by an oscillating electric and magnetic fields, also known as the ponderomotive force.

Franklin Chang-Diaz, et al. Electrostatic ion thrusters use the Coulomb force to move the propellant ions. When I was a little boy, the My First Big Book of Outer Space Rocketships type books I was constantly reading usually stated that ion drives would use mercury or cesium as propellant. But most NASA spacecraft are using xenon.

What's the story? Ionization energy represents a large percentage of the energy needed to run ion drives. In addition, the propellant should not erode the thruster to any great degree to permit long life; and should not contaminate the vehicle. Many current designs use xenon gas, as it is easy to ionize, has a reasonably high atomic number, is inert and causes low erosion.

However, xenon is globally in short supply and expensive. Older designs used mercury, but this is toxic and expensive, tended to contaminate the vehicle with the metal and was difficult to feed accurately. Other propellants, such as bismuth and iodine, show promise, particularly for gridless designs, such as Hall effect thrusters.

Field-Emission Electric Propulsion typically use caesium or indium as the propellant due to their high atomic weights, low ionization potentials and low melting points. Central City and the other bases that had been established with such labor were islands of life in an immense wilderness, oases in a silent desert of blazing light or inky darkness. There had been many who had asked whether the effort needed to survive here was worthwhile, since the colonization of Mars and Venus offered much greater opportunities.

But for all the problems it presented him, Man could not do without the Moon. It had been his first bridgehead in space, and was still the key to the planets. The liners that plied from world to world obtained all their propellent mass here, filling their great tanks with the finely divided dust which the ionic rockets would spit out in electrified jets. By obtaining that dust from the Moon, and not having to lift it through the enormous gravity field of Earth, it had been possible to reduce the cost of spacetravel more than ten-fold.

Indeed, without the Moon as a refueling base, economical space-flight could never have been achieved. The spacecraft then will attempt to redirect the object into a stable orbit around the moon. Within that limited ARM context, a conservative engineering approach using an existing deep-space propulsion system e. Our interest in near Earth objects NEOs should be more expansive than one or a few missions, though.

This essay examines an alternative propulsion system with substantial promise for future space industrialization using asteroidal resources returned to HEO. Electrostatic propulsion is the method used by many deep space probes currently in operation such as the Dawn spacecraft presently wending its way towards the asteroid Ceres. For that probe and several others, xenon gas is ionized and then electrical potential is used to accelerate the ions until they exit the engine at exhaust velocities of 15—50 kilometers per second, much higher than for chemical rocket engines, at which point the exhaust is electrically neutralized.

This method produces very low thrust and is not suitable for takeoff from planets or moons. However, in deep space and integrated over long periods of engine operation time, the gentle push of an ion engine can impart a very significant velocity change to a spacecraft, and do so extremely efficiently: for the Deep Space 1 spacecraft, the ion engine imparted 4.

The solar system has planets, asteroids, rocks, sand, and dust, all of which can pose dangers to space missions. The larger objects can be detected in advance and avoided, but the very tiny objects cannot, and it is of interest to understand the effects of hypervelocity impacts of microparticles on spacesuits, instruments and structures. For over a half century, researchers have been finding ways to accelerate microparticles to hypervelocities 1 to kilometers per second in vacuum chambers here on Earth, slamming those particles into various targets and then studying the resultant impact damage.

These microparticles are charged and then accelerated using an electrical potential field. It is a natural step to consider, instead of atomic-scale xenon ions, the application to deep space propulsion of the electrostatic acceleration of much, much larger microparticles :. However, their high exhaust velocity is poorly matched to typical mission requirements and therefore, wastes energy. A better match would be intermediate between the two forms of propulsion. This could be achieved by electrostatically accelerating solid powder grains.

Several papers have researched such a possibility. There are many potential sources of powder or dust in the solar system with which to power such a propulsion system. NEOs could be an ideal source, as hinted at in a presentation :. Asteroid sample return missions would benefit from development of an improved rocket engine… This could be achieved by electrostatically accelerating solid powder grains, raising the possibility that interplanetary material could be processed to use as reaction mass.

Imagine a vehicle that is accelerated to escape velocity by a conventional rocket. It then uses some powder lifted from Earth for deep-space propulsion to make its way to a NEO, where it lands, collects a large amount of already-fractured regolith, and then takes off again.

It is already known that larger NEOs such as Itokawa have extensive regolith blankets. Furthermore, recent research suggests that thermal fatigue is the driving force for regolith creation on NEOs ; if that is true, then even much smaller NEOs might have regolith layers. Additionally, some classes of NEOs such as carbonaceous chondrites are expected to have extremely low mechanical strength; for such NEOs, it would be immaterial whether or not pre-existing regolith layers were present, as the crumbly material of the NEO could be crushed easily.

After leaving the NEO, onboard crushers and grinders convert small amounts of the regolith to very fine powder. These processes would be perfected in low Earth orbit using regolith simulant long before the first asteroid mission. Electrostatic grids accelerate and expel the powder at high exit velocities.

Not all of the regolith onboard is powdered, only that which is used as propellant: a substantial amount of unprocessed regolith is returned to HEO. The Dawn spacecraft consumes about grams of xenon propellant per day. For asteroid redirect missions, a much higher power spacecraft with greater propellant capacity than Dawn is needed, and NASA is considering one with kilowatt arrays and 12 metric tons of xenon ion propellant , versus just 0.

If that 12 metric tons were consumed over a four-year period, then that would equate to 8. The machinery required to collect, crush, and powder a similar mass of regolith per hour need not be extremely large because initial hard rock fracturing would not be required. It is plausible that the entire system—regolith collection equipment, rock crushing, powdering, and other material processing equipment—might not be much larger than the 12 metric tons of xenon propellant envisioned by NASA.

One of the attractions of the scheme described here is that this system could be started with one or a few vehicles, and then later scaled to any desired throughput by adding vehicles. Suppose that, on average, a single vehicle could complete a round-trip and return tons of asteroidal material to HEO once every four years.

After arrival in HEO, maintenance is performed on the vehicle. Some of the remaining regolith is powdered and becomes propellant for the outbound leg of the next NEO mission. A fleet of ten such vehicles could return 1, tons per year on average of asteroidal material, while a fleet of such vehicles could return 10, tons per year.

The system described is scalable to any desired throughput by the addition of vehicles. Mass production of such vehicles would reduce unit costs. A system of many such vehicles would be resilient to the failure of any single one. If one of the many vehicles were lost, then the throughput rate of return of asteroidal material to HEO would be reduced, but the system as a whole would survive.

Replacement vehicles could be launched from Earth, or perhaps the failed vehicle could also be returned to HEO for repair by one of the other vehicles. The scheme discussed in this essay would use powdered asteroidal regolith instead of xenon, and would save not only the material cost of the xenon ion propellant itself, but also the vastly larger cost of launching that propellant from Earth each time.

Over several or many missions, the initial cost of developing the powdered asteroid propulsion approach would justify itself economically. Over dozens or hundreds of missions, the asteroidal material returned to HEO could serve as radiation shielding, as a powder propellant source for all sorts of beyond-Earth-orbit missions and transportation in cislunar space, and as input fodder for many industrial and manufacturing processes, such as the production of oxygen or solar cells.

All of this advanced processing could be conducted in HEO, where a telecommunications round-trip of a second or two would allow most operations to be economically controlled from the surface of the Earth using telerobotics. By contrast, the processing that happens outside of Earth orbit would be limited to the collection, crushing, and powdering of regolith.

These latter and simpler processes would be completed largely autonomously. Low Earth orbit LEO is reachable from the surface of the Earth in eight minutes, and geosynchronous orbit—the beginning of HEO—is reachable within eight hours. The proximity of LEO and HEO to the seven billion people on Earth and their associated economic activity is a strong indication that cislunar space will become the future economic home of humankind. In the architecture described here, raw material is slowly delivered to HEO over time via a fleet of regolith-processing, electrostatically-propelled vehicles; by contrast, humans arrive quickly to HEO from Earth.

This NEO-based ISRU architecture could be the foundation of massive economic growth off-planet, enabling the construction mostly from asteroidal materials of massive solar power stations, communications hubs, orbital hotels and habitats, and other facilities. One of the ideas I had been thinking of blogging about was the thought of augmenting Enhanced Gravity Tractor EGT asteroid deflection with in-situ derived propellants.

The gravitation attraction force is usually the bottleneck in how fast you can do an asteroid deflection, but in some situations the propellant load might matter too. That would imply getting somewhere between 16x the thrust per unit time as running the same amount of power through the HET. One nice thing is that some of this material can be gathered while landing to gather the additional mass for the enhanced gravity tractor. USER One of the things that makes ion thrusters so bulky and problematic are the magnetic shields required to protect from high temperatures, right?

And we have high temperatures because we use plasma, right? So why don't we just use fine metallic dust, charge it and feed it into an ion thruster to get rid of the temperature problem? The force acting on them is proportional to the charge and the external field applied, which we can treat as fixed for a specific engine design.

Naturally, the heavier the particle is, the less it is accelerated by this force. Now we can use an external voltage to charge this particle up. As the elementary charge is 1.

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