Arc-Driven Rail Gun Research
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Chapter 3 Dynamics of the Electromagnetic Fields
Chapter 3 Dynamics of the Electromagnetic Fields 3.1 Maxwell Displacement Current In the early 1860s (during the American civil war!) electricity including induction was well established experimentally. A big row was going on about theory. The warring camps were divided into the • Action-at-a-distance advocates and the • Field-theory advocates. James Clerk Maxwell was firmly in the field-theory camp. He invented mechanical analogies for the behavior of the fields locally in space and how the electric and magnetic influences were carried through space by invisible circulating cogs. Being a consumate mathematician he also formulated differential equations to describe the fields. In modern notation, they would (in 1860) have read: ρ �.E = Coulomb’s Law �0 ∂B � ∧ E = − Faraday’s Law (3.1) ∂t �.B = 0 � ∧ B = µ0j Ampere’s Law. (Quasi-static) Maxwell’s stroke of genius was to realize that this set of equations is inconsistent with charge conservation. In particular it is the quasi-static form of Ampere’s law that has a problem. Taking its divergence µ0�.j = �. (� ∧ B) = 0 (3.2) (because divergence of a curl is zero). This is fine for a static situation, but can’t work for a time-varying one. Conservation of charge in time-dependent case is ∂ρ �.j = − not zero. (3.3) ∂t 55 The problem can be fixed by adding an extra term to Ampere’s law because � � ∂ρ ∂ ∂E �.j + = �.j + �0�.E = �. j + �0 (3.4) ∂t ∂t ∂t Therefore Ampere’s law is consistent with charge conservation only if it is really to be written with the quantity (j + �0∂E/∂t) replacing j. -
High Speed Linear Induction Motor Efficiency Optimization
Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 2005-06 High speed linear induction motor efficiency optimization Johnson, Andrew P. (Andrew Peter) http://hdl.handle.net/10945/11052 High Speed Linear Induction Motor Efficiency Optimization by Andrew P. Johnson B.S. Electrical Engineering SUNY Buffalo, 1994 Submitted to the Department of Ocean Engineering and the Department of Electrical Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degree of Naval Engineer and Master of Science in Electrical Engineering and Computer Science at the Massachusetts Institute of Technology June 2005 ©Andrew P. Johnson, all rights reserved. MIT hereby grants the U.S. Government permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part. Signature of A uthor ................ ............................... D.epartment of Ocean Engineering May 7, 2005 Certified by. ..... ........James .... ... ....... ... L. Kirtley, Jr. Professor of Electrical Engineering // Thesis Supervisor Certified by......................•........... ...... ........................S•:• Timothy J. McCoy ssoci t Professor of Naval Construction and Engineering Thesis Reader Accepted by ................................................. Michael S. Triantafyllou /,--...- Chai -ommittee on Graduate Students - Depa fnO' cean Engineering Accepted by . .......... .... .....-............ .............. Arthur C. Smith Chairman, Committee on Graduate Students DISTRIBUTION -
This Chapter Deals with Conservation of Energy, Momentum and Angular Momentum in Electromagnetic Systems
This chapter deals with conservation of energy, momentum and angular momentum in electromagnetic systems. The basic idea is to use Maxwell’s Eqn. to write the charge and currents entirely in terms of the E and B-fields. For example, the current density can be written in terms of the curl of B and the Maxwell Displacement current or the rate of change of the E-field. We could then write the power density which is E dot J entirely in terms of fields and their time derivatives. We begin with a discussion of Poynting’s Theorem which describes the flow of power out of an electromagnetic system using this approach. We turn next to a discussion of the Maxwell stress tensor which is an elegant way of computing electromagnetic forces. For example, we write the charge density which is part of the electrostatic force density (rho times E) in terms of the divergence of the E-field. The magnetic forces involve current densities which can be written as the fields as just described to complete the electromagnetic force description. Since the force is the rate of change of momentum, the Maxwell stress tensor naturally leads to a discussion of electromagnetic momentum density which is similar in spirit to our previous discussion of electromagnetic energy density. In particular, we find that electromagnetic fields contain an angular momentum which accounts for the angular momentum achieved by charge distributions due to the EMF from collapsing magnetic fields according to Faraday’s law. This clears up a mystery from Physics 435. We will frequently re-visit this chapter since it develops many of our crucial tools we need in electrodynamics. -
United States Patent (19) 11 4,343,223 Hawke Et Al
United States Patent (19) 11 4,343,223 Hawke et al. 45) Aug. 10, 1982 54 MULTIPLESTAGE RAILGUN UCRL-52778, (7/6/79). Hawke. 75 Inventors: Ronald S. Hawke, Livermore; UCRL-82296, (10/2/79) Hawke et al. Jonathan K. Scudder, Pleasanton; Accel. Macropart, & Hypervel. EM Accelerator, Bar Kristian Aaland, Livermore, all of ber (3/72) Australian National Univ., Canberra ACT Calif. pp. 71,90–93. LA-8000-G (8/79) pp. 128, 135-137, 140, 144, 145 73) Assignee: The United States of America as (Marshall pp. 156-161 (Muller et al). represented by the United States Department of Energy, Washington, Primary Examiner-Sal Cangialosi D.C. Attorney, Agent, or Firm-L. E. Carnahan; Roger S. Gaither; Richard G. Besha . - (21) Appl. No.: 153,365 57 ABSTRACT 22 Filed: May 23, 1980 A multiple stage magnetic railgun accelerator (10) for 51) Int. Cl........................... F41F1/00; F41F 1/02; accelerating a projectile (15) by movement of a plasma F41F 7/00 arc (13) along the rails (11,12). The railgun (10) is di 52 U.S. Cl. ....................................... ... 89/8; 376/100; vided into a plurality of successive rail stages (10a-n) - 124/3 which are sequentially energized by separate energy 58) Field of Search .................... 89/8; 124/3; 310/12; sources (14a-n) as the projectile (15) moves through the 73/12; 376/100 bore (17) of the railgun (10). Propagation of energy from an energized rail stage back towards the breech 56) References Cited end (29) of the railgun (10) can be prevented by connec U.S. PATENT DOCUMENTS tion of the energy sources (14a-n) to the rails (11,12) 2,783,684 3/1957 Yoler ...r. -
Permanent Magnet DC Motors Catalog
Catalog DC05EN Permanent Magnet DC Motors Drives DirectPower Series DA-Series DirectPower Plus Series SC-Series PRO Series www.electrocraft.com www.electrocraft.com For over 60 years, ElectroCraft has been helping engineers translate innovative ideas into reality – one reliable motor at a time. As a global specialist in custom motor and motion technology, we provide the engineering capabilities and worldwide resources you need to succeed. This guide has been developed as a quick reference tool for ElectroCraft products. It is not intended to replace technical documentation or proper use of standards and codes in installation of product. Because of the variety of uses for the products described in this publication, those responsible for the application and use of this product must satisfy themselves that all necessary steps have been taken to ensure that each application and use meets all performance and safety requirements, including all applicable laws, regulations, codes and standards. Reproduction of the contents of this copyrighted publication, in whole or in part without written permission of ElectroCraft is prohibited. Designed by stilbruch · www.stilbruch.me ElectroCraft DirectPower™, DirectPower™ Plus, DA-Series, SC-Series & PRO Series Drives 2 Table of Contents Typical Applications . 3 Which PMDC Motor . 5 PMDC Drive Product Matrix . .6 DirectPower Series . 7 DP20 . 7 DP25 . 9 DP DP30 . 11 DirectPower Plus Series . 13 DPP240 . 13 DPP640 . 15 DPP DPP680 . 17 DPP700 . 19 DPP720 . 21 DA-Series. 23 DA43 . 23 DA DA47 . 25 SC-Series . .27 SCA-L . .27 SCA-S . .29 SC SCA-SS . 31 PRO Series . 33 PRO-A04V36 . 35 PRO-A08V48 . 37 PRO PRO-A10V80 . -
Magnetism Known to the Early Chinese in 12Th Century, and In
Magnetism Known to the early Chinese in 12th century, and in some detail by ancient Greeks who observed that certain stones “lodestones” attracted pieces of iron. Lodestones were found in the coastal area of “Magnesia” in Thessaly at the beginning of the modern era. The name of magnetism derives from magnesia. William Gilbert, physician to Elizabeth 1, made magnets by rubbing Fe against lodestones and was first to recognize the Earth was a large magnet and that lodestones always pointed north-south. Hence the use of magnetic compasses. Book “De Magnete” 1600. The English word "electricity" was first used in 1646 by Sir Thomas Browne, derived from Gilbert's 1600 New Latin electricus, meaning "like amber". Gilbert demonstrates a “lodestone” compass to ER 1. Painting by Auckland Hunt. John Mitchell (1750) found that like electric forces magnetic forces decrease with separation (conformed by Coulomb). Link between electricity and magnetism discovered by Hans Christian Oersted (1820) who noted a wire carrying an electric current affected a magnetic compass. Conformed by Andre Marie Ampere who shoes electric currents were source of magnetic phenomena. Force fields emanating from a bar magnet, showing Nth and Sth poles (credit: Justscience 2017) Showing magnetic force fields with Fe filings (Wikipedia.org.) Earth’s magnetic field (protects from damaging charged particles emanating from sun. (Credit: livescience.com) Magnetic field around wire carrying a current (stackexchnage.com) Right hand rule gives the right sign of the force (stackexchnage.com) Magnetic field generated by a solenoid (miniphyiscs.com) Van Allen radiation belts. Energetic charged particles travel along B lines Electric currents (moving charges) generate magnetic fields but can magnetic fields generate electric currents. -
Magnetohydrodynamics 1 19.1Overview
Contents 19 Magnetohydrodynamics 1 19.1Overview...................................... 1 19.2 BasicEquationsofMHD . 2 19.2.1 Maxwell’s Equations in the MHD Approximation . ..... 4 19.2.2 Momentum and Energy Conservation . .. 8 19.2.3 BoundaryConditions. 10 19.2.4 Magneticfieldandvorticity . .. 12 19.3 MagnetostaticEquilibria . ..... 13 19.3.1 Controlled thermonuclear fusion . ..... 13 19.3.2 Z-Pinch .................................. 15 19.3.3 Θ-Pinch .................................. 17 19.3.4 Tokamak.................................. 17 19.4 HydromagneticFlows. .. 18 19.5 Stability of Hydromagnetic Equilibria . ......... 22 19.5.1 LinearPerturbationTheory . .. 22 19.5.2 Z-Pinch: Sausage and Kink Instabilities . ...... 25 19.5.3 EnergyPrinciple ............................. 28 19.6 Dynamos and Reconnection of Magnetic Field Lines . ......... 29 19.6.1 Cowling’stheorem ............................ 30 19.6.2 Kinematicdynamos............................ 30 19.6.3 MagneticReconnection. 31 19.7 Magnetosonic Waves and the Scattering of Cosmic Rays . ......... 33 19.7.1 CosmicRays ............................... 33 19.7.2 Magnetosonic Dispersion Relation . ..... 34 19.7.3 ScatteringofCosmicRays . 36 0 Chapter 19 Magnetohydrodynamics Version 1219.1.K.pdf, 7 September 2012 Please send comments, suggestions, and errata via email to [email protected] or on paper to Kip Thorne, 350-17 Caltech, Pasadena CA 91125 Box 19.1 Reader’s Guide This chapter relies heavily on Chap. 13 and somewhat on the treatment of vorticity • transport in Sec. 14.2 Part VI, Plasma Physics (Chaps. 20-23) relies heavily on this chapter. • 19.1 Overview In preceding chapters, we have described the consequences of incorporating viscosity and thermal conductivity into the description of a fluid. We now turn to our final embellishment of fluid mechanics, in which the fluid is electrically conducting and moves in a magnetic field. -
Mutual Inductance
Chapter 11 Inductance and Magnetic Energy 11.1 Mutual Inductance ............................................................................................ 11-3 Example 11.1 Mutual Inductance of Two Concentric Coplanar Loops ............... 11-5 11.2 Self-Inductance ................................................................................................. 11-5 Example 11.2 Self-Inductance of a Solenoid........................................................ 11-6 Example 11.3 Self-Inductance of a Toroid........................................................... 11-7 Example 11.4 Mutual Inductance of a Coil Wrapped Around a Solenoid ........... 11-8 11.3 Energy Stored in Magnetic Fields .................................................................. 11-10 Example 11.5 Energy Stored in a Solenoid ........................................................ 11-11 Animation 11.1: Creating and Destroying Magnetic Energy............................ 11-12 Animation 11.2: Magnets and Conducting Rings ............................................. 11-13 11.4 RL Circuits ...................................................................................................... 11-15 11.4.1 Self-Inductance and the Modified Kirchhoff's Loop Rule....................... 11-15 11.4.2 Rising Current.......................................................................................... 11-18 11.4.3 Decaying Current..................................................................................... 11-20 11.5 LC Oscillations .............................................................................................. -
Discrete and Continuous Model of Three-Phase Linear Induction Motors “Lims” Considering Attraction Force
energies Article Discrete and Continuous Model of Three-Phase Linear Induction Motors “LIMs” Considering Attraction Force Nicolás Toro-García 1 , Yeison A. Garcés-Gómez 2 and Fredy E. Hoyos 3,* 1 Department of Electrical and Electronics Engineering & Computer Sciences, Universidad Nacional de Colombia—Sede Manizales, Cra 27 No. 64 – 60, Manizales, Colombia; [email protected] 2 Unidad Académica de Formación en Ciencias Naturales y Matemáticas, Universidad Católica de Manizales, Cra 23 No. 60 – 63, Manizales, Colombia; [email protected] 3 Facultad de Ciencias—Escuela de Física, Universidad Nacional de Colombia—Sede Medellín, Carrera 65 No. 59A-110, 050034, Medellín, Colombia * Correspondence: [email protected]; Tel.: +57-4-4309000 Received: 18 December 2018; Accepted: 14 February 2019; Published: 18 February 2019 Abstract: A fifth-order dynamic continuous model of a linear induction motor (LIM), without considering “end effects” and considering attraction force, was developed. The attraction force is necessary in considering the dynamic analysis of the mechanically loaded linear induction motor. To obtain the circuit parameters of the LIM, a physical system was implemented in the laboratory with a Rapid Prototype System. The model was created by modifying the traditional three-phase model of a Y-connected rotary induction motor in a d–q stationary reference frame. The discrete-time LIM model was obtained through the continuous time model solution for its application in simulations or computational solutions in order to analyze nonlinear behaviors and for use in discrete time control systems. To obtain the solution, the continuous time model was divided into a current-fed linear induction motor third-order model, where the current inputs were considered as pseudo-inputs, and a second-order subsystem that only models the currents of the primary with voltages as inputs. -
Lecture 4: Magnetohydrodynamics (MHD), MHD Equilibrium, MHD Waves
HSE | Valery Nakariakov | Solar Physics 1 Lecture 4: Magnetohydrodynamics (MHD), MHD Equilibrium, MHD Waves MHD describes large scale, slow dynamics of plasmas. More specifically, we can apply MHD when 1. Characteristic time ion gyroperiod and mean free path time, 2. Characteristic scale ion gyroradius and mean free path length, 3. Plasma velocities are not relativistic. In MHD, the plasma is considered as an electrically conducting fluid. Gov- erning equations are equations of fluid dynamics and Maxwell's equations. A self-consistent set of MHD equations connects the plasma mass density ρ, the plasma velocity V, the thermodynamic (also called gas or kinetic) pressure P and the magnetic field B. In strict derivation of MHD, one should neglect the motion of electrons and consider only heavy ions. The 1-st equation is mass continuity @ρ + r(ρV) = 0; (1) @t and it states that matter is neither created or destroyed. The 2-nd is the equation of motion of an element of the fluid, "@V # ρ + (Vr)V = −∇P + j × B; (2) @t also called the Euler equation. The vector j is the electric current density which can be expressed through the magnetic field B. Mind that on the lefthand side it is the total derivative, d=dt. The 3-rd equation is the energy equation, which in the simplest adiabatic case has the form d P ! = 0; (3) dt ργ where γ is the ratio of specific heats Cp=CV , and is normally taken as 5/3. The temperature T of the plasma can be determined from the density ρ and the thermodynamic pressure P , using the state equation (e.g. -
DC Motor Workshop
DC Motor Annotated Handout American Physical Society A. What You Already Know Make a labeled drawing to show what you think is inside the motor. Write down how you think the motor works. Please do this independently. This important step forces students to create a preliminary mental model for the motor, which will be their starting point. Since they are writing it down, they can compare it with their answer to the same question at the end of the activity. B. Observing and Disassembling the Motor 1. Use the small screwdriver to take the motor apart by bending back the two metal tabs that hold the white plastic end-piece in place. Pull off this plastic end-piece, and then slide out the part that spins, which is called the armature. 2. Describe what you see. 3. How do you think the motor works? Discuss this question with the others in your group. C. Mounting the Armature 1. Use the diagram below to locate the commutator—the split ring around the motor shaft. This is the armature. Shaft Commutator Coil of wire (electromagnetic) 2. Look at the drawing on the next page and find the brushes—two short ends of bare wire that make a "V". The brushes will make electrical contact with the commutator, and gravity will hold them together. In addition the brushes will support one end of the armature and cradle it to prevent side- to-side movement. 1 3. Using the cup, the two rubber bands, the piece of bare wire, and the three pieces of insulated wire, mount the armature as in the diagram below. -
31295005665780.Pdf
DESIGN AND CONSTRUCTION OF A THREE HUNDRED kA BREECH SIMULATION RAILGUN by BRETT D. SMITH, B.S. in M.E. A THESIS IN -ELECTRICAL ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING Jtpproved Accepted December, 1989 ACKNOWLEDGMENTS I would like to thank Dr. Magne Kristiansen for serving as the advisor for my grad uate work as well as serving as chairman of my thesis committee. I am also appreciative of the excellent working environment provided by Dr. Kristiansen at the laboratory. I would also like to thank my other two thesis committee members, Dr. Lynn Hatfield and Dr. Edgar O'Hair, for their advice on this thesis. I would like to thank Greg Engel for his help and advice in the design and construc tion of the experiment. I am grateful to Lonnie Stephenson for his advice and hard work in the construction of the experiment. I would also like to thank Danny Garcia, Mark Crawford, Ellis Loree, Diana Loree, and Dan Reynolds for their help in various aspects of this work. I owe my deepest appreciation to my parents for their constant support and encour agement. The engineering advice obtained from my father proved to be invaluable. 11 CONTENTS .. ACKNOWLEDGMENTS 11 ABSTRACT lV LIST OF FIGURES v CHAPTER I. INTRODUCTION 1 II. THEORY OF RAILGUN OPERATION 4 III. DESIGN AND CONSTRUCTION OF MAX II 27 Railgun System Design 28 Electrical Design and Construction 42 Mechanical Design and Construction 59 Diagnostics Design and Construction 75 IV.