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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. -
The University of Texas at Austin
The University of Texas at Austin Institute for Advanced Technology, The University of Texas at Austin - AUSA - February 2006 IAT Talk 1358 Eraser Institute for Advanced Technology, The University of Texas at Austin - AUSA - February 2006 IAT Talk 1358 Transitioning EM Railgun Technology to the Warfighter Dr. Harry D. Fair, Director Institute for Advanced Technology The University of Texas at Austin The Governator is correct! • At the IAT, we are harnessing large quantities of electric energy to enable radically new capabilities for the warfighter. • These new electric weapons are capable of accelerating high energy hypervelocity projectiles Electric guns are real. from electric railguns on land, sea, and air platforms, and are capable of protecting these platforms by electromagnetic protection systems. Institute for Advanced Technology, The University of Texas at Austin - AUSA - February 2006 IAT Talk 1358 Hypervelocity Electromagnetic Railguns What are they? How do they work? Why change to electromagnetic energy? How can we use them? When can we have them? What are the implications for the Army and the Navy? Institute for Advanced Technology, The University of Texas at Austin - AUSA - February 2006 IAT Talk 1358 What is an Electromagnetic Railgun? Converts Electricity to Kinetic Energy The barrel can have any cross section - round, The accelerating Force square, rectangular is provided by Electromagnetic Forces and can accelerate projectiles to very high velocities Force Muzzle view We routinely launch projectiles to hypervelocities -
Pulsed Rotating Machine Power Supplies for Electric Combat Vehicles
Pulsed Rotating Machine Power Supplies for Electric Combat Vehicles W.A. Walls and M. Driga Department of Electrical and Computer Engineering The University of Texas at Austin Austin, Texas 78712 Abstract than not, these test machines were merely modified gener- ators fitted with damper bars to lower impedance suffi- As technology for hybrid-electric propulsion, electric ciently to allow brief high current pulses needed for the weapons and defensive systems are developed for future experiment at hand. The late 1970's brought continuing electric combat vehicles, pulsed rotating electric machine research in fusion power, renewed interest in electromag- technologies can be adapted and evolved to provide the netic guns and other pulsed power users in the high power, maximum benefit to these new systems. A key advantage of intermittent duty regime. Likewise, flywheels have been rotating machines is the ability to design for combined used to store kinetic energy for many applications over the requirements of energy storage and pulsed power. An addi - years. In some cases (like utility generators providing tran- tional advantage is the ease with which these machines can sient fault ride-through capability), the functions of energy be optimized to service multiple loads. storage and power generation have been combined. Continuous duty alternators can be optimized to provide Development of specialized machines that were optimized prime power energy conversion from the vehicle engine. for this type of pulsed duty was needed. In 1977, the laser This paper, however, will focus on pulsed machines that are fusion community began looking for an alternative power best suited for intermittent and pulsed loads requiring source to capacitor banks for driving laser flashlamps. -
Arxiv:1701.07063V2 [Physics.Ins-Det] 23 Mar 2017 ACCEPTED by IEEE TRANSACTIONS on PLASMA SCIENCE, MARCH 2017 1
This work has been accepted for publication by IEEE Transactions on Plasma Science. The published version of the paper will be available online at http://ieeexplore.ieee.org. It can be accessed by using the following Digital Object Identifier: 10.1109/TPS.2017.2686648. c 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, including reprinting/republishing this material for advertising or promotional purposes, collecting new collected works for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. arXiv:1701.07063v2 [physics.ins-det] 23 Mar 2017 ACCEPTED BY IEEE TRANSACTIONS ON PLASMA SCIENCE, MARCH 2017 1 Review of Inductive Pulsed Power Generators for Railguns Oliver Liebfried Abstract—This literature review addresses inductive pulsed the inductor. Therefore, a coil can be regarded as a pressure power generators and their major components. Different induc- vessel with the magnetic field B as a pressurized medium. tive storage designs like solenoids, toroids and force-balanced The corresponding pressure p is related by p = 1 B2 to the coils are briefly presented and their advantages and disadvan- 2µ tages are mentioned. Special emphasis is given to inductive circuit magnetic field B with the permeability µ. The energy density topologies which have been investigated in railgun research such of the inductor is directly linked to the magnetic field and as the XRAM, meat grinder or pulse transformer topologies. One therefore, its maximum depends on the tensile strength of the section deals with opening switches as they are indispensable for windings and the mechanical support. -
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. -
Design and Optimization of an Electromagnetic Railgun
Michigan Technological University Digital Commons @ Michigan Tech Dissertations, Master's Theses and Master's Reports 2018 DESIGN AND OPTIMIZATION OF AN ELECTROMAGNETIC RAILGUN Nihar S. Brahmbhatt Michigan Technological University, [email protected] Copyright 2018 Nihar S. Brahmbhatt Recommended Citation Brahmbhatt, Nihar S., "DESIGN AND OPTIMIZATION OF AN ELECTROMAGNETIC RAILGUN", Open Access Master's Report, Michigan Technological University, 2018. https://doi.org/10.37099/mtu.dc.etdr/651 Follow this and additional works at: https://digitalcommons.mtu.edu/etdr Part of the Controls and Control Theory Commons DESIGN AND OPTIMIZATION OF AN ELECTROMAGNETIC RAIL GUN By Nihar S. Brahmbhatt A REPORT Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE In Electrical Engineering MICHIGAN TECHNOLOGICAL UNIVERSITY 2018 © 2018 Nihar S. Brahmbhatt This report has been approved in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE in Electrical Engineering. Department of Electrical and Computer Engineering Report Advisor: Dr. Wayne W. Weaver Committee Member: Dr. John Pakkala Committee Member: Dr. Sumit Paudyal Department Chair: Dr. Daniel R. Fuhrmann Table of Contents Abstract ........................................................................................................................... 7 Acknowledgments........................................................................................................... 8 List of Figures ................................................................................................................ -
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 .............................................................................................. -
Improvement of Electromagnetic Railgun Barrel Performance and Lifetime By
IMPROVEMENT OF ELECTROMAGNETIC RAILGUN BARREL PERFORMANCE AND LIFETIME BY METHOD OF INTERFACES AND AUGMENTED PROJECTILES A Thesis Presented to the Faculty of California Polytechnic State University San Luis Obispo In Partial Fulfillment of the Requirements for the Degree Master of Science in Aerospace Engineering by Aleksey Pavlov June 2013 c 2013 Aleksey Pavlov ALL RIGHTS RESERVED ii COMMITTEE MEMBERSHIP TITLE: Improvement of Electromagnetic Rail- gun Barrel Performance and Lifetime by Method of Interfaces and Augmented Pro- jectiles AUTHOR: Aleksey Pavlov DATE SUBMITTED: June 2013 COMMITTEE CHAIR: Kira Abercromby, Ph.D., Associate Professor, Aerospace Engineering COMMITTEE MEMBER: Eric Mehiel, Ph.D., Associate Professor, Aerospace Engineering COMMITTEE MEMBER: Vladimir Prodanov, Ph.D., Assistant Professor, Electrical Engineering COMMITTEE MEMBER: Thomas Guttierez, Ph.D., Associate Professor, Physics iii Abstract Improvement of Electromagnetic Railgun Barrel Performance and Lifetime by Method of Interfaces and Augmented Projectiles Aleksey Pavlov Several methods of increasing railgun barrel performance and lifetime are investigated. These include two different barrel-projectile interface coatings: a solid graphite coating and a liquid eutectic indium-gallium alloy coating. These coatings are characterized and their usability in a railgun application is evaluated. A new type of projectile, in which the electrical conductivity varies as a function of position in order to condition current flow, is proposed and simulated with FEA software. The graphite coating was found to measurably reduce the forces of friction inside the bore but was so thin that it did not improve contact. The added contact resistance of the graphite was measured and gauged to not be problematic on larger scale railguns. The liquid metal was found to greatly improve contact and not introduce extra resistance but its hazardous nature and tremendous cost detracted from its usability. -
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. -
Comparison of Main Magnetic Force Computation Methods for Noise and Vibration Assessment in Electrical Machines
JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, SEPTEMBER 2017 1 Comparison of main magnetic force computation methods for noise and vibration assessment in electrical machines Raphael¨ PILE13, Emile DEVILLERS23, Jean LE BESNERAIS3 1 Universite´ de Toulouse, UPS, INSA, INP, ISAE, UT1, UTM, LAAS, ITAV, F-31077 Toulouse Cedex 4, France 2 L2EP, Ecole Centrale de Lille, Villeneuve d’Ascq 59651, France 3 EOMYS ENGINEERING, Lille-Hellemmes 59260, France (www.eomys.com) In the vibro-acoustic analysis of electrical machines, the Maxwell Tensor in the air-gap is widely used to compute the magnetic forces applying on the stator. In this paper, the Maxwell magnetic forces experienced by each tooth are compared with different calculation methods such as the Virtual Work Principle based nodal forces (VWP) or the Maxwell Tensor magnetic pressure (MT) following the stator surface. Moreover, the paper focuses on a Surface Permanent Magnet Synchronous Machine (SPMSM). Firstly, the magnetic saturation in iron cores is neglected (linear B-H curve). The saturation effect will be considered in a second part. Homogeneous media are considered and all simulations are performed in 2D. The technique of equivalent force per tooth is justified by finding similar resultant force harmonics between VWP and MT in the linear case for the particular topology of this paper. The link between slot’s magnetic flux and tangential force harmonics is also highlighted. The results of the saturated case are provided at the end of the paper. Index Terms—Electromagnetic forces, Maxwell Tensor, Virtual Work Principle, Electrical Machines. I. INTRODUCTION TABLE I MAGNETO-MECHANICAL COUPLING AMONG SOFTWARE FOR N electrical machines, the study of noise and vibrations due VIBRO-ACOUSTIC I to magnetic forces first requires the accurate calculation of EM Soft Struct. -
Rehabilitation Technologies: Biomechatronics Point of View
1 Rehabilitation Technologies: Biomechatronics Point of View Erhan Akdoğan and M. Hakan Demir Yıldız Technical University Turkey 1. Introduction Rehabilitation aims to bring back the patient’s physical, sensory, and mental capabilities that were lost due to injury, illness, and disease, and to support the patient to compensate for deficits that cannot be treated medically (http://www.ehendrick.org/healthy, June 2010). After the Spinal Cord Injury (SCI), stroke, muscle disorder, and surgical operation such as knee artroplasticy, patients need rehabilitation to recover their movement capability (mobilization) (Bradly et al., 2000; Inal, 2000; Metrailler et al., 2007; Okada et al., 2000; Reinkensmeyer, 2003 and http://www.manchesterneurophysio.co.uk, November 2010). The number of those who need rehabilitation is steadily increasing everyday. Parallel to this, equipment and techniques used in the field of rehabilitation are becoming more advanced and sophisticated. On the other hand, mechatronics, an interdisciplinary science, is a combination of machinery, electric-electronics and computer sciences plays an important role in rehabilitation technologies. In particular mechatronics systems provide important benefits for movements that are related to physical exercises in rehabilitation process. Biomechatronics is a sub-discipline of mechatronics. It is related to develop mechatronics systems which assist or restore to human body. A biomechatronic system has four units: Biosensors, Mechanical Sensors, Controller, and Actuator. Biosensors detect intentions of human using biological reactions coming from nervous or muscle system. The controller acts as a translator between biological and electronic systems, and also monitors the movements of the biomechatronic device. Mechanical sensors measure information about the biomechatronic device and relay to the biosensor or controller.