The Larmor Formula (Chapters 18-19)
|
|
- Isabella Elliott
- 5 years ago
- Views:
Transcription
1 Dispersive Media, Lecture 12 - Thomas Johnson 1 The Larmor Formula (Chapters 18-19) T. Johnson
2 Outline Brief repetition of emission formula The emission from a single free particle - the Larmor formula Applications of the Larmor formula Harmonic oscillator Cyclotron radiation Thompson scattering Bremstrahlung Next lecture: Relativistic generalisation of Larmor formula Repetition of basic relativity Co- and contra-variant tensor notation and Lorentz transformations Relativistic Larmor formula The Lienard-Wiechert potentials Inductive and radiative electromagnetic fields Alternative derivation of the Larmor formula Abraham-Lorentz force Dispersive Media, Lecture 12 - Thomas Johnson 2
3 Repetition: Emission formula The energy emitted by a wave mode M (using antihermitian part of the propagator), when integrating over the δ-function in ω the emission formula for U M ; the density of emission in k-space Emission per frequency and solid angle Rewrite integral: d " k = k % dkd % Ω = k % '( )(+) '+ dωd% Ω Here k/ is the unit vector in the k-direction Dispersive Media, Lecture 12 - Thomas Johnson 3
4 Repetition: Emission from multipole moments Multipole moments are related to the Fourier transform of the current: Emission formula (k-space power density) Emission formula (integrated over solid angles) Dispersive Media, Lecture 12 - Thomas Johnson 4
5 Current from a single particle Let s calculate the radiation from a single particle at X(t) with charge q. The density, n, and current, J, from the particle: or in Fourier space 5 J ω, k = q 3 dt e d " k e 8k:x X t δ x X t = 5 = q 3 dt e i k : X(t) + X t = 5 = iωqx ω + 3 dt e 68+9 i k : X(t) X t + Dipole: d=qx Dispersive Media, Lecture 12 - Thomas Johnson 5
6 Dispersive Media, Lecture 12 - Thomas Johnson 6 Dipole current from single particle Thus, the field from a single particle is approximately a dipole field When is this approximation valid? Assume oscillating motion: - The dipole approximation is based on the small term: Dipole approx. valid for non-relativistic motion
7 Dispersive Media, Lecture 12 - Thomas Johnson 7 Emission from a single particle Emission from single particle; use dipole formulas from last lecture: V F ω, Ω = q % 2πc " ε K n F ω M for the special case of purely transverse waves q % e F : X(ω) % 1 e F : κ % V F ω, Ω = 2πc " n ε F ω M κ X(ω) % K Note: this is emission per unit frequency and unit solid angle Integrate over solid angle for transverse waves Note: there s no preferred direction, thus 2-tensor is proportional to Kroneker delta ~δ jm ; but k j k j =k 2, thus
8 Dispersive Media, Lecture 12 - Thomas Johnson 8 Emission from single particle Thus, the energy per unit frequency emitted to transverse waves from single non-relativistic particle 4π V F ω = q % 6π % c " ε K n F ω % X(ω) % An alternative is in terms of the acceleration a and the net force F 4π V F ω = q % 6π % c " ε K n F a (ω) % 4π V F ω = q % F (ω) 6π % c " n ε F K m %
9 Dispersive Media, Lecture 12 - Thomas Johnson 9 Larmor formula for the emission from single particle Total energy W radiated in vacuum (n M =1) W = 4π 3 dω K 5 V F ω = q % 6π % c " ε K 3 dω Rewrite by noting that a(ω) is even and then use the power theorem K 5 a (ω) % Thus, the energy radiated over all time is a time integral The average radiated power, P ave, will be given by the average acceleration a ave The Larmor formula
10 Dispersive Media, Lecture 12 - Thomas Johnson 10 Larmor formula for the emission from single particle Strictly, the Larmor formula gives the time averaged radiated power In many cases the Larmor formula describes roughly the power radiated during an event Larmor formula then gives the radiated power averaged over the event Therefore, the conventional way to write the Larmor formula goes one step further and describe the instantaneous emission radiation is only emitted when particles are accelerated!
11 Outline Brief repetition of emission formula The emission from a single free particle - the Larmor formula Applications of the Larmor formula Harmonic oscillator Cyclotron radiation Thompson scattering Bremstrahlung Dispersive Media, Lecture 12 - Thomas Johnson 11
12 Applications: Harmonic oscillator As a first example, consider the emission from a particle performing an harmonic oscillation harmonic oscillations Larmor formula: the emitted power associated with this acceleration oscillation cos 2 (ω 0 t) should be averaged over a period Dispersive Media, Lecture 12 - Thomas Johnson 12
13 Dispersive Media, Lecture 12 - Thomas Johnson 13 Applications: Harmonic oscillator frequency spectum Express the particle as a dipole d, use truncation for Fourier transform The time-averaged power emitted from a dipole
14 Applications: cyclotron emission An important emission process from magnetised particles is from the acceleration involved in cyclotron motion consider a charged particle moving in a static magnetic field B=B z e z where is the cyclotron frequency z where we have the Larmor radius Dispersive Media, Lecture 12 - Thomas Johnson 14
15 Dispersive Media, Lecture 12 - Thomas Johnson 15 Applications: cyclotron emission Cyclotron emission from a single particle where is the velocity perpendicular to B. Sum the emission over a Maxwellian distribution function, f M (v) where n is the particle density and T is the temperature in Joules. Magnetized plasma; power depends on the density and temperature: Electron cyclotron emission is one of the most common ways to measure the temperature of a fusion plasma!
16 Applications: wave scattering Consider a particle being accelerated by an external wave field The Larmor formula then tell us the average emitted power Note: that this is only valid in vacuum (restriction of Larmor formula) Rewrite in term of the wave energy density W 0 in vacuum : P\ dw K dt = 8π 3 q % 4πε K mc % cw K Interpretation: this is the fraction of the power density that is scattered by the particle, i.e. first absorbed and then re-emitted Dispersive Media, Lecture 12 - Thomas Johnson 16
17 Dispersive Media, Lecture 12 - Thomas Johnson 17 Applications: wave scattering The scattering process can be interpreted as a collision Consider a density of wave quanta representing the energy density W 0 The wave quanta, or photons, move with velocity c (speed of light) Imagine a charged particle as a ball with a cross section σ T The power of from photons bouncing off the charged particle, i.e. scattered, per unit time is given by thus the effective cross section for wave scattering is hω Cross section area σ T of the particle r 0 Density of incoming photons Photons hitting this area are scattered
18 Dispersive Media, Lecture 12 - Thomas Johnson 18 Applications: Thomson scattering Scattering of waves against electrons is called Thomson scattering from this process the classical radius of the electron was defined as Note: this is an effective radius for Thomson scattering and not a measure of the real size of the electron Examples of Thomson scattering: In fusion devices, Thomson scattering of a high-intensity laser beam is used for measuring the electron temperatures and densities. The cosmic microwave background is thought to be linearly polarized as a result of Thomson scattering The continous spectrum from the solar corona is the result of the Thomson scattering of solar radiation with free electrons
19 Thompson scattering system at the fusion experiment JET Thompson scattering systems at JET primarily measures temperatures Laser beam Laser source in a different room Dispersive Media, Lecture 12 - Thomas Johnson 19
20 Dispersive Media, Lecture 12 - Thomas Johnson 20 Thompson scattering system at the fusion experiment JET Detectors Scattered light scattering
21 Applications: Bremsstrahlung Bremsstrahlung (~Braking radiation) come from the acceleration associated with electrostatic collisions between charged particles (called Coulomb collisions) Note that the electrostatic force is long range E~1/r 2 thus electrostatic collisions between charged particles is a smooth continuous processes unlike collision between balls on a pool table Consider an electron moving near an ion with charge Ze since the ion is heavier than the electron, we assume X ion (t)=0 the equation of motion for the electron and the emitted power are this is the Bremsstrahlung radiation at one time of one single collision to estimate the total power from a medium we need to integrate over both the entire collision and all ongoing collisions! Dispersive Media, Lecture 12 - Thomas Johnson 21
22 Dispersive Media, Lecture 12 - Thomas Johnson 22 Bremsstrahlung: Coulomb collisions Lets try and integrate the emission over all times where we integrate in the distance to the ion r Now we need r min and So, let the ion be stationary at the origin Let the electron start at (x,y,z)=(,b,0) with velocity v=(-v 0,0,0) The conservation of angular momentum and energy gives b This is the Kepler problem for the motion of the planets! Next we need the minimum distance between ion and electron r min
23 Dispersive Media, Lecture 12 - Thomas Johnson 23 Bremsstrahlung: Coulomb collisions Coulomb collisions are mainly due to long range interactions, i.e. particles are far apart, and only slightly change their trajectories (there are exceptions in high density plasmas) thus and we are then ready to evaluate the time integrated emission This is the emission from a single collision The cumulative emission from all particles and with all possible b and v 0 has no simple general solution (and is outside the scope of this course) An approximate: Bremsstrahlung can be used to derive information about both the charge, density and temperature of the media
24 X-ray tubes Typical frequency of Bremsstrahlung is in X-ray regime Bremsstrahlung is the main source of radiation in X-ray tubes electrons are accelerated to high velocity When impacting on a metal surface they emit bremsstrahlung X-ray tubes may also emit line radiation. Counts per second Line radiation Wavelength, (pm) Dispersive Media, Lecture 12 - Thomas Johnson 24
25 Applications for X-ray and bremsstrahlung X-rays have been used in medicine since Wilhelm Röntgen s discovery of the X-ray in 1895 Radiographs produce images of e.g. bones Radiotherapy is used to treat cancer for skin cancer, use low energy X-ray, not to penetrate too deep for breast or cancer, use higher energies for deeper penetration Crystallography: used to identify the crystal/atomic patterns of a material study diffraction of X-rays X-ray flourescence: scattered X-ray carry information about chemical composition. Industrial CT scanner e.g. airport and cargo scanners Dispersive Media, Lecture 12 - Thomas Johnson 25
26 Applications of Bremsstrahlung Astrophysics: High temerature stellar objects T ~ K radiate primarily in via bremsstrahlung Note: surface of the sun K Fusion: Measurements of Bremsstrahlung provide information on the prescence of impurities with high charge, temperature and density Energy losses by Bremsstrahlung and cyclotron radiation: Temperature at the centre of fusion plasma: ~10 8 K ; the walls are ~10 3 K Main challenge for fusion is to confine heat in plasma core Bremsstrahlung and cyclotron radiation leave plasma at speed of light! In reactor, radiation losses will be of importance limits the reactor design If plasma gets too hot, then radiation losses cool down the plasma. Inirtial fusion: lasers shines on a tube that emits bremstrahlung, which then heats the D-T pellet Dispersive Media, Lecture 12 - Thomas Johnson 26
27 Summary When charged particles accelerated they emits radiation This emission is described by the Larmor formula P = 1 6πε K c " q% a % Important applications: Cyclotron emission magnetised plasmas Thompson scattering photons bounce off electrons Bremstrahlung main source of X-ray radiation All these are used extensively for studying e.g. fusion plasmas Dispersive Media, Lecture 12 - Thomas Johnson 27
Special relativity and light RL 4.1, 4.9, 5.4, (6.7)
Special relativity and light RL 4.1, 4.9, 5.4, (6.7) First: Bremsstrahlung recap Braking radiation, free-free emission Important in hot plasma (e.g. coronae) Most relevant: thermal Bremsstrahlung What
More informationCLASSICAL ELECTRICITY
CLASSICAL ELECTRICITY AND MAGNETISM by WOLFGANG K. H. PANOFSKY Stanford University and MELBA PHILLIPS Washington University SECOND EDITION ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo
More informationElectrodynamics of Radiation Processes
Electrodynamics of Radiation Processes 7. Emission from relativistic particles (contd) & Bremsstrahlung http://www.astro.rug.nl/~etolstoy/radproc/ Chapter 4: Rybicki&Lightman Sections 4.8, 4.9 Chapter
More informationBremsstrahlung Radiation
Bremsstrahlung Radiation Wise (IR) An Example in Everyday Life X-Rays used in medicine (radiographics) are generated via Bremsstrahlung process. In a nutshell: Bremsstrahlung radiation is emitted when
More informationClassical Electrodynamics
Classical Electrodynamics Third Edition John David Jackson Professor Emeritus of Physics, University of California, Berkeley JOHN WILEY & SONS, INC. Contents Introduction and Survey 1 I.1 Maxwell Equations
More informationRadiative Processes in Astrophysics
Radiative Processes in Astrophysics 9. Synchrotron Radiation Eline Tolstoy http://www.astro.rug.nl/~etolstoy/astroa07/ Useful reminders relativistic terms, and simplifications for very high velocities
More informationAstrophysical Radiation Processes
PHY3145 Topics in Theoretical Physics Astrophysical Radiation Processes 3: Relativistic effects I Dr. J. Hatchell, Physics 407, J.Hatchell@exeter.ac.uk Course structure 1. Radiation basics. Radiative transfer.
More informationNotes on x-ray scattering - M. Le Tacon, B. Keimer (06/2015)
Notes on x-ray scattering - M. Le Tacon, B. Keimer (06/2015) Interaction of x-ray with matter: - Photoelectric absorption - Elastic (coherent) scattering (Thomson Scattering) - Inelastic (incoherent) scattering
More informationBremsstrahlung. Rybicki & Lightman Chapter 5. Free-free Emission Braking Radiation
Bremsstrahlung Rybicki & Lightman Chapter 5 Bremsstrahlung Free-free Emission Braking Radiation Radiation due to acceleration of charged particle by the Coulomb field of another charge. Relevant for (i)
More informationRadiative Processes in Astrophysics
Radiative Processes in Astrophysics 6. Relativistic Covariance & Kinematics Eline Tolstoy http://www.astro.rug.nl/~etolstoy/astroa07/ Practise, practise, practise... mid-term, 31st may, 9.15-11am As we
More informationRadiative processes from energetic particles II: Gyromagnetic radiation
Hale COLLAGE 2017 Lecture 21 Radiative processes from energetic particles II: Gyromagnetic radiation Bin Chen (New Jersey Institute of Technology) e - Shibata et al. 1995 e - magnetic reconnection Previous
More information- Potentials. - Liénard-Wiechart Potentials. - Larmor s Formula. - Dipole Approximation. - Beginning of Cyclotron & Synchrotron
- Potentials - Liénard-Wiechart Potentials - Larmor s Formula - Dipole Approximation - Beginning of Cyclotron & Synchrotron Maxwell s equations in a vacuum become A basic feature of these eqns is the existence
More informationAccelerator Physics NMI and Synchrotron Radiation. G. A. Krafft Old Dominion University Jefferson Lab Lecture 16
Accelerator Physics NMI and Synchrotron Radiation G. A. Krafft Old Dominion University Jefferson Lab Lecture 16 Graduate Accelerator Physics Fall 17 Oscillation Frequency nq I n i Z c E Re Z 1 mode has
More informationˆd = 1 2π. d(t)e iωt dt. (1)
Bremsstrahlung Initial questions: How does the hot gas in galaxy clusters cool? What should we see in their inner portions, where the density is high? As in the last lecture, we re going to take a more
More informationClassical Field Theory
April 13, 2010 Field Theory : Introduction A classical field theory is a physical theory that describes the study of how one or more physical fields interact with matter. The word classical is used in
More informationRetarded Potentials and Radiation
Retarded Potentials and Radiation No, this isn t about potentials that were held back a grade :). Retarded potentials are needed because at a given location in space, a particle feels the fields or potentials
More informationIntroduction to Plasma Physics
Introduction to Plasma Physics Hartmut Zohm Max-Planck-Institut für Plasmaphysik 85748 Garching DPG Advanced Physics School The Physics of ITER Bad Honnef, 22.09.2014 A simplistic view on a Fusion Power
More informationCompton Scattering I. 1 Introduction
1 Introduction Compton Scattering I Compton scattering is the process whereby photons gain or lose energy from collisions with electrons. It is an important source of radiation at high energies, particularly
More informationLaser Cooling and Trapping of Atoms
Chapter 2 Laser Cooling and Trapping of Atoms Since its conception in 1975 [71, 72] laser cooling has revolutionized the field of atomic physics research, an achievement that has been recognized by the
More informationElectromagnetic Waves
Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 23 Electromagnetic Waves Marilyn Akins, PhD Broome Community College Electromagnetic Theory Theoretical understanding of electricity and magnetism
More informationCHAPTER 3 The Experimental Basis of Quantum Theory
CHAPTER 3 The Experimental Basis of Quantum Theory 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 Discovery of the X Ray and the Electron Determination of Electron Charge Line Spectra Quantization As far as I can
More informationPhysics 221B Spring 2018 Notes 34 The Photoelectric Effect
Copyright c 2018 by Robert G. Littlejohn Physics 221B Spring 2018 Notes 34 The Photoelectric Effect 1. Introduction In these notes we consider the ejection of an atomic electron by an incident photon,
More informationRadiation processes and mechanisms in astrophysics I. R Subrahmanyan Notes on ATA lectures at UWA, Perth 18 May 2009
Radiation processes and mechanisms in astrophysics I R Subrahmanyan Notes on ATA lectures at UWA, Perth 18 May 009 Light of the night sky We learn of the universe around us from EM radiation, neutrinos,
More informationAstrophysical Radiation Processes
PHY3145 Topics in Theoretical Physics Astrophysical Radiation Processes 5:Synchrotron and Bremsstrahlung spectra Dr. J. Hatchell, Physics 406, J.Hatchell@exeter.ac.uk Course structure 1. Radiation basics.
More informationScattering of Electromagnetic Radiation. References:
Scattering of Electromagnetic Radiation References: Plasma Diagnostics: Chapter by Kunze Methods of experimental physics, 9a, chapter by Alan Desilva and George Goldenbaum, Edited by Loveberg and Griem.
More informationGravity and action at a distance
Gravitational waves Gravity and action at a distance Newtonian gravity: instantaneous action at a distance Maxwell's theory of electromagnetism: E and B fields at distance D from charge/current distribution:
More informationInsertion Devices Lecture 2 Wigglers and Undulators. Jim Clarke ASTeC Daresbury Laboratory
Insertion Devices Lecture 2 Wigglers and Undulators Jim Clarke ASTeC Daresbury Laboratory Summary from Lecture #1 Synchrotron Radiation is emitted by accelerated charged particles The combination of Lorentz
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 1 (2/3/04) Overview -- Interactions, Distributions, Cross Sections, Applications
.54 Neutron Interactions and Applications (Spring 004) Chapter 1 (/3/04) Overview -- Interactions, Distributions, Cross Sections, Applications There are many references in the vast literature on nuclear
More informationThe atom cont. +Investigating EM radiation
The atom cont. +Investigating EM radiation Announcements: First midterm is 7:30pm on Sept 26, 2013 Will post a past midterm exam from 2011 today. We are covering Chapter 3 today. (Started on Wednesday)
More informationRelativistic corrections of energy terms
Lectures 2-3 Hydrogen atom. Relativistic corrections of energy terms: relativistic mass correction, Darwin term, and spin-orbit term. Fine structure. Lamb shift. Hyperfine structure. Energy levels of the
More informationPhysics Important Terms and their Definitions
Physics Important Terms and their S.No Word Meaning 1 Acceleration The rate of change of velocity of an object with respect to time 2 Angular Momentum A measure of the momentum of a body in rotational
More informationApplied Nuclear Physics (Fall 2006) Lecture 19 (11/22/06) Gamma Interactions: Compton Scattering
.101 Applied Nuclear Physics (Fall 006) Lecture 19 (11//06) Gamma Interactions: Compton Scattering References: R. D. Evans, Atomic Nucleus (McGraw-Hill New York, 1955), Chaps 3 5.. W. E. Meyerhof, Elements
More informationRadiative Processes in Flares I: Bremsstrahlung
Hale COLLAGE 2017 Lecture 20 Radiative Processes in Flares I: Bremsstrahlung Bin Chen (New Jersey Institute of Technology) The standard flare model e - magnetic reconnection 1) Magnetic reconnection and
More informationDipole Approxima7on Thomson ScaEering
Feb. 28, 2011 Larmor Formula: radia7on from non- rela7vis7c par7cles Dipole Approxima7on Thomson ScaEering The E, B field at point r and 7me t depends on the retarded posi7on r(ret) and retarded 7me t(ret)
More informationMITOCW watch?v=wr88_vzfcx4
MITOCW watch?v=wr88_vzfcx4 PROFESSOR: So we're building this story. We had the photoelectric effect. But at this moment, Einstein, in the same year that he was talking about general relativity, he came
More informationPhysics 504, Lecture 22 April 19, Frequency and Angular Distribution
Last Latexed: April 16, 010 at 11:56 1 Physics 504, Lecture April 19, 010 Copyright c 009 by Joel A Shapiro 1 Freuency and Angular Distribution We have found the expression for the power radiated in a
More informationPhysics Lecture 6
Physics 3313 - Lecture 6 Monday February 8, 2010 Dr. Andrew Brandt 1. HW1 Due today HW2 weds 2/10 2. Electron+X-rays 3. Black body radiation 4. Compton Effect 5. Pair Production 2/8/10 3313 Andrew Brandt
More informationStudy of Optical Properties of Tokamak Plasma
Study of Optical Properties of Tokamak Plasma Sabri Naima Ghoutia 1, Benouaz Tayeb 2 1 University of Bechar, POB 417, Street Kenadsa, Bechar,08000, Algeria. 2 University of Tlemcen, POB 119, 13000, Algeria.
More informationCHAPTER 11 RADIATION 4/13/2017. Outlines. 1. Electric Dipole radiation. 2. Magnetic Dipole Radiation. 3. Point Charge. 4. Synchrotron Radiation
CHAPTER 11 RADIATION Outlines 1. Electric Dipole radiation 2. Magnetic Dipole Radiation 3. Point Charge Lee Chow Department of Physics University of Central Florida Orlando, FL 32816 4. Synchrotron Radiation
More informationIntroduction to electron and photon beam physics. Zhirong Huang SLAC and Stanford University
Introduction to electron and photon beam physics Zhirong Huang SLAC and Stanford University August 03, 2015 Lecture Plan Electron beams (1.5 hrs) Photon or radiation beams (1 hr) References: 1. J. D. Jackson,
More informationChapter 37 Early Quantum Theory and Models of the Atom
Chapter 37 Early Quantum Theory and Models of the Atom Units of Chapter 37 37-7 Wave Nature of Matter 37-8 Electron Microscopes 37-9 Early Models of the Atom 37-10 Atomic Spectra: Key to the Structure
More informationParticle nature of light & Quantization
Particle nature of light & Quantization A quantity is quantized if its possible values are limited to a discrete set. An example from classical physics is the allowed frequencies of standing waves on a
More information1 Monday, October 31: Relativistic Charged Particles
1 Monday, October 31: Relativistic Charged Particles As I was saying, before the midterm exam intervened, in an inertial frame of reference K there exists an electric field E and a magnetic field B at
More informationRecap Lecture + Thomson Scattering. Thermal radiation Blackbody radiation Bremsstrahlung radiation
Recap Lecture + Thomson Scattering Thermal radiation Blackbody radiation Bremsstrahlung radiation LECTURE 1: Constancy of Brightness in Free Space We use now energy conservation: de=i ν 1 da1 d Ω1 dt d
More informationCHAPTER 3 Prelude to Quantum Theory. Observation of X Rays. Thomson s Cathode-Ray Experiment. Röntgen s X-Ray Tube
CHAPTER Prelude to Quantum Theory.1 Discovery of the X Ray and the Electron. Determination of Electron Charge. Line Spectra.4 Quantization.5 Blackbody Radiation.6 Photoelectric Effect.7 X-Ray Production.8
More informationEP118 Optics. Content TOPIC 1 LIGHT. Department of Engineering Physics University of Gaziantep
EP11 Optics TOPIC 1 LIGHT Department of Engineering Physics University of Gaziantep July 2011 Sayfa 1 Content 1. History of Light 2. Wave Nature of Light 3. Quantum Theory of Light 4. Elecromagnetic Wave
More informationRb, which had been compressed to a density of 1013
Modern Physics Study Questions for the Spring 2018 Departmental Exam December 3, 2017 1. An electron is initially at rest in a uniform electric field E in the negative y direction and a uniform magnetic
More informationChapter 11. Radiation. How accelerating charges and changing currents produce electromagnetic waves, how they radiate.
Chapter 11. Radiation How accelerating charges and changing currents produce electromagnetic waves, how they radiate. 11.1.1 What is Radiation? Assume a radiation source is localized near the origin. Total
More information1 Monday, November 7: Synchrotron Radiation for Beginners
1 Monday, November 7: Synchrotron Radiation for Beginners An accelerated electron emits electromagnetic radiation. The most effective way to accelerate an electron is to use electromagnetic forces. Since
More informationRadiative Processes in Astrophysics
Radiative Processes in Astrophysics 11. Synchrotron Radiation & Compton Scattering Eline Tolstoy http://www.astro.rug.nl/~etolstoy/astroa07/ Synchrotron Self-Absorption synchrotron emission is accompanied
More informationElectromagnetic Spectra. AST443, Lecture 13 Stanimir Metchev
Electromagnetic Spectra AST443, Lecture 13 Stanimir Metchev Administrative Homework 2: problem 5.4 extension: until Mon, Nov 2 Reading: Bradt, chapter 11 Howell, chapter 6 Tenagra data: see bottom of Assignments
More informationis the minimum stopping potential for which the current between the plates reduces to zero.
Module 1 :Quantum Mechanics Chapter 2 : Introduction to Quantum ideas Introduction to Quantum ideas We will now consider some experiments and their implications, which introduce us to quantum ideas. The
More informationUniqueness theorems, Separation of variables for Poisson's equation
NPTEL Syllabus Electrodynamics - Web course COURSE OUTLINE The course is a one semester advanced course on Electrodynamics at the M.Sc. Level. It will start by revising the behaviour of electric and magnetic
More informationBethe-Block. Stopping power of positive muons in copper vs βγ = p/mc. The slight dependence on M at highest energies through T max
Bethe-Block Stopping power of positive muons in copper vs βγ = p/mc. The slight dependence on M at highest energies through T max can be used for PID but typically de/dx depend only on β (given a particle
More informationModern Physics for Scientists and Engineers International Edition, 4th Edition
Modern Physics for Scientists and Engineers International Edition, 4th Edition http://optics.hanyang.ac.kr/~shsong Review: 1. THE BIRTH OF MODERN PHYSICS 2. SPECIAL THEORY OF RELATIVITY 3. THE EXPERIMENTAL
More informationFrequency: the number of complete waves that pass a point in a given time. It has the symbol f. 1) SI Units: Hertz (Hz) Wavelength: The length from
Frequency: the number of complete waves that pass a point in a given time. It has the symbol f. 1) SI Units: Hertz (Hz) Wavelength: The length from the one crest of a wave to the next. I. Electromagnetic
More informationSingle Particle Motion
Single Particle Motion C ontents Uniform E and B E = - guiding centers Definition of guiding center E gravitation Non Uniform B 'grad B' drift, B B Curvature drift Grad -B drift, B B invariance of µ. Magnetic
More informationDEFINITIONS. Linear Motion. Conservation of Momentum. Vectors and Scalars. Circular Motion. Newton s Laws of Motion
DEFINITIONS Linear Motion Mass: The mass of a body is the amount of matter in it. Displacement: The displacement of a body from a point is its distance from a point in a given direction. Velocity: The
More informationElectricity & Magnetism Study Questions for the Spring 2018 Department Exam December 4, 2017
Electricity & Magnetism Study Questions for the Spring 2018 Department Exam December 4, 2017 1. a. Find the capacitance of a spherical capacitor with inner radius l i and outer radius l 0 filled with dielectric
More informationElectromagnetic Radiation. Physical Principles of Remote Sensing
Electromagnetic Radiation Physical Principles of Remote Sensing Outline for 4/3/2003 Properties of electromagnetic radiation The electromagnetic spectrum Spectral emissivity Radiant temperature vs. kinematic
More informationRoger Johnson Structure and Dynamics: X-ray Diffraction Lecture 6
6.1. Summary In this Lecture we cover the theory of x-ray diffraction, which gives direct information about the atomic structure of crystals. In these experiments, the wavelength of the incident beam must
More informationPhysics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/3
Physics 201 p. 1/3 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/3 What are electromagnetic waves? Electromagnetic waves consist of electric fields and magnetic fields which
More informationParticles and Waves Particles Waves
Particles and Waves Particles Discrete and occupy space Exist in only one location at a time Position and velocity can be determined with infinite accuracy Interact by collisions, scattering. Waves Extended,
More informationLecture 03. The Cosmic Microwave Background
The Cosmic Microwave Background 1 Photons and Charge Remember the lectures on particle physics Photons are the bosons that transmit EM force Charged particles interact by exchanging photons But since they
More informationElectromagnetic Waves Properties. The electric and the magnetic field, associated with an electromagnetic wave, propagating along the z=axis. Can be represented by E = E kˆ, = iˆ E = E ˆj, = ˆj b) E =
More informationPHYSICS OF HOT DENSE PLASMAS
Chapter 6 PHYSICS OF HOT DENSE PLASMAS 10 26 10 24 Solar Center Electron density (e/cm 3 ) 10 22 10 20 10 18 10 16 10 14 10 12 High pressure arcs Chromosphere Discharge plasmas Solar interior Nd (nω) laserproduced
More informationModern physics ideas are strange! L 36 Modern Physics [2] The Photon Concept. How are x-rays produced? The uncertainty principle
L 36 Modern Physics [2] X-rays & gamma rays How lasers work Medical applications of lasers Applications of high power lasers Medical imaging techniques CAT scans MRI s Modern physics ideas are strange!
More informationIntroduction to the Diagnosis of Magnetically Confined Thermonuclear Plasma
Introduction to the Diagnosis of Magnetically Confined Thermonuclear Plasma Core diagnostics II: Bolometry and Soft X-rays J. Arturo Alonso Laboratorio Nacional de Fusión EURATOM-CIEMAT E6 P2.10 arturo.alonso@ciemat.es
More informationSemiconductor Physics and Devices
Introduction to Quantum Mechanics In order to understand the current-voltage characteristics, we need some knowledge of electron behavior in semiconductor when the electron is subjected to various potential
More informationThe Plasma Phase. Chapter 1. An experiment - measure and understand transport processes in a plasma. Chapter 2. An introduction to plasma physics
The Plasma Phase Chapter 1. An experiment - measure and understand transport processes in a plasma Three important vugraphs What we have just talked about The diagnostics Chapter 2. An introduction to
More informationCHAPTER 27. Continuum Emission Mechanisms
CHAPTER 27 Continuum Emission Mechanisms Continuum radiation is any radiation that forms a continuous spectrum and is not restricted to a narrow frequency range. In what follows we briefly describe five
More informationRadiation from a Moving Charge
Radiation from a Moving Charge 1 The Lienard-Weichert radiation field For details on this theory see the accompanying background notes on electromagnetic theory (EM_theory.pdf) Much of the theory in this
More informationThermal Bremsstrahlung
Thermal Bremsstrahlung ''Radiation due to the acceleration of a charge in the Coulomb field of another charge is called bremsstrahlung or free-free emission A full understanding of the process requires
More informationExplain how Planck resolved the ultraviolet catastrophe in blackbody radiation. Calculate energy of quanta using Planck s equation.
Objectives Explain how Planck resolved the ultraviolet catastrophe in blackbody radiation. Calculate energy of quanta using Planck s equation. Solve problems involving maximum kinetic energy, work function,
More informationPh.D. QUALIFYING EXAMINATION DEPARTMENT OF PHYSICS AND ASTRONOMY WAYNE STATE UNIVERSITY PART I. FRIDAY, May 5, :00 12:00
Ph.D. QUALIFYING EXAMINATION DEPARTMENT OF PHYSICS AND ASTRONOMY WAYNE STATE UNIVERSITY PART I FRIDAY, May 5, 2017 10:00 12:00 ROOM 245 PHYSICS RESEARCH BUILDING INSTRUCTIONS: This examination consists
More informationChapter 28. Atomic Physics
Chapter 28 Atomic Physics Quantum Numbers and Atomic Structure The characteristic wavelengths emitted by a hot gas can be understood using quantum numbers. No two electrons can have the same set of quantum
More informationUNIVERSITY OF TECHNOLOGY Laser & Opto-Electronic Eng. Dept rd YEAR. The Electromagnetic Waves
Spectroscopy Interaction of electromagnetic radiation with matter yields that energy is absorbed or emitted by matter in discrete quantities (quanta). Measurement of the frequency or (wave length) of the
More informationRadiation by Moving Charges
May 27, 2008 1 1 J.D.Jackson, Classical Electrodynamics, 3rd Edition, Chapter 14 Liénard - Wiechert Potentials The Liénard-Wiechert potential describes the electromagnetic effect of a moving charge. Built
More informationWaves, Polarization, and Coherence
Waves, Polarization, and Coherence Lectures 5 Biophotonics Jae Gwan Kim jaekim@gist.ac.kr, X 2220 School of Information and Communication Engineering Gwangju Institute of Sciences and Technology Outline
More informationNeutrinos, nonzero rest mass particles, and production of high energy photons Particle interactions
Neutrinos, nonzero rest mass particles, and production of high energy photons Particle interactions Previously we considered interactions from the standpoint of photons: a photon travels along, what happens
More informationThe Cosmic Microwave Background
The Cosmic Microwave Background Class 22 Prof J. Kenney June 26, 2018 The Cosmic Microwave Background Class 22 Prof J. Kenney November 28, 2016 Cosmic star formation history inf 10 4 3 2 1 0 z Peak of
More informationFI 3103 Quantum Physics
FI 3103 Quantum Physics Alexander A. Iskandar Physics of Magnetism and Photonics Research Group Institut Teknologi Bandung General Information Lecture schedule 17 18 9136 51 5 91 Tutorial Teaching Assistant
More informationChapter 6 Electronic structure of atoms
Chapter 6 Electronic structure of atoms light photons spectra Heisenberg s uncertainty principle atomic orbitals electron configurations the periodic table 6.1 The wave nature of light Visible light is
More informationThe Correct Derivation of Magnetism from Electrostatics Based on Covariant Formulation of Coulomb's Law
The Correct Derivation of Magnetism from Electrostatics Based on Covariant Formulation of Coulomb's Law Mueiz Gafer KamalEldeen An Independent Researcher mueizphysics@gmail.com Abstract It is shown, by
More informationX-ray non-resonant and resonant magnetic scattering Laurent C. Chapon, Diamond Light Source. European School on Magnetism L. C.
X-ray non-resonant and resonant magnetic scattering Laurent C. Chapon, Diamond Light Source 1 The Diamond synchrotron 3 GeV, 300 ma Lienard-Wiechert potentials n.b: Use S.I units throughout. rq : position
More informationChapter 2 Radiation of an Accelerated Charge
Chapter 2 Radiation of an Accelerated Charge Whatever the energy source and whatever the object, (but with the notable exception of neutrino emission that we will not consider further, and that of gravitational
More information1 Photoelectric effect - Classical treatment. 2 Photoelectric effect - Quantum treatment
1 OF 5 NOTE: This problem set is to be handed in to my mail slot (SMITH) located in the Clarendon Laboratory by 5:00 PM Tuesday, 10 May. 1 Photoelectric effect - Classical treatment A laser beam with an
More informationPhysics 2D Lecture Slides Lecture 11: Jan. 27 th Sunil Sinha UCSD Physics
Physics 2D Lecture Slides Lecture 11: Jan. 27 th 2010 Sunil Sinha UCSD Physics Einstein s Explanation of PhotoElectric Effect What Maxwell Saw of EM Waves What Einstein Saw of EM Waves Light as bullets
More informationand another with a peak frequency ω 2
Physics Qualifying Examination Part I 7-Minute Questions September 13, 2014 1. A sealed container is divided into two volumes by a moveable piston. There are N A molecules on one side and N B molecules
More informationLarbert High School. Quanta and Waves. Homework Exercises ADVANCED HIGHER PHYSICS
Larbert High School ADVANCED HIGHER PHYSICS Quanta and Waves Homework Exercises 3.1 3.6 3.1 Intro to Quantum Theory HW 1. (a) Explain what is meant by term black body. (1) (b) State two observations that
More informationCHAPTER 3 The Experimental Basis of Quantum
CHAPTER 3 The Experimental Basis of Quantum 3.1 Discovery of the X Ray and the Electron 3.2 Determination of Electron Charge 3.3 Line Spectra 3.4 Quantization 3.5 Blackbody Radiation 3.6 Photoelectric
More informationThe Development of Particle Physics. Dr. Vitaly Kudryavtsev E45, Tel.:
The Development of Particle Physics Dr. Vitaly Kudryavtsev E45, Tel.: 0114 2224531 v.kudryavtsev@sheffield.ac.uk Discovery of the muon and the pion Energy losses of charged particles. This is an important
More informationAtomic Transitions II & Molecular Structure
Atomic Transitions II & Molecular Structure Atomic Transitions II Transition Probability Dipole Approximation Line Broadening Transition Probability: The Hamiltonian To calculate explicitly the transition
More informationWhat does the Sun tell us about circular polarization on stars? Stephen White
What does the Sun tell us about circular polarization on stars? Stephen White The Radio Sun at 4.6 GHz Combination of: optically thick upper chromosphere, optically thick coronal gyroresonance where B>500
More informationClassical electric dipole radiation
B Classical electric dipole radiation In Chapter a classical model was used to describe the scattering of X-rays by electrons. The equation relating the strength of the radiated to incident X-ray electric
More informationLecture 0. NC State University
Chemistry 736 Lecture 0 Overview NC State University Overview of Spectroscopy Electronic states and energies Transitions between states Absorption and emission Electronic spectroscopy Instrumentation Concepts
More information- Synchrotron emission: A brief history. - Examples. - Cyclotron radiation. - Synchrotron radiation. - Synchrotron power from a single electron
- Synchrotron emission: A brief history - Examples - Cyclotron radiation - Synchrotron radiation - Synchrotron power from a single electron - Relativistic beaming - Relativistic Doppler effect - Spectrum
More informationAnnouncements. A test of General Relativity. Gravitational Radiation. Other Consequences of GR
Announcements HW1: Ch.2-70, 75, 76, 87, 92, 97, 99, 104, 111 *** Lab start-up meeting with TA This Week *** Lab manual is posted on the course web *** Course Web Page *** http://highenergy.phys.ttu.edu/~slee/2402/
More informationElectromagnetism Phys 3230 Exam 2005
Electromagnetism Phys Exam 5 All four questions in Phys should be addressed. If one is not certain in maths, one should try to present explanations in words. 1. Maxwell s equations (5% from 1 given for
More informationParticle Nature of Matter. Chapter 4
Particle Nature of Matter Chapter 4 Modern physics When my grandfather was born, atoms were just an idea. That year, 1897, was marked by the discovery of the electron by J.J. Thomson. The nuclear model
More information