Chapter 2 Motion of Charged Particles in Fields
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Chapter 4 SINGLE PARTICLE MOTIONS
Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction We wish now to consider the effects of magnetic fields on plasma behaviour. Especially in high temperature plasma, where collisions are rare, it is important to study the single particle motions as governed by the Lorentz force in order to understand particle confinement. Unfortunately, only for the simplest geometries can exact solutions for the force equation be obtained. For example, in a constant and uniform magnetic field we find that a charged particle spirals in a helix about the line of force. This helix, however, defines a fundamental time unit – the cyclotron frequency ωc and a fundamental distance scale – the Larmor radius rL. For inhomogeneous and time varying fields whose length L and time ω scales are large compared with ωc and rL it is often possible to expand the orbit equations in rL/L and ω/ωc. In this “drift”, guiding centre or “adiabatic” approximation, the motion is decomposed into the local helical gyration together with an equation of motion for the instantaneous centre of this gyration (the guiding centre). It is found that certain adiabatic invariants of the motion greatly facilitate understanding of the motion in complex spatio-temporal fields. We commence this chapter with an analysis of particle motions in uniform and time-invariant fields. This is followed by an analysis of time-varying electric and magnetic fields and finally inhomogeneous fields. 4.2 Constant and Uniform Fields The equation of motion is the Lorentz equation dv F = m = q(E + v×B) (4.1) dt 88 4.2.1 Electric field only In this case the particle velocity increases linearly with time (i.e. -
Particle Motion
Physics of fusion power Lecture 5: particle motion Gyro motion The Lorentz force leads to a gyration of the particles around the magnetic field We will write the motion as The Lorentz force leads to a gyration of the charged particles Parallel and rapid gyro-motion around the field line Typical values For 10 keV and B = 5T. The Larmor radius of the Deuterium ions is around 4 mm for the electrons around 0.07 mm Note that the alpha particles have an energy of 3.5 MeV and consequently a Larmor radius of 5.4 cm Typical values of the cyclotron frequency are 80 MHz for Hydrogen and 130 GHz for the electrons Often the frequency is much larger than that of the physics processes of interest. One can average over time One can not however neglect the finite Larmor radius since it lead to specific effects (although it is small) Additional Force F Consider now a finite additional force F For the parallel motion this leads to a trivial acceleration Perpendicular motion: The equation above is a linear ordinary differential equation for the velocity. The gyro-motion is the homogeneous solution. The inhomogeneous solution Drift velocity Inhomogeneous solution Solution of the equation Physical picture of the drift The force accelerates the particle leading to a higher velocity The higher velocity however means a larger Larmor radius The circular orbit no longer closes on itself A drift results. Physics picture behind the drift velocity FxB Electric field Using the formula And the force due to the electric field One directly obtains the so-called ExB velocity Note this drift is independent of the charge as well as the mass of the particles Electric field that depends on time If the electric field depends on time, an additional drift appears Polarization drift. -
Decays of the Tau Lepton*
SLAC - 292 UC - 34D (E) DECAYS OF THE TAU LEPTON* Patricia R. Burchat Stanford Linear Accelerator Center Stanford University Stanford, California 94305 February 1986 Prepared for the Department of Energy under contract number DE-AC03-76SF00515 Printed in the United States of America. Available from the National Techni- cal Information Service, U.S. Department of Commerce, 5285 Port Royal Road, Springfield, Virginia 22161. Price: Printed Copy A07, Microfiche AOl. JC Ph.D. Dissertation. Abstract Previous measurements of the branching fractions of the tau lepton result in a discrepancy between the inclusive branching fraction and the sum of the exclusive branching fractions to final states containing one charged particle. The sum of the exclusive branching fractions is significantly smaller than the inclusive branching fraction. In this analysis, the branching fractions for all the major decay modes are measured simultaneously with the sum of the branching fractions constrained to be one. The branching fractions are measured using an unbiased sample of tau decays, with little background, selected from 207 pb-l of data accumulated with the Mark II detector at the PEP e+e- storage ring. The sample is selected using the decay products of one member of the r+~- pair produced in e+e- annihilation to identify the event and then including the opposite member of the pair in the sample. The sample is divided into subgroups according to charged and neutral particle multiplicity, and charged particle identification. The branching fractions are simultaneously measured using an unfold technique and a maximum likelihood fit. The results of this analysis indicate that the discrepancy found in previous experiments is possibly due to two sources. -
Charged Particle Radiotherapy
Corporate Medical Policy Charged Particle Radiotherapy File Name: charged_particle_radiotherapy Origination: 3/12/96 Last CAP Review: 5/2021 Next CAP Review: 5/2022 Last Review: 5/2021 Description of Procedure or Service Cha rged-particle beams consisting of protons or helium ions or carbon ions are a type of particulate ra dia tion therapy (RT). They contrast with conventional electromagnetic (i.e., photon) ra diation therapy due to several unique properties including minimal scatter as particulate beams pass through tissue, and deposition of ionizing energy at precise depths (i.e., the Bragg peak). Thus, radiation exposure of surrounding normal tissues is minimized. The theoretical advantages of protons and other charged-particle beams may improve outcomes when the following conditions a pply: • Conventional treatment modalities do not provide adequate local tumor control; • Evidence shows that local tumor response depends on the dose of radiation delivered; and • Delivery of adequate radiation doses to the tumor is limited by the proximity of vital ra diosensitive tissues or structures. The use of proton or helium ion radiation therapy has been investigated in two general categories of tumors/abnormalities. However, advances in photon-based radiation therapy (RT) such as 3-D conformal RT, intensity-modulated RT (IMRT), a nd stereotactic body ra diotherapy (SBRT) a llow improved targeting of conventional therapy. 1. Tumors located near vital structures, such as intracranial lesions or lesions a long the a xial skeleton, such that complete surgical excision or adequate doses of conventional radiation therapy are impossible. These tumors/lesions include uveal melanomas, chordomas, and chondrosarcomas at the base of the skull and a long the axial skeleton. -
Basic Physics of Magnetoplasmas-I: Single Particle Drift Montions
310/1749-5 ICTP-COST-CAWSES-INAF-INFN International Advanced School on Space Weather 2-19 May 2006 _____________________________________________________________________ Basic Physics of Magnetoplasmas-I: Single Particle Drift Montions Vladimir CADEZ Astronomical Observatory Volgina 7 11160 Belgrade SERBIA AND MONTENEGRO ___________________________________________________________________________ These lecture notes are intended only for distribution to participants LECTURE 1 SINGLE PARTICLE DRIFT MOTIONS Vladimir M. Cade·z· Astronomical Observatory Belgrade Volgina 7, 11160 Belgrade, Serbia&Montenegro Email: [email protected] Gaseous plasma is a mixture of moving particles of di®erent species ® having mass m® and charge q®. UsuallyP but not necessarily always, such a plasma is globally electro-neutral, i.e. ® q® = 0. In astrophysical plasmas, we often have mixtures of two species ® = e; p or electron-proton plasmas as protons are the ionized atoms of Hydrogen, the most abundant element in the universe. Another plasma constituent of astrophysical signi¯cance are dust particles of various sizes and charges. For example, the electron-dust and electron-proton-dust plasmas (® = e; d and ® = e; p; d resp.) are now frequently studied in scienti¯c literature. Some astrophysical con¯gura- tions allow for more exotic mixtures like electron-positron plasmas (® = e¡; e+) which are steadily gaining interest among theoretical astrophysicists. In what follows, we shall primarily deal with the electron-proton, electro- neutral plasmas in magnetic ¯eld con¯gurations typical of many solar-terrestrial phenomena. To understand the physics of plasma processes in detail it is necessary to apply complex mathematical treatments of kinetic theory of ionized gases. For practical reasons, numerous approximations are introduced to the full kinetic approach which results in simpli¯ed and more applicable plasma theories. -
The Basic Interactions Between Photons and Charged Particles With
Outline Chapter 6 The Basic Interactions between • Photon interactions Photons and Charged Particles – Photoelectric effect – Compton scattering with Matter – Pair productions Radiation Dosimetry I – Coherent scattering • Charged particle interactions – Stopping power and range Text: H.E Johns and J.R. Cunningham, The – Bremsstrahlung interaction th physics of radiology, 4 ed. – Bragg peak http://www.utoledo.edu/med/depts/radther Photon interactions Photoelectric effect • Collision between a photon and an • With energy deposition atom results in ejection of a bound – Photoelectric effect electron – Compton scattering • The photon disappears and is replaced by an electron ejected from the atom • No energy deposition in classical Thomson treatment with kinetic energy KE = hν − Eb – Pair production (above the threshold of 1.02 MeV) • Highest probability if the photon – Photo-nuclear interactions for higher energies energy is just above the binding energy (above 10 MeV) of the electron (absorption edge) • Additional energy may be deposited • Without energy deposition locally by Auger electrons and/or – Coherent scattering Photoelectric mass attenuation coefficients fluorescence photons of lead and soft tissue as a function of photon energy. K and L-absorption edges are shown for lead Thomson scattering Photoelectric effect (classical treatment) • Electron tends to be ejected • Elastic scattering of photon (EM wave) on free electron o at 90 for low energy • Electron is accelerated by EM wave and radiates a wave photons, and approaching • No -
Charged Current Anti-Neutrino Interactions in the Nd280 Detector
CHARGED CURRENT ANTI-NEUTRINO INTERACTIONS IN THE ND280 DETECTOR BRYAN E. BARNHART HIGH ENERGY PHYSICS UNIVERSITY OF COLORADO AT BOULDER ADVISOR: ALYSIA MARINO Abstract. For the neutrino beamline oscillation experiment Tokai to Kamioka, the beam is clas- sified before oscillation by the near detector complex. The detector is used to measure the flux of different particles through the detector, and compare them to Monte Carlo Simulations. For this work, theν ¯µ background of the detector was isolated by examining the Monte Carlo simulation and determining cuts which removed unwanted particles. Then, a selection of the data from the near detector complex underwent the same cuts, and compared to the Monte Carlo to determine if the Monte Carlo represented the data distribution accurately. The data was found to be consistent with the Monte Carlo Simulation. Date: November 11, 2013. 1 Bryan E. Barnhart University of Colorado at Boulder Advisor: Alysia Marino Contents 1. The Standard Model and Neutrinos 4 1.1. Bosons 4 1.2. Fermions 5 1.3. Quarks and the Strong Force 5 1.4. Leptons and the Weak Force 6 1.5. Neutrino Oscillations 7 1.6. The Relative Neutrino Mass Scale 8 1.7. Neutrino Helicity and Anti-Neutrinos 9 2. The Tokai to Kamioka Experiment 9 2.1. Japan Proton Accelerator Research Complex 10 2.2. The Near Detector Complex 12 2.3. The Super-Kamiokande Detector 17 3. Isolation of the Anti-Neutrino Component of Neutrino Beam 19 3.1. Experiment details 19 3.2. Selection Cuts 20 4. Cut Descriptions 20 4.1. Beam Data Quality 20 4.2. -
The Electron Drift Velocity in the HARP TPC
HARP Collaboration HARP Memo 08-103 8 October 2008 http://cern.ch/harp-cdp/driftvelocity.pdf The electron drift velocity in the HARP TPC V. Ammosov, A. Bolshakova, I. Boyko, G. Chelkov, D. Dedovitch, F. Dydak, A. Elagin, M. Gostkin, A. Guskov, V. Koreshev, Z. Kroumchtein, Yu. Nefedov, K. Nikolaev, J. Wotschack, A. Zhemchugov Abstract Apart from the electric field strength, the drift velocity depends on gas pressure and temperature, on the gas composition and on possible gas impurities. We show that the relevant gas temperature, while uniform across the TPC volume, depends significantly on the temperature and flow rate of fresh gas. We present the correction algorithms for changes of pressure and temperature, and the precise measurement of the electron drift velocity in the HARP TPC. Contents 1 Introduction 2 2 Theoretical expectation on drift velocity variations 2 3 The TPC gas 3 4 Drift velocity variation with gas temperature 4 5 Drift velocity variation with gas pressure 6 6 The algorithm for temperature and pressure correction 7 7 Drift velocity variation with gas composition and impurities 9 8 Small-radius and large-radius tomographies 12 9 Comparison with ‘Official’ HARP's analysis 15 1 1 Introduction In a TPC, the longitudinal z coordinate is measured via the drift time. Therefore, the drift velocity of electrons in the TPC gas is a centrally important quantity for the reconstruction of charged-particle tracks. Since we are not concerned here with the drift velocity of ions, we will henceforth refer to the drift velocity of electrons simply as `drift velocity'. In this paper, we discuss first the expected dependencies of the drift velocity on temperature, pressure and gas impurities. -
Chapter 3. Fundamentals of Dosimetry
Chapter 3. Fundamentals of Dosimetry Slide series of 44 slides based on the Chapter authored by E. Yoshimura of the IAEA publication (ISBN 978-92-0-131010-1): Diagnostic Radiology Physics: A Handbook for Teachers and Students Objective: To familiarize students with quantities and units used for describing the interaction of ionizing radiation with matter Slide set prepared by E.Okuno (S. Paulo, Brazil, Institute of Physics of S. Paulo University) IAEA International Atomic Energy Agency Chapter 3. TABLE OF CONTENTS 3.1. Introduction 3.2. Quantities and units used for describing the interaction of ionizing radiation with matter 3.3. Charged particle equilibrium in dosimetry 3.4. Cavity theory 3.5. Practical dosimetry with ion chambers IAEA Diagnostic Radiology Physics: a Handbook for Teachers and Students – chapter 3, 2 3.1. INTRODUCTION Subject of dosimetry : determination of the energy imparted by radiation to matter. This energy is responsible for the effects that radiation causes in matter, for instance: • a rise in temperature • chemical or physical changes in the material properties • biological modifications Several of the changes produced in matter by radiation are proportional to absorbed dose , giving rise to the possibility of using the material as the sensitive part of a dosimeter There are simple relations between dosimetric and field description quantities IAEA Diagnostic Radiology Physics: a Handbook for Teachers and Students – chapter 3, 3 3.2. QUANTITIES AND UNITS USED FOR DESCRIBING THE INTERACTION OF IONIZING RADIATION -
Neutrino Physics
Neutrino Physics Steve Boyd University of Warwick Course Map 1. History and properties of the neutrino, neutrino interactions, beams and detectors 2. Neutrino mass, direct mass measurements, double beta decay, flavour oscillations 3. Unravelling neutrino oscillations experimentally 4. Where we are and where we're going References K. Zuber, “Neutrino Physics”, IoP Publishing 2004 C. Giunti and C.W.Kim, “Fundamentals of Neutrino Physics and Astrophysics”, Oxford University Press, 2007. R. N. Mohaptara and P. B. Pal, “Massive Neutrinos in Physics and Astrophysics”, World Scientific (2nd Edition), 1998 H.V. Klapdor-Kleingrothaus & K. Zuber, “Particle Astrophysics”,IoP Publishing, 1997. Two Scientific American articles: “Detecting Massive Neutrinos”, E. Kearns, T. Kajita, Y. Totsuka, Scientific American, August 1999. “Solving the Solar Neutrino Problem”, A.B. McDonald, J.R. Klein, D.L. Wark, Scientific American, April 2003. Plus other Handouts Lecture 1 In which history is unravelled, desperation is answered, and the art of neutrino generation and detection explained Crisis It is 1914 – the new study of atomic physics is in trouble (Z+1,A) Spin 1/2 (Z,A) Spin 1/2 Spin 1/2 electron Spin ½ ≠ spin ½ + spin ½ E ≠ E +e Ra Bi “At the present stage of atomic “Desperate remedy.....” theory we have no arguments “I do not dare publish this idea....” for upholding the concept of “I admit my way out may look energy balance in the case of improbable....” b-ray disintegrations.” “Weigh it and pass sentence....” “You tell them. I'm off to a party” Detection of the Neutrino 1950 – Reines and Cowan set out to detect n 1951 1951 1951 I. -
Exam 1 Solutions
PHY2054 Spring 2009 Prof. Pradeep Kumar Prof. Paul Avery Prof. Yoonseok Lee Feb. 4, 2009 Exam 1 Solutions 1. A proton (+e) originally has a speed of v = 2.0 ×105 m/s as it goes through a plate as shown in the figure. It shoots through the tiny +++ +++ holes in the two plates across which 16 V | 100 V | 2 V of electric potential is applied. Find the speed as it leaves the second plate. V − − − − − − Answer: 1.92 × 105 m/s | 1.44 × 105 m/s | 1.99 × 105 m/s Solution: The proton is slowed down by the electric field between v the two plates, so the velocity will be reduced. Conservation of en- 11222 ergy yields 22mvp ipf−Δ eV = mv , so vveVmf =−Δip2/. 2. Five identical charges of +1μC are located on the 5 vertices of a regular hexagon y of 1 m side leaving one vertex empty. A −1μC | −2μC | +2μC point charge is placed at the center of the hexagon. Find the magnitude and direction of the net x Coulomb force on this charge. Answer: 9.0 × 10−3 N −x-direction | 1.8 × 10−2 N −x-direction | 1.8 × 10−2 N +x-direction Solution: Only the charge on the far left contributes to the net force on the charge in the center because its contribution is not cancelled by an opposing charge. If Q represents the charge at each hexagon vertex, q is the charge at the center and d is the length of a hexagon side (note that the distance from each hexagon point to the center is also d), the force on q is kQq/ d 2 along the +x direction if Qq is positive and along the −x direction if Qq is negative.