Lecture 1 Introduction to RF for Accelerators. Dr G Burt Lancaster University Engineering
|
|
- Cecily Lawrence
- 5 years ago
- Views:
Transcription
1 Lecture 1 Introduction to RF for Accelerators Dr G Burt Lancaster University Engineering
2 Electrostatic Acceleration
3 Van-de Graaff s A standard electrostatic accelerator is a Van de Graaf These devices are limited to about 30 MV by the voltage hold off across ceramic insulators used to generate the high voltages (dielectric breakdown).
4 RF Acceleration By switching the charge on the plates in phase with the particle motion we can cause the particles to always see an acceleration You only need to hold off the voltage between two plates not the full accelerating voltage of the accelerator. We cannot use smooth wall waveguide to contain rf in order to accelerate a beam as the phase velocity is faster than the speed of light, hence we cannot keep a bunch in phase with the wave.
5 Early Linear Accelerators (Drift Tube) Proposed by Ising (195) First built by Wideröe (198) Alvarez version (1955) Replace static fields by time-varying fields by only exposing the bunch to the wave at certain selected points. Long drift tubes shield the electric field for at least half the RF cycle. The gaps increase length with distance.
6 Cavity Linacs These devices store large amounts of energy at a specific frequency allowing low power sources to reach high fields.
7 Cavity Quality Factor An important definition is the cavity Q factor, given by Q = ωu Where U is the stored energy given by, U = 0 1 µ 0 The Q factor is π times the number of rf cycles it takes to dissipate the energy stored in the cavity. U The Q factor determines the maximum energy the cavity can fill to with a given input power. P c H dv ωt = U0 exp Q0
8 Cavities If we place metal walls at each end of the waveguide we create a cavity. The waves are reflected at both walls creating a standing wave. If we superimpose a number of plane waves by reflection inside a cavities surface we can get cancellation of E and B T at the cavity walls. The boundary conditions must also be met on these walls. These are met at discrete frequencies only when there is an integer number of half wavelengths in all directions. L The resonant frequency of a rectangular cavity can be given by (ω/c) =(mπ/a) + (nπ/b) + (pπ/l) Where a, b and L are the width, height and length of the cavity and m, n and p are integers a
9 Pillbox Cavities Wave equation in cylindrical co-ordinates 1 1 r + + µεω k z ψ r r r r ϕ = 0 Solution to the wave equation ψ = A J ( k r) e 1 m t ± imϕ Transverse Electric (TE) modes H Transverse Magnetic (TM) modes E z z ς ' a z, 1 m Ht = th z ς ' m, n m, n ± imϕ ( r ϕ) = A J e ς r a z, 1 m Et = te z ς m, n m, n ± imϕ ( r ϕ) = A J e r ik ik a a E t H iµωa = ˆ ς t ' m, n iεωa = ˆ ς m, n ( z H ) t ( z E ) t z z
10 Bessel Function J m (k T r) m=0 m=1 m= m= First four Bessel functions. k T r E z (TM) and H z (TE) vary as Bessel functions in pill box cavities. All functions have zero at the centre except the 0th order Bessel functions. One of the transverse fields varies with the differential of the Bessel function J All J are zero in the centre except the 1 st order Bessel functions
11 Cavity Modes r θ TE 1,1 TE 0,1 TM 0,1 TE,1 TE r,θ Cylindrical (or pillbox) cavities are more common than rectangular cavities. The indices here are m = number of full wave variations around theta n = number of half wave variations along the diameter P = number of half wave variations along the length The frequencies of these cavities are given by f = c/(π) * (ζ/r) Where ζ is the n th root of the m th bessel function for TE modes or the n th root of the derivative of the m th bessel function for TE modes or
12 TM 010 Accelerating mode Electric Fields Almost every RF cavity operates using the TM 010 accelerating mode. Magnetic Fields This mode has a longitudinal electric field in the centre of the cavity which accelerates the electrons. The magnetic field loops around this and caused ohmic heating.
13 TM 010 Monopole Mode.405r Ez = EJ 0 0 e R H = 0 H z r = 0 i.405r H EJ e E E ϕ = 0 1 Z0 R ϕ r = 0 = 0 iωt iωt Z 0 =377 Ohms H E Beam
14 A standing wave cavity
15 Accelerating Voltage Ez, at t=0 Ez, at t=z/v Position, z Position, z Normally voltage is the potential difference between two points but an electron can never see this voltage as it has a finite velocity (ie the field varies in the time it takes the electron to cross the cavity The voltage now depends on what phase the electron enters the cavity at. If we calculate the voltage at two phases 90 degrees apart we get real and imaginary components
16 Accelerating voltage An electron travelling close to the speed of light traverses through a cavity. During its transit it sees a time varying electric field. If we use the voltage as complex, the maximum possible energy gain is given by the magnitude, + L / iω z/ c E evb e Ez( z, t) e dz L / = = To receive the maximum kick with multiple cells the particle should traverse the cavity in a half RF period (see end of lecture). L = c f
17 Transit time factor An electron travelling close to the speed of light traverses through a cavity. During its transit it sees a time varying electric field. If we use the voltage as complex, the maximum possible energy gain is given by the magnitude, E ev + L / iω z/ c e Ez ( z, t) e dz E0LT L / = = = Where T is the transit time factor given by T + L / i z/ c Ez ( z, t) e dz sin L / = = + L / L / E z (, ) z t dz ( g ) ω π βλ π g βλ For a gap length, g. For a given Voltage (=E 0 L) it is clear that we get maximum energy gain for a small gap. Transit time factor, T g/βλ
18 Overvoltage To provide a stable bunch you often will accelerate off crest. This means the particles do not experience the maximum beam energy. V b =V c cos(φ s ) = V c q Where V c is the cavity voltage and V b is the voltage experienced by the particle, φ is the phase shift and q is known as the overvoltage. V V p Stable region φ s φ Phase stability is given by off-crest acceleration
19 For TM010 mode = R + L / iω z/ c V Ez ( z, t) e dz L / = E + L / 0 L / E ( ω ) ( ωz c) = 0 = E 0 cos z / c dz sin / ω / c ( ωl c) sin / ω / c + L / L / This is often approximated as Where L=c/f, T=/π Ez, at t=z/v Position, z Hence voltage is maximised when L=c/f V = E LT z0 cos ( ϕ ) V = E0 cos( ϕ ) L π
20 Does this mean we don t get breakdown in vacuum? Gas Breakdown If we apply a high voltage across a gap we can ionise the molecules in the intervening gas. At high pressure the mean free path is too low to gain enough momentum At low pressure there are not enough molecules to ionise.
21 Field Emission High electric fields can lead to electrons quantum tunnelling out of the structure creating a field emitted current. Once emitted this field emitted current can interact with the cavity fields. Although initially low energy, the electrons can potentially be accelerated to close to the speed of light with the main electron beam, if the fields are high enough. This is known as dark current trapping.
22 Field Enhancement The surface of an accelerating structure will have a number of imperfections at the surface caused by grain boundaries, scratches, bumps etc. As the surface is an equipotential the electric fields at these small imperfections can be greatly enhanced. In some cases the field can be increase by a factor of several hundred. b E local =β E 0 h Beta h/b
23 Vacuum Breakdown Breakdown occurs when a plasma discharge is generated in the cavity. This is almost always associated with some of the cavity walls being heated until it vaporises and the gas is then ionised by field emission. The exact mechanisms are still not well understood. When this occurs all the incoming RF is reflected back up the coupler. This is the major limitation to gradient in most pulsed RF cavities and can permanently damage the structure.
24 Kilpatrick Limits A rough empirical formula for the peak surface electric field is It is not clear why the field strength decreases with frequency. It is also noted that breakdown is mitigated slightly by going to lower group velocity structures. The maximum field strength also varies with pulse length as t -0.5 (only true for a limited number of pulse lengths) As a SCRF cavity would quench long before breakdown, we only see breakdown in normal conducting structures.
25 Dark Current Trapping When we looked at beam dynamics we saw that we could inject a low energy bunch in a beta=v/c=1 structure and it could be accelerated to the speed of light and arrive on crest. If we have field emitted electrons in the structure these could also be capture and can travel with the main beam. The gradient at which this occurs is given by
26 Surface Resistance As we have seen when a time varying magnetic field impinges on a conducting surface current flows in the conductor to shield the fields inside the conductor. However if the conductivity is finite the fields will not be completely shielded at the surface and the δ field will penetrate into the surface. This causes currents to flow and hence power is absorbed in the surface which is converted to heat. Skin depth is the distance in the surface that the current has reduced to 1/e of the value at the surface, denoted by. δ = σωµ The surface resistance is defined as R surf = 1 δσ For copper 1/σ = 1.7 x 10-8 Ωm x Current Density, J.
27 Power Dissipation The power lost in the cavity walls due to ohmic heating is given by, R surface is the surface resistance 1 Pc = Rsurface H ds This is important as all power lost in the cavity must be replaced by an rf source. A significant amount of power is dissipated in cavity walls and hence the cavities are heated, this must be water cooled in warm cavities and cooled by liquid helium in superconducting cavities.
28 Pulsed Heating Pulsed RF however has problems due to heat diffusion effects. Over short timescales (<10ms) the heat doesn t diffuse far enough into the material to reach the water cooling. This means that all the heat is deposited in a small volume with no cooling. Cyclic heating can lead to surface damage if the temperature rise creates thermal stress (~40 K). The power deposited is P = d RH s max T = P d R s t = pulse πρκc e µω 0 σ And the temperature on the surface is ρ is density, κ is thermal conductivity and c e is specific heat
29 Peak Surface Fields The accelerating gradient is the average gradient seen by an electron bunch, Vc Eacc = L The limit to the energy in the cavity is often given by the peak surface electric and magnetic fields. Thus, it is useful to introduce the ratio between the peak surface electric field and the accelerating gradient, and the ratio between the peak surface magnetic field and the accelerating gradient. E E max acc = π For a pillbox H E max / acc A m = 430 MV / m Electric Field Magnitude
30 Maximum Gradient Limits All the limiting factors scale differently with frequency. They also mostly vary with pulse length. The limiting factor tends to be different from cavity to cavity. For a CW machine the gradient is limited by average heating instead. Also need to think about the electricity bill as 1 MW is 00 per day.
31 Average Heating In normal conducting cavities, the RF deposits large amounts of power as heat in the cavity walls. This heat is removed by flushing cooling water through special copper cooling channels in the cavity. The faster the water flows (and the cooler), the more heat is removed. For CW cavities, the cavity temperature reaches steady state when the water cooling removes as much power as is deposited in the RF structure. (Limit is ~ 1 MW but 500 kw is safer) This usually is required to be calculated in a Finite Element code to determine temperature rises. Temperature rises can cause surface deformation, surface cracking, outgassing or even melting. By pulsing the RF we can reach much higher gradients as the average power flow is much less than the peak power flow.
32 Q factor Pillbox E Pc = π R R+ L Rsurface J Z 0 ( ) (.405) 0 1 U πε E = Q RLJ ( ) ωµ RL 453 L/ R R+ L R R 1 + L/ R 0 = = ( ) ( ) ( ) surface 453 L/ R G = = L/ R surface
33 Shunt Impedance Another useful definition is the shunt impedance, 1 Vc Rs = Pc This quantity is useful for equivalent circuits as it relates the voltage in the circuit (cavity) to the power dissipated in the resistor (cavity walls). Shunt Impedance is also important as it is related to the power induced in the mode by the beam (important for unwanted cavity modes)
34 TM010 Shunt Impedance V c H = EL 0 π i.405r ϕ = EJ 0 1 Z0 R 1 Pc = Rsurface H ds E.405r P = R r J dr R 0 c, ends surface 1 Z π 0 E P RL R J 0 c, walls = π Z0 surface 1 E Pc = π R R+ L Rsurface J Z (.405) 0 ( ) (.405) 0 1 R s ( ZL 0 ) ( + ) (.405) 5x10 = = 3 π R R L R J R surface 1 4 surface
35 Similarly larger apertures lead to higher peak fields. Using thicker walls has a similar effect. Higher frequencies need smaller apertures as well Cavity geometry Figures borrowed from Sami Tantawi The shunt impedance is strongly dependant on aperture
36 Multicell It takes x4 power to double the voltage in one cavity but only x to use two cavities/cells to achieve the same voltage (R s ~number of cells). To make it more efficient we can add either more cavities or more cells. This unfortunately makes it worse for wakefields (see later lectures) and you get less gradient per unit power. In order to make our accelerator more compact and cheaper we can add more cells. We have lots of cavities coupled together so that we only need one coupler. For N cells the shunt impedance is given by R total = NR sin gle This however adds complexity in tuning, wakefields and the gradient of all cells is limited by the worst cell.
CERN Accelerator School. RF Cavities. Erk Jensen CERN BE-RF
CERN Accelerator School RF Cavities Erk Jensen CERN BE-RF CERN Accelerator School, Varna 010 - "Introduction to Accelerator Physics" What is a cavity? 3-Sept-010 CAS Varna/Bulgaria 010- RF Cavities Lorentz
More informationLinac JUAS lecture summary
Linac JUAS lecture summary Part1: Introduction to Linacs Linac is the acronym for Linear accelerator, a device where charged particles acquire energy moving on a linear path. There are more than 20 000
More informationSuperconducting RF Accelerators: Why all the interest?
Superconducting RF Accelerators: Why all the interest? William A. Barletta Director, United States Particle Accelerator School Dept. of Physics, MIT The HEP prespective ILC PROJECT X Why do we need RF
More informationD B. An Introduction to the Physics and Technology of e+e- Linear Colliders. Lecture 2: Main Linac. Peter (PT) Tenenbaum (SLAC)
An Introduction to the Physics and Technology of e+e- Linear Colliders Lecture : Main Linac Peter (PT) Tenenbaum (SLAC) Nick Walker DESY DESY Summer Student Lecture USPAS Santa Barbara, CA, 16-7 31 st
More informationFundamental Concepts of Particle Accelerators III : High-Energy Beam Dynamics (2) Koji TAKATA KEK. Accelerator Course, Sokendai. Second Term, JFY2012
.... Fundamental Concepts of Particle Accelerators III : High-Energy Beam Dynamics (2) Koji TAKATA KEK koji.takata@kek.jp http://research.kek.jp/people/takata/home.html Accelerator Course, Sokendai Second
More informationCERN Accelerator School Wakefields. Prof. Dr. Ursula van Rienen, Franziska Reimann University of Rostock
CERN Accelerator School Wakefields Prof. Dr. Ursula van Rienen, Franziska Reimann University of Rostock Contents The Term Wakefield and Some First Examples Basic Concept of Wakefields Basic Definitions
More informationLongitudinal Dynamics
Longitudinal Dynamics F = e (E + v x B) CAS Bruges 16-25 June 2009 Beam Dynamics D. Brandt 1 Acceleration The accelerator has to provide kinetic energy to the charged particles, i.e. increase the momentum
More informationFrom the Wideröe gap to the linac cell
Module 3 Coupled resonator chains Stability and stabilization Acceleration in periodic structures Special accelerating structures Superconducting linac structures From the Wideröe gap to the linac cell
More informationLongitudinal Beam Dynamics
Longitudinal Beam Dynamics Shahin Sanaye Hajari School of Particles and Accelerators, Institute For Research in Fundamental Science (IPM), Tehran, Iran IPM Linac workshop, Bahman 28-30, 1396 Contents 1.
More informationAccelerators Ideal Case
Accelerators Ideal Case Goal of an accelerator: increase energy of CHARGED par:cles Increase energy ΔE = r 2 F dr = q ( E + v B)d r The par:cle trajectory direc:on dr parallel to v ΔE = increase of energy
More informationHistorical developments. of particle acceleration
Historical developments of particle acceleration Y.Papaphilippou N. Catalan-Lasheras USPAS, Cornell University, Ithaca, NY 20 th June 1 st July 2005 1 Outline Principles of Linear Acceleration Electrostatic
More informationPhysics 610. Adv Particle Physics. April 7, 2014
Physics 610 Adv Particle Physics April 7, 2014 Accelerators History Two Principles Electrostatic Cockcroft-Walton Van de Graaff and tandem Van de Graaff Transformers Cyclotron Betatron Linear Induction
More informationRF cavities (Lecture 25)
RF cavities (Lecture 25 February 2, 2016 319/441 Lecture outline A good conductor has a property to guide and trap electromagnetic field in a confined region. In this lecture we will consider an example
More informationLectures on accelerator physics
Lectures on accelerator physics Lecture 3 and 4: Examples Examples of accelerators 1 Rutherford s Scattering (1909) Particle Beam Target Detector 2 Results 3 Did Rutherford get the Nobel Prize for this?
More informationLongitudinal dynamics Yannis PAPAPHILIPPOU CERN
Longitudinal dynamics Yannis PAPAPHILIPPOU CERN United States Particle Accelerator School, University of California - Santa-Cruz, Santa Rosa, CA 14 th 18 th January 2008 1 Outline Methods of acceleration
More informationGeometrical and RF Considerations for All Beam Collisions via Crab- Crossing
ARB Technical Note - raft - 1/7/97 Geometrical and RF Considerations for All Beam Collisions via Crab- Crossing Frank Zimmermann and avid H Whittum In this note we sketch the geometry for a crab-crossing
More informationCavity basics. 1 Introduction. 2 From plane waves to cavities. E. Jensen CERN, Geneva, Switzerland
Cavity basics E. Jensen CERN, Geneva, Switerland Abstract The fields in rectangular and circular waveguides are derived from Maxwell s equations by superposition of plane waves. Subsequently the results
More informationSpoke and other TEM-class superconducting cavities. J.L. Muñoz, ESS-Bilbao Academy-Industry Matching Event CIEMAT, Madrid, 27.May.
Spoke and other TEM-class superconducting cavities J.L. Muñoz, ESS-Bilbao Academy-Industry Matching Event CIEMAT, Madrid, 27.May.2013 Outline Introduction Basic design of TEM cavities Cavity design issues
More informationElectromagnetism. Christopher R Prior. ASTeC Intense Beams Group Rutherford Appleton Laboratory
lectromagnetism Christopher R Prior Fellow and Tutor in Mathematics Trinity College, Oxford ASTeC Intense Beams Group Rutherford Appleton Laboratory Contents Review of Maxwell s equations and Lorentz Force
More informationAn ion follows a circular path in a uniform magnetic field. Which single change decreases the radius of the path?
T5-1 [237 marks] 1. A circuit is formed by connecting a resistor between the terminals of a battery of electromotive force (emf) 6 V. The battery has internal resistance. Which statement is correct when
More informationDielectric Accelerators at CLARA. G. Burt, Lancaster University On behalf of ASTeC, Lancaster U., Liverpool U., U. Manchester, and Oxford U.
Dielectric Accelerators at CLARA G. Burt, Lancaster University On behalf of ASTeC, Lancaster U., Liverpool U., U. Manchester, and Oxford U. Dielectric Accelerators Types Photonic structures Dielectric
More informationEstimates of local heating due to trapped modes in vacuum chamber
Estimates of local heating due to trapped modes in vacuum chamber Gennady Stupakov SLAC National Accelerator Laboratory, Menlo Park, CA 94025 CERN, April 29, 2016 2 Motivation The motivation for this analysis
More informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 7 Electrostatics and electrodynamics Capacitance and capacitors capacitors with dielectrics Electric current current and drift speed resistance and Ohm s law http://www.physics.wayne.edu/~apetrov/phy2140/
More informationDielectric wave guides, resonance, and cavities
Dielectric wave guides, resonance, and cavities 1 Dielectric wave guides Instead of a cavity constructed of conducting walls, a guide can be constructed of dielectric material. In analogy to a conducting
More informationLecture 5: Photoinjector Technology. J. Rosenzweig UCLA Dept. of Physics & Astronomy USPAS, 7/1/04
Lecture 5: Photoinjector Technology J. Rosenzweig UCLA Dept. of Physics & Astronomy USPAS, 7/1/04 Technologies Magnetostatic devices Computational modeling Map generation RF cavities 2 cell devices Multicell
More informationAccelerators. W. Udo Schröder, 2004
1 Accelerators Overview Electrostatic Accelerators Cascade Van de Graaff V.d.G. Tandem generator Accelerator 2-3 stages steady (DC) beam, high quality focusing, energy, currents; but low energies Accelerators
More informationELECTROMAGNETIC SIMULATION CODES FOR DESIGNING CAVITIES -1
INDIAN INSTITUTE OF TECHNOLOGY ROORKEE ELECTROMAGNETIC SIMULATION CODES FOR DESIGNING CAVITIES -1 Puneet Jain IIT ROORKEE SRFSAT Workshop, IUAC N. Delhi September 21, 2017 2 OUTLINE 1. Overview of Electromagnetic
More informationIntroduction to Accelerators. Scientific Tools for High Energy Physics and Synchrotron Radiation Research
Introduction to Accelerators. Scientific Tools for High Energy Physics and Synchrotron Radiation Research Pedro Castro Introduction to Particle Accelerators DESY, July 2010 What you will see Pedro Castro
More informationReview of proposals of ERL injector cryomodules. S. Belomestnykh
Review of proposals of ERL injector cryomodules S. Belomestnykh ERL 2005 JLab, March 22, 2005 Introduction In this presentation we will review injector cryomodule designs either already existing or under
More informationRF LINACS. Alessandra Lombardi BE/ ABP CERN
1 RF LINACS Alessandra Lombardi BE/ ABP CERN Contents PART 1 (yesterday) : Introduction : why?,what?, how?, when? Building bloc I (1/) : Radio Frequency cavity From an RF cavity to an accelerator PART
More informationAccelerators. There are some accelerators around the world Nearly all are for industrial (20 000) or clinical use (10 000)
Accelerators There are some 30 000 accelerators around the world Nearly all are for industrial (20 000) or clinical use (10 000) Scientific research community (~ 100) Synchrotron light sources Ion beam
More informationSAST Lecture - III. Linear Accelerators. P N Prakash. IUAC, New Delhi
Lecture - III Linear Accelerators P N Prakash IUAC, New Delhi School on Accelerator Science and Technology (SAST ) Inter-University Accelerator Centre, New Delhi May 16-27, Outline: Lecture - III Figures
More informationAnnouncements. l LON-CAPA #7 and Mastering Physics (to be posted) due Tuesday March 11
Announcements l LON-CAPA #7 and Mastering Physics (to be posted) due Tuesday March 11 Resistance l l l The amount of current that flows in a circuit depends not only on the voltage but also on the electrical
More informationAcceleration to higher energies
Acceleration to higher energies While terminal voltages of 20 MV provide sufficient beam energy for nuclear structure research, most applications nowadays require beam energies > 1 GeV How do we attain
More informationHigh gradient superconducting cavities
High gradient superconducting cavities A worthy challenge Physical motivation Superconductivity revisited Needed quantities Surface treatment Diagnostic methods or How do we learn? Goals achieved so far
More informationSimulation of RF Cavity Dark Current in Presence of Helical Magnetic Field
Preprint FERMILAB-TM-2467-TP. Simulation of RF Cavity Dark Current in Presence of Helical Magnetic Field GennadyRomanov, Vladimir Kashikhin Abstract. In order to produce muon beam of high enough quality
More informationJoel A. Shapiro January 21, 2010
Joel A. shapiro@physics.rutgers.edu January 21, 20 rmation Instructor: Joel Serin 325 5-5500 X 3886, shapiro@physics Book: Jackson: Classical Electrodynamics (3rd Ed.) Web home page: www.physics.rutgers.edu/grad/504
More informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 4 Electrostatics and electrodynamics Capacitance and capacitors capacitors with dielectrics Electric current current and drift speed resistance and Ohm s law resistivity
More informationEngines of Discovery
Engines of Discovery R.S. Orr Department of Physics University of Toronto Berkley 1930 1 MeV Geneva 20089 14 TeV Birth of Particle Physics and Accelerators 1909 Geiger/Marsden MeV a backscattering - Manchester
More informationConducting surface - equipotential. Potential varies across the conducting surface. Lecture 9: Electrical Resistance.
Lecture 9: Electrical Resistance Electrostatics (time-independent E, I = 0) Stationary Currents (time-independent E and I 0) E inside = 0 Conducting surface - equipotential E inside 0 Potential varies
More informationProblem set 3. Electromagnetic waves
Second Year Electromagnetism Michaelmas Term 2017 Caroline Terquem Problem set 3 Electromagnetic waves Problem 1: Poynting vector and resistance heating This problem is not about waves but is useful to
More informationPhysics (
Question 2.12: A charge of 8 mc is located at the origin. Calculate the work done in taking a small charge of 2 10 9 C from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm).
More informationParticle Accelerators. The Electrostatic Accelerators
Particle Accelerators The Electrostatic Accelerators References K. Wille The Physics of Particle Accelerator, Oxford University press pag 1-29 H. Wiedeman Particle accelerator physics volume 1, chapter
More informationTheory of Electromagnetic Fields
Theory of Electromagnetic Fields Andrzej Wolski University of Liverpool, and the Cockcroft Institute, UK Abstract We discuss the theory of electromagnetic fields, with an emphasis on aspects relevant to
More information5. ELECTRIC CURRENTS
5. ELECTRIC CURRENTS TOPIC OUTLINE Section Recommended Time Giancoli Section 5.1 Potential Difference, Current, Resistance 5.2 Electric Circuits 3h 19.1, 19.2 6.2 Electric Field and Force 6.3 Magnetic
More informationAccelerator Physics. Tip World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI BANGALORE. Second Edition. S. Y.
Accelerator Physics Second Edition S. Y. Lee Department of Physics, Indiana University Tip World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI BANGALORE Contents Preface Preface
More informationCompact Wideband THz Source
Compact Wideband THz Source G. A. Krafft Center for Advanced Studies of Accelerators Jefferson Lab Newport News, VA 3608 Previously, I have published a paper describing compact THz radiation sources based
More informationVarying accelerating fields
Varying accelerating fields Two approaches for accelerating with time-varying fields Linear Accelerators Circular Accelerators Use many accelerating cavities through which the particle beam passes once.
More informationIntroduction to Longitudinal Beam Dynamics
Introduction to Longitudinal Beam Dynamics B.J. Holzer CERN, Geneva, Switzerland Abstract This chapter gives an overview of the longitudinal dynamics of the particles in an accelerator and, closely related
More informationIntroduction to accelerators for teachers (Korean program) Mariusz Sapiński CERN, Beams Department August 9 th, 2012
Introduction to accelerators for teachers (Korean program) Mariusz Sapiński (mariusz.sapinski@cern.ch) CERN, Beams Department August 9 th, 2012 Definition (Britannica) Particle accelerator: A device producing
More informationLow Emittance Machines
Advanced Accelerator Physics Course RHUL, Egham, UK September 2017 Low Emittance Machines Part 1: Beam Dynamics with Synchrotron Radiation Andy Wolski The Cockcroft Institute, and the University of Liverpool,
More informationTECHNO INDIA BATANAGAR
TECHNO INDIA BATANAGAR ( DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING) QUESTION BANK- 2018 1.Vector Calculus Assistant Professor 9432183958.mukherjee@tib.edu.in 1. When the operator operates on
More informationAccelerator Physics Particle Acceleration. G. A. Krafft Old Dominion University Jefferson Lab Lecture 10
Accelerator Physics Particle Acceleration G. A. Krafft Old Dominion University Jefferson Lab Lecture 1 Graduate Accelerator Physics Fall 17 RF Acceleration Characteriing Superconducting RF (SRF) Accelerating
More informationParticle physics experiments
Particle physics experiments Particle physics experiments: collide particles to produce new particles reveal their internal structure and laws of their interactions by observing regularities, measuring
More informationAP Physics C. Electric Circuits III.C
AP Physics C Electric Circuits III.C III.C.1 Current, Resistance and Power The direction of conventional current Suppose the cross-sectional area of the conductor changes. If a conductor has no current,
More informationTHz Electron Gun Development. Emilio Nanni 3/30/2016
THz Electron Gun Development Emilio Nanni 3/30/2016 Outline Motivation Experimental Demonstration of THz Acceleration THz Generation Accelerating Structure and Results Moving Forward Parametric THz Amplifiers
More informationShort Introduction to CLIC and CTF3, Technologies for Future Linear Colliders
Short Introduction to CLIC and CTF3, Technologies for Future Linear Colliders Explanation of the Basic Principles and Goals Visit to the CTF3 Installation Roger Ruber Collider History p p hadron collider
More informationWhere k = 1. The electric field produced by a point charge is given by
Ch 21 review: 1. Electric charge: Electric charge is a property of a matter. There are two kinds of charges, positive and negative. Charges of the same sign repel each other. Charges of opposite sign attract.
More informationHigh Power Diode Lasers
Lecture 10/1 High Power Diode Lasers Low Power Lasers (below tenth of mw) - Laser as a telecom transmitter; - Laser as a spectroscopic sensor; - Laser as a medical diagnostic tool; - Laser as a write-read
More informationWakefield induced Losses in the Manual Valves of the TESLA Cryomodule
Wakefield induced Losses in the Manual Valves of the TESLA Cryomodule Abstract M. Dohlus, H.-P. Wedekind, K. Zapfe Deutsches Elektronen Synchrotron Notkestr. 85, D-22603 Hamburg, Germany The beam pipe
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 Summary of last lecture Equipotential surfaces: Surfaces where the potential is the same everywhere, e.g. the
More informationVirtual Prototype of a Dielectric Window for High Power Microwave Tubes
Virtual Prototype of a Dielectric Window for High Power Microwave Tubes Alberto Leggieri, Davide Passi and Franco Di Paolo Università degli Studi di Roma Tor Vergata, Department of Electronic Engineering,
More informationSUMMARY Phys 2523 (University Physics II) Compiled by Prof. Erickson. F e (r )=q E(r ) dq r 2 ˆr = k e E = V. V (r )=k e r = k q i. r i r.
SUMMARY Phys 53 (University Physics II) Compiled by Prof. Erickson q 1 q Coulomb s Law: F 1 = k e r ˆr where k e = 1 4π =8.9875 10 9 N m /C, and =8.85 10 1 C /(N m )isthepermittivity of free space. Generally,
More informationTopic Student Checklist R A G
Personalised Learning Checklist AQA TRILOGY Physics (8464) from 2016 Topics T6.1. Energy Topic Student Checklist R A G 6.1.1 Energy changes in a system, and the ways energy is stored before and after such
More informationWaves Final Review. Name: Date: 1. On which one of the following graphs is the wavelength λ and the amplitude a of a wave correctly represented?
Name: Date: Waves Final Review 1. On which one of the following graphs is the wavelength λ and the amplitude a of a wave correctly represented? A. Displacement λ a Distance along wave B. Displacement λ
More informationPHYS General Physics for Engineering II FIRST MIDTERM
Çankaya University Department of Mathematics and Computer Sciences 2010-2011 Spring Semester PHYS 112 - General Physics for Engineering II FIRST MIDTERM 1) Two fixed particles of charges q 1 = 1.0µC and
More informationGuided waves - Lecture 11
Guided waves - Lecture 11 1 Wave equations in a rectangular wave guide Suppose EM waves are contained within the cavity of a long conducting pipe. To simplify the geometry, consider a pipe of rectangular
More informationDesign of an RF Photo-Gun (PHIN)
Design of an RF Photo-Gun (PHIN) R. Roux 1, G. Bienvenu 1, C. Prevost 1, B. Mercier 1 1) CNRS-IN2P3-LAL, Orsay, France Abstract In this note we show the results of the RF simulations performed with a 2-D
More informationANALYSIS OF HIGH ORDER MODES IN 1.3 GHZ CW SRF ELECTRON LINAC FOR A LIGHT SOURCE
ANALYSIS OF HIGH ORDER MODES IN 1.3 GHZ CW SRF ELECTRON LINAC FOR A LIGHT SOURCE A. Sukhanov, A. Vostrikov, V. Yakovlev, Fermilab, Batavia, IL 60510, USA Abstract Design of a Light Source (LS) based on
More informationGraduate Accelerator Physics. G. A. Krafft Jefferson Lab Old Dominion University Lecture 1
Graduate Accelerator Physics G. A. Krafft Jefferson Lab Old Dominion University Lecture 1 Course Outline Course Content Introduction to Accelerators and Short Historical Overview Basic Units and Definitions
More informationPre-Leaving Certificate Examination, 2014 Triailscrúdú na hardteistiméireachta, 2014
*B16* Pre-Leaving Certificate Examination, 2014 Triailscrúdú na hardteistiméireachta, 2014 PHYSICS ORDINARY LEVEL TIME: 3 HOURS Answer three questions from Section A and five questions from Section B.
More informationBeam heat load due to geometrical and resistive wall impedance in COLDDIAG
Beam heat load due to geometrical and resistive wall impedance in COLDDIAG Sara Casalbuoni, Mauro Migliorati, Andrea Mostacci, Luigi Palumbo, Bruno Spataro 2012 JINST 7 P11008, http://iopscience.iop.org/17480221/7/11/p11008
More informationNIU Ph.D. Candidacy Examination Fall 2018 (8/21/2018) Electricity and Magnetism
NIU Ph.D. Candidacy Examination Fall 2018 (8/21/2018) Electricity and Magnetism You may solve ALL FOUR problems if you choose. The points of the best three problems will be counted towards your final score
More informationBernhard Holzer, CERN-LHC
Bernhard Holzer, CERN-LHC * Bernhard Holzer, CERN CAS Prague 2014 x Liouville: in reasonable storage rings area in phase space is constant. A = π*ε=const x ε beam emittance = woozilycity of the particle
More informationNicolas PICHOFF. France CEA-Direction d Île de France Service de Physique et Applications des Accélérateurs (SP2A)
Nicolas PICHOFF France CEA-Direction d Île de France Service de Physique et Applications des Accélérateurs (SP2A) Topics Some common structures The Radio Frequency Quadrupole (RFQ) The Drift-Tube Linacs
More informationGood Luck! Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter PH. Electromagnetism and Optics - Winter PH
1 Notes: 1. To submit a problem, just click the Submit button under it. The Submit All button is not necessary. 2. A problem accepted as correct by CAPA will be highlighted in green. Once you see this,
More informationUNIT I ELECTROSTATIC FIELDS
UNIT I ELECTROSTATIC FIELDS 1) Define electric potential and potential difference. 2) Name few applications of gauss law in electrostatics. 3) State point form of Ohm s Law. 4) State Divergence Theorem.
More informationElectromagnetics in COMSOL Multiphysics is extended by add-on Modules
AC/DC Module Electromagnetics in COMSOL Multiphysics is extended by add-on Modules 1) Start Here 2) Add Modules based upon your needs 3) Additional Modules extend the physics you can address 4) Interface
More informationStatus of linear collider designs:
Status of linear collider designs: Main linacs Design overview, principal open issues G. Dugan March 11, 2002 Linear colliders: main linacs The main linac is the heart of the linear collider TESLA, NLC/JLC,
More informationMULTIPACTOR ON A DIELECTRIC SURFACE WITH LONGITUDINAL RF ELECTRIC FIELD ACTION
Progress In Electromagnetics Research Letters, Vol. 24, 177 185, 211 MULTIPACTOR ON A DIELECTRIC SURFACE WITH LONGITUDINAL RF ELECTRIC FIELD ACTION F. Zhu *, Z. Zhang, J. Luo, and S. Dai Key Laboratory
More informationAccelerator Basics. Abhishek Rai IUAC
Accelerator Basics Abhishek Rai IUAC School on Accelerator Science and Technology May 7-18, 2018 Some basics Charge on an electron(e) = 1.6 10-19 Coulomb (1 unit of charge) 1 Atomic mass unit (amu) = 1.66
More informationCoulomb s constant k = 9x10 9 N m 2 /C 2
1 Part 2: Electric Potential 2.1: Potential (Voltage) & Potential Energy q 2 Potential Energy of Point Charges Symbol U mks units [Joules = J] q 1 r Two point charges share an electric potential energy
More informationOverview of Acceleration
Overview of Acceleration R B Palmer, Scott Berg, Steve Kahn (presented by Steve Kahn) Nufact-04 RF Frequency Acc types and System Studies Linacs RLA s FFAG s Injection/Extraction US Study 2a acceleration
More informationSynchrotron Motion with Space-Charge
Synchrotron Motion with Space-Charge Basic Principles without space-charge RF resonant cavity providing accelerating voltage V (t). Often V = V 0 sin(φ s + ω rf t), where ω rf is the angular frequency
More informationImpedance & Instabilities
Impedance & Instabilities The concept of wakefields and impedance Wakefield effects and their relation to important beam parameters Beam-pipe geometry and materials and their impact on impedance An introduction
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 informationPhysics 212 Midterm 2 Form A
1. A wire contains a steady current of 2 A. The charge that passes a cross section in 2 s is: A. 3.2 10-19 C B. 6.4 10-19 C C. 1 C D. 2 C E. 4 C 2. In a Physics 212 lab, Jane measures the current versus
More informationEvaluation of In-Vacuum Wiggler Wakefield Impedances for SOLEIL and MAX IV
26/11/2014 European Synchrotron Light Source Workshop XXII 1 Evaluation of In-Vacuum Wiggler Wakefield Impedances for SOLEIL and MAX IV F. Cullinan, R. Nagaoka (SOLEIL, St. Aubin, France) D. Olsson, G.
More informationPHYS 241 EXAM #1 October 5, 2006
1. ( 5 points) Two point particles, one with charge 8 10 9 C and the other with charge 2 10 9 C, are separated by 4 m. The magnitude of the electric field (in N/C) midway between them is: A. 9 10 9 B.
More informationPH2200 Practice Final Exam Summer 2003
INSTRUCTIONS 1. Write your name and student identification number on the answer sheet. 2. Please cover your answer sheet at all times. 3. This is a closed book exam. You may use the PH2200 formula sheet
More informationAQA Physics Checklist
Topic 1. Energy Video: Energy changes in a system To understand the ways in which energy can be stored in a system and can be transferred from one energy store to another within a system To understand
More informationChapter 26 & 27. Electric Current and Direct- Current Circuits
Chapter 26 & 27 Electric Current and Direct- Current Circuits Electric Current and Direct- Current Circuits Current and Motion of Charges Resistance and Ohm s Law Energy in Electric Circuits Combination
More informationGCSE PHYSICS REVISION LIST
GCSE PHYSICS REVISION LIST OCR Gateway Physics (J249) from 2016 Topic P1: Matter P1.1 Describe how and why the atomic model has changed over time Describe the structure of the atom and discuss the charges
More informationMetal Deposition. Filament Evaporation E-beam Evaporation Sputter Deposition
Metal Deposition Filament Evaporation E-beam Evaporation Sputter Deposition 1 Filament evaporation metals are raised to their melting point by resistive heating under vacuum metal pellets are placed on
More information100 Physics Facts. 1. The standard international unit (SI unit) for mass (m) is. kg (kilograms) s (seconds)
100 Physics Facts 1. The standard international unit (SI unit) for mass (m) is. kg (kilograms) 2. The standard international unit (SI unit) for time (t) is. s (seconds) 3. The standard international unit
More informationTo be published in the Proceedings of ICEC-22, Seoul Korea, July 2008 MICE Note 232 1
To be published in the Proceedings of ICEC-22, Seoul Korea, 21-25 July 2008 MICE Note 232 1 AC Loss Analysis on the Superconducting Coupling in MICE H. Wu, L. Wang, M. A. Green*, L. K. Li, F. Y. Xu, X.
More informationToday in Physics 122: resistance
Today in Physics 122: resistance Ohm s Law Resistivity and the physics behind resistance Resistors of different shapes and sizes, and how to calculate their resistance from their resistivity Resistor networks
More informationInvestigation of Coherent Emission from the NSLS VUV Ring
SPIE Accelerator Based Infrared Sources and Spectroscopic Applications Proc. 3775, 88 94 (1999) Investigation of Coherent Emission from the NSLS VUV Ring G.L. Carr, R.P.S.M. Lobo, J.D. LaVeigne, D.H. Reitze,
More information5) Ohm s Law gives the relationship between potential difference and current for a.
) During any process, the net charge of a closed system. a) increases b) decreases c) stays constant ) In equilibrium, the electric field in a conductor is. a) always changing b) a constant non-zero value
More informationBEAM DYNAMICS ISSUES IN THE SNS LINAC
BEAM DYNAMICS ISSUES IN THE SNS LINAC A. Shishlo # on behalf of the SNS Accelerator Group, ORNL, Oak Ridge, TN 37831, U.S.A. Abstract A review of the Spallation Neutron Source (SNS) linac beam dynamics
More information