USPAS Accelerator Physics 2013 Duke University
|
|
- Godwin Greer
- 5 years ago
- Views:
Transcription
1 USPAS Accelerator Physics 2013 Duke University Lattice Extras: Linear Errors, Doglegs, Chicanes, Achromatic Conditions, Emittance Exchange Todd Satogata (Jefferson Lab) / satogata@jlab.org Waldo MacKay (BNL, retired) / waldo@bnl.gov Timofey Zolkin (FNAL/Chicago) / t.v.zolkin@gmail.com 1
2 x x s 0 +C betatron phase advance Review Hill s equation x + K(s)x =0 quasi periodic ansatz solution x(s) =A β(s) cos[ψ(s)+ψ 0 ] β(s) =β(s + C) α(s) 1 2 β (s) = γ(s) 1+α(s)2 β(s) ds Ψ(s) = β(s) cos µ + α(0) sin µ β(0) sin µ x γ(0) sin µ cos µ α(0) sin µ x µ = M = I cos µ + J sin µ I = s0 +C s ds β(s) J(s 0 ) Tr M = 2 cos µ α(0) γ(0) s 0 β(0) α(0) J 2 = I M = e J(s)µ 2
3 General Non-Periodic Transport Matrix We can parameterize a general non-periodic transport matrix from s 1 to s 2 using lattice parameters and Ψ = Ψ(s 2 ) Ψ(s 1 ) β(s2 ) β(s M s1 s 2 = 1 ) [cos Ψ + α(s 1)sin Ψ] β(s1 )β(s 2 )sin Ψ [α(s 2) α(s 1 )] cos Ψ+[1+α(s 1 )α(s 2 )] sin Ψ β(s1 ) β(s 2 ) [cos Ψ α(s 2)sin Ψ] β(s1 )β(s 2 ) This does not have a pretty form like the periodic matrix However both can be expressed as C S M = C S where the C and S terms are cosine-like and sine-like; the second row is the s-derivative of the first row! A common use of this matrix is the m 12 term: (C&M Eqn 5.52) x(s 2 )= β(s 1 )β(s 2 )sin( Ψ) x (s 1 ) Effect of angle kick on downstream position General phase advance, NOT phase advance/cell µ 3
4 Design Orbit Perturbations design trajectory Magnets RF Cavity Sometimes need a local change x(s) to the design orbit But we really only get changes in angle x from magnets e.g. small dipole corrector : x = B corrector L corrector /(Bρ) Changes to/corrections of design orbit from dipole correctors Linear errors add up via linear superposition x(s2 ) C S 0 x = (s 2 ) C S x (s 1 ) x(s 2 )= x (s 1 ) β(s 1 )β(s 2 )sin Ψ x (s 2 )= x β(s 1 ) (s 1 ) β(s 2 ) [cos Ψ α(s 2)sin Ψ] 4
5 Checking Optics with Difference Orbits Horizontal Vertical Steering changes through linear elements are linear Compare calculated optical transport of Δx to measured Can localize focusing errors with enough BPMs Above picture is for single-pass AGS to RHIC transfer line Strong nonlinearities introduce dependence on initial orbits Physics of the AGS to RHIC Transfer Line Commissioning, T. Satogata, W.W. MacKay, et al, EPAC 96 5
6 Checking Optics with Difference Orbits Line: Predicted FODO orbit Dots: Measured orbit (with errors at s=700m) PEP-II vertical orbit during commissioning Projected vertical betatron oscillation in near-fodo lattice Discrepancy starts at s~700m Later found two quadrupole pairs had ~0.1% errors Can clearly discriminate systematic optics errors from random BPM errors Y. Cai, 1998, from M. Minty and F. Zimmermann, Beam Techniques: Beam Control and Manipulation 6
7 Control: Two-Bump x(s 2 )= x (s 1 ) β(s 1 )β(s 2 )sin Ψ x (s 2 )= x β(s 1 ) (s 1 ) β(s 2 ) [cos Ψ α(s 2)sin Ψ] x (s 1 ) x (s 2 ) A single orbit error changes all later positions and angles Add another dipole corrector at a location where Ψ = kπ At this point the distortion from the original dipole corrector is all x that we can cancel with the second dipole corrector. x (s 2 )= x β(s 1 ) (s 1 ) β(s 2 ) + angle from s 2 dipole Called a two-bump: localized orbit distortion from two correctors But requires Ψ = kπ between correctors 7
8 Control: Three-Bump (see computer lab) A general local orbit distortion from three dipole correctors Constraint is that net orbit change from sum of all three kicks must be zero Bump amplitude x b = S 1 x 1 Only three-bump requirement is that S 1, S 2 0 8
9 Steering Error in Synchrotron Ring Short steering error x in a ring with periodic matrix M Solve for new periodic solution or design orbit (x 0,x 0 ) M x0 x x Note that (x 0 =0,x 0 =0) is not the periodic solution any more! x0 x =(I M) x 0 = x0 (I M) 1 =(I e (2πQ)J ) 1 = [e πqj e πqj e πqj 1 New closed orbit x 0 = β 0 x 0 2 x 0 = (2J sin(πq)) 1 e πqj 1 1 = (J cos(πq)+i sin(πq)) 2 sin(πq) tan(πq) x 0 = x 0 2 [1 α 0 cot(πq)] if Q = kπ integer resonances 9
10 Steering Error in Synchrotron Ring We can use the general propagation matrix to find the new closed orbit displacement at all locations around the synchrotron x(s) = x 0 β0 β(s) cos[ Ψ πq] 2 sin(πq) This displacement of the closed orbit changes its path length If the revolution (RF) frequency is constant, then the beam energy changes, and there is an extra (small) term in the closed orbit displacement x(s) = x 0 β0 β(s) cos[ Ψ πq]+ x η 0 η(s) 0 2 sin(πq) α p C dl where α p L /dp p is the momentum compaction and C is the accelerator circumference. 10
11 RHIC Vertical Difference Orbit Where is the cusp? Predicted difference orbit Measured difference orbit Ring difference orbits also measure optics Compare against modeled/design orbit Integer part of tune readily visible: Q~30 Can easily find reversed, broken BPMs Can also find (or eliminate) focusing errors 11
12 RHIC Vertical Difference Orbit Where is the cusp? Predicted difference orbit Measured difference orbit Ring difference orbits also measure optics Compare against modeled/design orbit Integer part of tune readily visible: Q~30 Can easily find reversed, broken BPMs Can also find (or eliminate) focusing errors 12
13 LOCO and SVD Statistical Methods NSLS VUV synchrotron: before optics correction NSLS VUV synchrotron: after optics correction Measuring many difference orbits in a ring gives a ton of information about optics, BPM and corrector errors Singular value decomposition (SVD) optimization of error fits Has become standard method for correction of synchrotron lattices, particularly synchrotron light sources, led to other methods e.g. model independent analysis (MIA), independent component analysis (ICA) J. Safranek, Experimental Determination of Storage Ring Optics using Orbit Response Measurements,
14 Focusing Error in Synchrotron Ring Short focusing error in a ring with periodic matrix M Now solve for Tr M to find effects on tune Q For small errors Can be used for a simple measurement of M new = M at the quadrupole f Tr M = cos(2πq new) = cos(2πq 0 ) 1 2 β 0 Q new = Q 0 + Q Q 1 4π β 0 f β 0 f sin(2πq 0) we can expand to find Quadrupole errors also cause resonances when Q = k/2 : half-integer resonances 14
15 Natural chromaticity Chromaticity Correction ξ N Q p / Q p 0 = 1 4πQ K(s)β(s) ds How can we control chromaticity in our synchrotron ring? We need a way to connect momentum offset δ to focusing Dispersion (momentum-dependent position) and sextupoles (nonlinear focusing depending on position) come to rescue x(s) =x betatron (s)+η x (s)δ Sextupole B field B y = b 2 x 2 B y (sext) = b 2 [x betatron (s)+η x (s)δ] 2 b 2 x 2 betatron +2b 2 x betatron (s)η x (s)δ Nonlinear! Total chromaticity from all sources is then ξ = 1 [K(s) b 2 (s)η x (s)]ds 4πQ like a quadrupole K(s)! Strong focusing (large K) requires large sextupoles, nonlinearity! 15
16 Doglegs +ˆx θ bend +θ bend Drift L or other optics Displaces beam transversely without changing direction What is effect on 6D optics? M dipole (ρ, θ) = cos θ ρsin θ ρ(1 cos θ) sin θ cos θ sin θ ρθ sin θ ρ(1 cos θ) L/(γ 2 β 2 ) ρ(θ sin θ) ρ Be careful about the coordinate system and signs!! If ρ,θ>0, positive displacement points out from dipole curvature Be careful about order of matrix multiplication! (C&M 3.102) 16
17 Reverse Bend Dipole Transport What is the correct 6x6 transport matrix of a reverse bend dipole? It turns out to be achieved by reversing both ρ and θ ρθ=l (which stays positive) so both must change sign M dipole ( ρ, θ) = cos θ ρsin θ ρ(1 cos θ) sin θ cos θ sin θ ρθ sin θ ρ(1 cos θ) L/(γ 2 β 2 ) ρ(θ sin θ) ρ M drift = 1 L L L/(γ 2 β 2 )
18 Aside: Longitudinal Phase Space Drift Wait, what was that M 56 term with the relativistic effects? Recall longitudinal coordinates are (z, δ) This extra term is called ballistic drift : not in all codes! Important at low to modest energies and for bunch compression Relativistic terms enter converting momentum p to velocity v Positive δ move forward in bunch δ (e-3) Negative δ move backward in bunch relative z position [mm] 18
19 Weak Dogleg +ˆx M dipole ( ρ, θ) Drift L M dipole (ρ, θ) M dogleg = M dipole (ρ, θ)m drift M dipole ( ρ, θ) M weak dogleg = 1 ρθ 2 ρθ 1 L θ ρθ 2 ρθ θ L +2ρθ Lθ (η, η ) in =0 = (η, η ) out =( Lθ, 0) Strong dogleg can also be derived: D = L cos θ sin θ D = L sin2 θ ρ 19
20 Dogleg Dispersion For weak dogleg (η, η ) in =0 (η, η ) out =( Lθ, 0) L = 14 m θ =0.08 rad Lθ =1.12 m Does this make sense? x (δ) = BL (Bρ) = q p(1 + δ) [BL] q p [BL](1 δ) =(1 δ) x (δ = 0) 20
21 Achromatic Dogleg How can we make an achromatic dogleg? (η, η ) in =(0m, 0) (η, η ) out =(0m, 0) Use an I insertion (e.g. four consecutive π/2 insertions) α β M π/2 = = J (Recall J 4 = I) γ α M achromatic dogleg = cos(2θ) ρ sin(2θ) 0 sin(2θ) ρ cos(2θ) achromatic! Any transport with net phase advance of 2nπ will be achromatic (nπ if all dipoles bend in same direction) common trick for matching dispersive bending arcs to nondispersive straight sections. 21
22 Achromatic Dogleg 22
23 Achromatic Dogleg: Steffen CERN School Notes K. Steffen, CERN V-1, 1985, p
24 First-Order Achromat Theorem A lattice of n repetitive cells is achromatic (to first order, or in the linear approximation) iff M n = I or each cell is achromatic Proof: Consider R M d 0 1 For n cells : R n = where x x δ 2 x = R x δ 1 M16 d = M 26 M n (M n 1 + M n I) d 0 1 but (M n 1 + M n I) =(M n I)(M I) 1 So for n cells : R n M n (M = n I)(M I) 1 d 0 1 So the lattice is achromatic only if d =0or M n = I M n = I cos µ tot + J sin µ tot µ tot =2πk S.Y. Lee, Accelerator Physics 24
25 Chicane +ˆx θ bend +θ bend +θ bend θ bend Divert beam around an obstruction e.g. vertical bypass chicane in Fermilab Main Ring e.g. horizontal injection chicane in CEBAF recirculating linac Essentially a design orbit 4-bump (4 dipoles) Usually need some focusing, optics between dipoles Usually design optics to be achromatic Operationally null orbit motion at end of chicane vs changes in input beam energy Naively expect M 56 <0 (bunch lengthening or decompression) Higher energy particles (+δ) have shorter path lengths But can compress bunches with introduction of longitudinal correlation 25
26 AGS to RHIC Transfer Line (vertical dogleg) The ATR vertical dogleg is not strictly a dogleg since the planes of the AGS and RHIC accelerators are not parallel 26
27 CEBAF Spreader Injection chicane Recombiner 27
28 CEBAF Spreaders/Recombiners Problem: Separate different energy beams for transport into arcs of CEBAF, and recombine before next linac Achromats: arcs are FODO-like, linacs are dispersion-free I insertion: 1 betatron wavelength between dipoles Single dogleg: unacceptably high beta functions Two consecutive staircase doglegs with same total phase advance was solution Still quite a challenge in physical layout of real magnets! D. Douglas, R.C. York, J. Kewisch, Optical Design of the CEBAF Beam Transport System,
29 CEBAF Spreaders/Recombiners Dispersion One step recombiner Unacceptably large vertical beta function/beam size (550 m) Staircase two-step recombiner Acceptable beta functions and beam sizes in both planes (100 m) Dispersion 29
30 Mobius Insertion Fully coupled equal-emittance optics for e + e - CESR collisions Symmetrically exchange horizontal/vertical motion in insertion Horizontal/vertical motion are coupled Only one transverse tune degree of freedom! Q x,y : unrotated tunes Q 1,2 = Q x + Q y ± 1 Q 1 Q 2 = Match insertion to points where β x =β y and α x =α y with phase advances that differ by π between planes Normal insertion: M erect = T 0 0 T Rotated by 45 degrees around s axis: M mobius = 0 T T 0 A purely transverse example of an emittance exchanger 30
31 Transverse/Longitudinal Emittance Exchange J.C.T. Thangaraj, Experimental Studies on an Emittance Exchange Beamline at the A0 Photoinjector,
32 Fermilab A0 Emittance Exchanger Dogleg Dogleg θ : Bending angle η : dogleg dispersion L : dogleg length L c : RF cell length M = L 1 c 4 (4L+L c) 4η η θ(4l+l c) η θ θ η θ(4l+l c) 4 1+ θl c θ 2 L c 4η 4 1 η 4L+L c 4η θl c 4η 2 1+ θl c 4η J.C.T. Thangaraj, Experimental Studies on an Emittance Exchange Beamline at the A0 Photoinjector,
33 (xkcd interlude) This is known in accelerator lattice design language as a double bend achromat 33
34 Double Bend Achromat (approximate) You calculated constraints for the double bend achromat in your homework last night Keep lowest-order terms in θ, including θ 2 in upper right term since ρθ=l 34
35 Double Bend Achromat (approximate) M DBA = M DBA = C S D C S D
36 Double Bend Achromat (approximate) The periodic solutions for dispersion for the general M matrix were derived in class and the text It turns out that the η(periodic) = [1 S ]D + SD 2(1 cos µ) η (periodic) = [1 C]D + C D 2(1 cos µ) equation is satisfied automatically! This is a consequence of the mirror symmetry of the system η η The equation is satisfied if D=0: (L + l)(4f L 2l) D = θ =0 2f 4f L 2l =0 f = L +2l 4 =0 =0 ˆη = (L +2l)θ 2 =2fθ 36
37 Double Bend Achromat ˆη =2fθ =0.03 m L = l =2m θ =0.01 rad f = L +2l 4 Exact DBA : f = l 2 + ρ 2 =1.5 m (KL quad )=0.667 m 1 tan(θ/2) ˆη = ρ(1 cos θ)+l sin θ DBA is also known as a Chasman-Green lattice Used in early third-generation light sources (e.g. NSLS at BNL) More after we discuss synchrotron radiation, H functions 37
38 Triple Bend Achromat Cell (ALS at LBL) Good reasons to minimize integral of dispersion (next week) Extra quadrupoles help with matching at ends of cell, α x,y =0 L. Yang et al, Global Optimization of an Accelerator Lattice Using Multiobjective Genetic Algorithms,
USPAS Accelerator Physics 2017 University of California, Davis
USPAS Accelerator Physics 207 University of California, Davis Lattice Extras: Linear Errors, Doglegs, Chicanes, Achromatic Conditions, Emittance Exchange Todd Satogata (Jefferson Lab) / satogata@jlab.org
More informationThu June 16 Lecture Notes: Lattice Exercises I
Thu June 6 ecture Notes: attice Exercises I T. Satogata: June USPAS Accelerator Physics Most o these notes ollow the treatment in the class text, Conte and MacKay, Chapter 6 on attice Exercises. The portions
More informationIntroduction to Accelerator Physics 2011 Mexican Particle Accelerator School
Introduction to Accelerator Physics 20 Mexican Particle Accelerator School Lecture 3/7: Quadrupoles, Dipole Edge Focusing, Periodic Motion, Lattice Functions Todd Satogata (Jefferson Lab) satogata@jlab.org
More informationTransverse dynamics Selected topics. Erik Adli, University of Oslo, August 2016, v2.21
Transverse dynamics Selected topics Erik Adli, University of Oslo, August 2016, Erik.Adli@fys.uio.no, v2.21 Dispersion So far, we have studied particles with reference momentum p = p 0. A dipole field
More informationAccelerator Physics Homework #3 P470 (Problems: 1-5)
Accelerator Physics Homework #3 P470 (Problems: -5). Particle motion in the presence of magnetic field errors is (Sect. II.2) y + K(s)y = B Bρ, where y stands for either x or z. Here B = B z for x motion,
More informationaccelerator physics and ion optics summary longitudinal optics
accelerator physics and ion optics summary longitudinal optics Sytze Brandenburg sb/accphys007_5/1 coupling energy difference acceleration phase stability when accelerating on slope of sine low energy:
More informationaccelerator physics and ion optics summary longitudinal optics
accelerator physics and ion optics summary longitudinal optics Sytze Brandenburg sb/accphys003_5/1 feedback energy difference acceleration phase stability when accelerating on slope of sine low energy:
More informationS9: Momentum Spread Effects and Bending S9A: Formulation
S9: Momentum Spread Effects and Bending S9A: Formulation Except for brief digressions in S1 and S4, we have concentrated on particle dynamics where all particles have the design longitudinal momentum at
More informationBeam Dynamics. D. Brandt, CERN. CAS Bruges June 2009 Beam Dynamics D. Brandt 1
Beam Dynamics D. Brandt, CERN D. Brandt 1 Some generalities D. Brandt 2 Units: the electronvolt (ev) The electronvolt (ev)) is the energy gained by an electron travelling, in vacuum, between two points
More informationIntroduction to Accelerator Physics 2011 Mexican Particle Accelerator School
Introduction to Accelerator Physics 2011 Mexican Particle Accelerator School Lecture 5/7: Dispersion (including FODO), Dispersion Suppressor, Light Source Lattices (DBA, TBA, TME) Todd Satogata (Jefferson
More informationLattice Design for the Taiwan Photon Source (TPS) at NSRRC
Lattice Design for the Taiwan Photon Source (TPS) at NSRRC Chin-Cheng Kuo On behalf of the TPS Lattice Design Team Ambient Ground Motion and Civil Engineering for Low Emittance Electron Storage Ring Workshop
More informationAccelerator Physics Final Exam pts.
Accelerator Physics Final Exam - 170 pts. S. M. Lund and Y. Hao Graders: C. Richard and C. Y. Wong June 14, 2018 Problem 1 P052 Emittance Evolution 40 pts. a) 5 pts: Consider a coasting beam composed of
More informationE. Wilson - CERN. Components of a synchrotron. Dipole Bending Magnet. Magnetic rigidity. Bending Magnet. Weak focusing - gutter. Transverse ellipse
Transverse Dynamics E. Wilson - CERN Components of a synchrotron Dipole Bending Magnet Magnetic rigidity Bending Magnet Weak focusing - gutter Transverse ellipse Fields and force in a quadrupole Strong
More informationLattice Design and Performance for PEP-X Light Source
Lattice Design and Performance for PEP-X Light Source Yuri Nosochkov SLAC National Accelerator Laboratory With contributions by M-H. Wang, Y. Cai, X. Huang, K. Bane 48th ICFA Advanced Beam Dynamics Workshop
More informationMagnets and Lattices. - Accelerator building blocks - Transverse beam dynamics - coordinate system
Magnets and Lattices - Accelerator building blocks - Transverse beam dynamics - coordinate system Both electric field and magnetic field can be used to guide the particles path. r F = q( r E + r V r B
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 informationLECTURE 7. insertion MATCH POINTS. Lattice design: insertions and matching
LECTURE 7 Lattice design: insertions and matching Linear deviations from an ideal lattice: Dipole errors and closed orbit deformations Lattice design: insertions and matching The bacbone of an accelerator
More informationCOMBINER RING LATTICE
CTFF3 TECHNICAL NOTE INFN - LNF, Accelerator Division Frascati, April 4, 21 Note: CTFF3-2 COMBINER RING LATTICE C. Biscari 1. Introduction The 3 rd CLIC test facility, CTF3, is foreseen to check the feasibility
More informationAccelerator Physics. Accelerator Development
Accelerator Physics The Taiwan Light Source (TLS) is the first large accelerator project in Taiwan. The goal was to build a high performance accelerator which provides a powerful and versatile light source
More informationEquations of motion in an accelerator (Lecture 7)
Equations of motion in an accelerator (Lecture 7) January 27, 2016 130/441 Lecture outline We consider several types of magnets used in accelerators and write down the vector potential of the magnetic
More informationILC Spin Rotator. Super B Workshop III. Presenter: Jeffrey Smith, Cornell University. with
ILC Spin Rotator Super B Workshop III Presenter: Jeffrey Smith, Cornell University with Peter Schmid, DESY Peter Tenenbaum and Mark Woodley, SLAC Georg Hoffstaetter and David Sagan, Cornell Based on NLC
More information{ } Double Bend Achromat Arc Optics for 12 GeV CEBAF. Alex Bogacz. Abstract. 1. Dispersion s Emittance H. H γ JLAB-TN
JLAB-TN-7-1 Double Bend Achromat Arc Optics for 12 GeV CEBAF Abstract Alex Bogacz Alternative beam optics is proposed for the higher arcs to limit emittance dilution due to quantum excitations. The new
More informationStorage Ring Optics Measurement, Model, and Correction. Yiton T. Yan SLAC, 2575 Sand Hill Road, Menlo Park, CA 94025, USA.
SLAC-PUB-12438 April 2007 Storage Ring Optics Measurement, Model, and Correction Yiton T. Yan SLAC, 2575 Sand Hill Road, Menlo Park, CA 94025, USA 1 Introduction To improve the optics of a storage ring,
More informationTransverse dynamics. Transverse dynamics: degrees of freedom orthogonal to the reference trajectory
Transverse dynamics Transverse dynamics: degrees of freedom orthogonal to the reference trajectory x : the horizontal plane y : the vertical plane Erik Adli, University of Oslo, August 2016, Erik.Adli@fys.uio.no,
More informationLecture 2: Modeling Accelerators Calculation of lattice functions and parameters. X. Huang USPAS, January 2015 Hampton, Virginia
Lecture 2: Modeling Accelerators Calculation of lattice functions and parameters X. Huang USPAS, January 2015 Hampton, Virginia 1 Outline Closed orbit Transfer matrix, tunes, Optics functions Chromatic
More informationBernhard Holzer, CERN-LHC
Bernhard Holzer, CERN-LHC * Bernhard Holzer, CERN CAS Prague 2014 Lattice Design... in 10 seconds... the Matrices Transformation of the coordinate vector (x,x ) in a lattice x(s) x = M 0 x'(s) 1 2 x' 0
More informationD. Brandt, CERN. CAS Frascati 2008 Accelerators for Newcomers D. Brandt 1
Accelerators for Newcomers D. Brandt, CERN D. Brandt 1 Why this Introduction? During this school, you will learn about beam dynamics in a rigorous way but some of you are completely new to the field of
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 informationPractical Lattice Design
Practical Lattice Design Dario Pellegrini (CERN) dario.pellegrini@cern.ch USPAS January, 15-19, 2018 1/17 D. Pellegrini - Practical Lattice Design Lecture 5. Low Beta Insertions 2/17 D. Pellegrini - Practical
More informationLattices and Emittance
Lattices and Emittance Introduction Design phases Interfaces Space Lattice building blocks local vs. global Approximations Fields and Magnets Beam dynamics pocket tools Transfer matrices and betafunctions
More informationCERN Accelerator School. Intermediate Accelerator Physics Course Chios, Greece, September Low Emittance Rings
CERN Accelerator School Intermediate Accelerator Physics Course Chios, Greece, September 2011 Low Emittance Rings Part 1: Beam Dynamics with Synchrotron Radiation Andy Wolski The Cockcroft Institute, and
More informationLow Emittance Machines
Advanced Accelerator Physics Course Trondheim, Norway, August 2013 Low Emittance Machines Part 3: Vertical Emittance Generation, Calculation, and Tuning Andy Wolski The Cockcroft Institute, and the University
More informationAccelerator Physics Multipoles and Closed Orbits. G. A. Krafft Old Dominion University Jefferson Lab Lecture 13
Accelerator Physics Multipoles and Closed Orbits G. A. Krafft Old Dominion University Jefferson Lab Lecture 13 Graduate Accelerator Physics Fall 015 Oscillators Similtaneously Excited u i t it u u Fe 1
More informationParticle Accelerators: Transverse Beam Dynamics
Particle Accelerators: Transverse Beam Dynamics Volker Ziemann Department of Physics and Astronomy Uppsala University Research Training course in Detector Technology Stockholm, Sept. 8, 2008 080908 V.
More informationPretzel scheme of CEPC
Pretzel scheme of CEPC H. Geng, G. Xu, Y. Zhang, Q. Qin, J. Gao, W. Chou, Y. Guo, N. Wang, Y. Peng, X. Cui, T. Yue, Z. Duan, Y. Wang, D. Wang, S. Bai, F. Su HKUST, Hong Kong IAS program on High Energy
More informationAccelerator. Physics of PEP-I1. Lecture #7. March 13,1998. Dr. John Seeman
Accelerator Physics of PEP-1 Lecture #7 March 13,1998 Dr. John Seeman Accelerator Physics of PEPJ John Seeman March 13,1998 1) What is PEP-? Lecture 1 2) 3) Beam parameters for an luminosity of 3~1~~/cm~/sec
More informationCompressor Lattice Design for SPL Beam
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN A&B DIVISION AB-Note-27-34 BI CERN-NUFACT-Note-153 Compressor Lattice Design for SPL Beam M. Aiba Abstract A compressor ring providing very short proton
More informationAccelerator Physics Closed Orbits and Chromaticity. G. A. Krafft Old Dominion University Jefferson Lab Lecture 14
Accelerator Physics Closed Orbits and Chromaticity G. A. Krafft Old Dominion University Jefferson Lab Lecture 4 Kick at every turn. Solve a toy model: Dipole Error B d kb d k B x s s s il B ds Q ds i x
More informationSimulation of Optics Correction for ERLs. V. Sajaev, ANL
Simulation of Optics Correction for ERLs V. Sajaev, ANL Introduction Minimization of particle losses in ERL arcs requires use of sextupoles As in storage rings, trajectory errors in the presence of sextupoles
More information6 Bunch Compressor and Transfer to Main Linac
II-159 6 Bunch Compressor and Transfer to Main Linac 6.1 Introduction The equilibrium bunch length in the damping ring (DR) is 6 mm, too long by an order of magnitude for optimum collider performance (σ
More informationOn-axis injection into small dynamic aperture
On-axis injection into small dynamic aperture L. Emery Accelerator Systems Division Argonne National Laboratory Future Light Source Workshop 2010 Tuesday March 2nd, 2010 On-Axis (Swap-Out) injection for
More informationBernhard Holzer, CERN-LHC
Bernhard Holzer, CERN-LHC * 1 ... in the end and after all it should be a kind of circular machine need transverse deflecting force Lorentz force typical velocity in high energy machines: old greek dictum
More informationStudy of Alternative Optics for the NLC Prelinac Collimation section
LCC 0057 03/01 Linear Collider Collaboration Tech Notes Study of Alternative Optics for the NLC Prelinac Collimation section March 2001 Yuri Nosochkov, Pantaleo Raimondi, Tor Raubenheimer Stanford Linear
More informationÆThe Betatron. Works like a tranformer. Primary winding : coils. Secondary winding : beam. Focusing from beveled gap.
Weak Focusing Not to be confused with weak folk cussing. Lawrence originally thought that the cyclotron needed to have a uniform (vertical) field. Actually unstable: protons with p vert 0 would crash into
More informationTransverse Beam Dynamics II
Transverse Beam Dynamics II II) The State of the Art in High Energy Machines: The Theory of Synchrotrons: Linear Beam Optics The Beam as Particle Ensemble Emittance and Beta-Function Colliding Beams &
More informationEffect of Insertion Devices. Effect of IDs on beam dynamics
Effect of Insertion Devices The IDs are normally made of dipole magnets ith alternating dipole fields so that the orbit outside the device is un-altered. A simple planer undulator ith vertical sinusoidal
More informationWed Jan 25 Lecture Notes: Coordinate Transformations and Nonlinear Dynamics
Wed Jan 25 Lecture Notes: Coordinate Transformations and Nonlinear Dynamics T. Satogata: January 2017 USPAS Accelerator Physics Most of these notes kindasortasomewhat follow the treatment in the class
More informationSTATUS REPORT ON STORAGE RING REALIGNMENT AT SLRI
STATUS REPORT ON STORAGE RING REALIGNMENT AT SLRI S. Srichan #, A. Kwankasem, S. Boonsuya, B. Boonwanna, V. Sooksrimuang, P. Klysubun Synchrotron Light Research Institute, 111 University Ave, Muang District,
More informationLow Emittance Storage Ring for Light Source. Sukho Kongtawong PHY 554 Fall 2016
Low Emittance Storage Ring for Light Source Sukho Kongtawong PHY 554 Fall 2016 Content Brightness and emittance Radiative effect and emittance Theory Theoretical Minimum Emittance (TME) cell Double-bend
More informationLHeC Recirculator with Energy Recovery Beam Optics Choices
LHeC Recirculator with Energy Recovery Beam Optics Choices Alex Bogacz in collaboration with Frank Zimmermann and Daniel Schulte Alex Bogacz 1 Alex Bogacz 2 Alex Bogacz 3 Alex Bogacz 4 Alex Bogacz 5 Alex
More informationIntroduction to Transverse Beam Dynamics
Introduction to Transverse Beam Dynamics B.J. Holzer CERN, Geneva, Switzerland Abstract In this chapter we give an introduction to the transverse dynamics of the particles in a synchrotron or storage ring.
More informationELECTRON DYNAMICS WITH SYNCHROTRON RADIATION
ELECTRON DYNAMICS WITH SYNCHROTRON RADIATION Lenny Rivkin Ecole Polythechnique Federale de Lausanne (EPFL) and Paul Scherrer Institute (PSI), Switzerland CERN Accelerator School: Introduction to Accelerator
More informationIntroduction to particle accelerators
Introduction to particle accelerators Walter Scandale CERN - AT department Lecce, 17 June 2006 Introductory remarks Particle accelerators are black boxes producing either flux of particles impinging on
More information09.lec Momentum Spread Effects in Bending and Focusing*
09.lec Momentum Spread Effects in Bending and Focusing* Outline Review see: 09.rev.momentum_spread 9) Momentum Spread Effects in Bending and Focusing Prof. Steven M. Lund Physics and Astronomy Department
More informationCollider Rings and IR Design for MEIC
Collider Rings and IR Design for MEIC Alex Bogacz for MEIC Collaboration Center for Advanced Studies of Accelerators EIC Collaboration Meeting The Catholic University of America Washington, DC, July 29-31,
More informationHE-LHC Optics Development
SLAC-PUB-17224 February 2018 HE-LHC Optics Development Yunhai Cai and Yuri Nosochkov* SLAC National Accelerator Laboratory, Menlo Park, CA, USA Mail to: yuri@slac.stanford.edu Massimo Giovannozzi, Thys
More informationLOW EMITTANCE MODEL FOR THE ANKA SYNCHROTRON RADIATION SOURCE
Karlsruhe Institute of Technology (KIT, Karlsruhe, Germany) Budker Institute of Nuclear Physics (BINP, Novosibirsk, Russia) LOW EMITTANCE MODEL FOR THE ANKA SYNCHROTRON RADIATION SOURCE (A.Papash - on
More informationarxiv: v2 [physics.acc-ph] 18 Nov 2015
International Journal of Modern Physics: Conference Series c The Authors arxiv:1511.0039v [physics.acc-ph] 18 Nov 015 Studies of systematic limitations in the EDM searches at storage rings Artem Saleev
More informationILC Damping Ring Alternative Lattice Design **
ILC Damping Ring Alternative Lattice Design ** Yi-Peng Sun *,1,2, Jie Gao 1, Zhi-Yu Guo 2 1 Institute of High Energy Physics, CAS, Beijing 2 Key Laboratory of Heavy Ion Physics, Peking University, Beijing
More informationS1: Particle Equations of Motion S1A: Introduction: The Lorentz Force Equation
S1: Particle Equations of Motion S1A: Introduction: The Lorentz Force Equation The Lorentz force equation of a charged particle is given by (MKS Units):... particle mass, charge... particle coordinate...
More informationFirst propositions of a lattice for the future upgrade of SOLEIL. A. Nadji On behalf of the Accelerators and Engineering Division
First propositions of a lattice for the future upgrade of SOLEIL A. Nadji On behalf of the Accelerators and Engineering Division 1 SOLEIL : A 3 rd generation synchrotron light source 29 beamlines operational
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 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 informationTransverse Dynamics II
Transverse Dynamics II JAI Accelerator Physics Course Michaelmas Term 217 Dr. Suzie Sheehy Royal Society University Research Fellow University of Oxford Acknowledgements These lectures have been produced
More informationLow Emittance Machines
CERN Accelerator School Advanced Accelerator Physics Course Trondheim, Norway, August 2013 Low Emittance Machines Part 1: Beam Dynamics with Synchrotron Radiation Andy Wolski The Cockcroft Institute, and
More informationLecture 3: Modeling Accelerators Fringe fields and Insertion devices. X. Huang USPAS, January 2015 Hampton, Virginia
Lecture 3: Modeling Accelerators Fringe fields and Insertion devices X. Huang USPAS, January 05 Hampton, Virginia Fringe field effects Dipole Quadrupole Outline Modeling of insertion devices Radiation
More informationSummary Report: Working Group 2 Storage Ring Sources Future Light Source Workshop SLAC, March 1-5, S. Krinsky and R. Hettel
Summary Report: Working Group 2 Storage Ring Sources Future Light Source Workshop SLAC, March 1-5, 2010 S. Krinsky and R. Hettel Sessions 1. Low Emittance Ring Design --Y. Cai 2. Novel Concepts --D. Robin
More informationThe optimization for the conceptual design of a 300 MeV proton synchrotron *
The optimization for the conceptual design of a 300 MeV proton synchrotron * Yu-Wen An ( 安宇文 ) 1,2), Hong-Fei Ji ( 纪红飞 ) 1,2), Sheng Wang ( 王生 ) 1,2), Liang-Sheng Huang ( 黄良生 ) 1,2;1) 1 Institute of High
More informationBeam Dynamics Activities at the Thomas Jefferson National Accelerator Facility (Jefferson Lab)
JLAB-ACC-96-23 0.1 Beam Dynamics Activities at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) David R. Douglas douglasajlab.org Jefferson Lab 12000 Jefferson Avenue The Thomas Jefferson
More informationChoosing the Baseline Lattice for the Engineering Design Phase
Third ILC Damping Rings R&D Mini-Workshop KEK, Tsukuba, Japan 18-20 December 2007 Choosing the Baseline Lattice for the Engineering Design Phase Andy Wolski University of Liverpool and the Cockcroft Institute
More informationNonlinear Single-Particle Dynamics in High Energy Accelerators
Nonlinear Single-Particle Dynamics in High Energy Accelerators Part 1: Introduction Examples of nonlinear dynamics in accelerator systems Nonlinear Single-Particle Dynamics in High Energy Accelerators
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 informationMAX-lab. MAX IV Lattice Design: Multibend Achromats for Ultralow Emittance. Simon C. Leemann
Workshop on Low Emittance Rings 2010 CERN Jan 12 15, 2010 MAX-lab MAX IV Lattice Design: Multibend Achromats for Ultralow Emittance Simon C. Leemann simon.leemann@maxlab.lu.se Brief Overview of the MAX
More informationConceptual design of an accumulator ring for the Diamond II upgrade
Journal of Physics: Conference Series PAPER OPEN ACCESS Conceptual design of an accumulator ring for the Diamond II upgrade To cite this article: I P S Martin and R Bartolini 218 J. Phys.: Conf. Ser. 167
More informationLinear Collider Collaboration Tech Notes. A New Structure for the NLC Positron Predamping Ring Lattice
Linear Collider Collaboration Tech Notes LCC-0066 CBP Tech Note - 233 June 2001 A New Structure for the NLC Positron Predamping Ring Lattice A. Wolski Lawrence Berkeley National Laboratory Berkeley, CA
More informationDiagnostics at the MAX IV 3 GeV storage ring during commissioning. PPT-mall 2. Åke Andersson On behalf of the MAX IV team
Diagnostics at the MAX IV 3 GeV storage ring during commissioning PPT-mall 2 Åke Andersson On behalf of the MAX IV team IBIC Med 2016, linje Barcelona Outline MAX IV facility overview Linac injector mode
More informationTWISS FUNCTIONS. Lecture 1 January P.J. Bryant. JUAS18_01- P.J. Bryant - Lecture 1 Twiss functions
TWISS FUNCTIONS Lecture January 08 P.J. Bryant JUAS8_0- P.J. Bryant - Lecture Slide Introduction These lectures assume knowledge of : The nd order differential equations of motion in hard-edge field models
More informationSmall Synchrotrons. Michael Benedikt. CERN, AB-Department. CAS, Zeegse, 30/05/05 Small Synchrotrons M. Benedikt 1
Small Synchrotrons Michael Benedikt CERN, AB-Department CAS, Zeegse, 30/05/05 Small Synchrotrons M. Benedikt 1 Contents Introduction Synchrotron linac - cyclotron Main elements of the synchrotron Accelerator
More informationIntroduction to Accelerator Physics Old Dominion University. Nonlinear Dynamics Examples in Accelerator Physics
Introduction to Accelerator Physics Old Dominion University Nonlinear Dynamics Examples in Accelerator Physics Todd Satogata (Jefferson Lab) email satogata@jlab.org http://www.toddsatogata.net/2011-odu
More informationStart-to-end beam optics development and multi-particle tracking for the ILC undulator-based positron source*
SLAC-PUB-12239 January 27 (A) Start-to-end beam optics development and multi-particle tracking for the ILC undulator-based positron source* F. Zhou, Y. Batygin, Y. Nosochkov, J. C. Sheppard, and M. D.
More informationStatus of Optics Design
17th B2GM, February 5, 2014 Status of Optics Design Y. Ohnishi /KEK 17th B2GM KEK, February 5, 2014 Contents! Lattice parameters! Dynamic aperture under influence of beam-beam effect! Lattice preparation
More informationFODO Cell Introduction to OptiM
FODO Cell Introduction to OptiM S. Alex Bogacz Jefferson Lab 1 FODO Optics cell Most accelerator lattices are designed in modular ways Design and operational clarity, separation of functions One of the
More informationCoherent synchrotron radiation in magnetic bunch compressors. Qiang Gao, ZhaoHeng Guo, Alysson Vrielink
Coherent synchrotron radiation in magnetic bunch compressors Qiang Gao, ZhaoHeng Guo, Alysson Vrielink 1 Outline Magnetic bunch compressor Coherent synchrotron radiation (CSR) Background Theory Effects
More informationClass Review. Content
193 Cla Review Content 1. A Hitory of Particle Accelerator 2. E & M in Particle Accelerator 3. Linear Beam Optic in Straight Sytem 4. Linear Beam Optic in Circular Sytem 5. Nonlinear Beam Optic in Straight
More informationLinear Collider Collaboration Tech Notes
LCC 0035 07/01/00 Linear Collider Collaboration Tech Notes More Options for the NLC Bunch Compressors January 7, 2000 Paul Emma Stanford Linear Accelerator Center Stanford, CA Abstract: The present bunch
More informationCOMMISSIONING OF NSLS-II*
COMMISSIONING OF NSLS-II* F. Willeke, BNL, Upton, NY 11973, USA Figure 1: Aerial view of NSLS-II. Abstract NSLS-II, the new 3rd generation light source at BNL was designed for a brightness of 10 22 photons
More informationOperational Experience with HERA
PAC 07, Albuquerque, NM, June 27, 2007 Operational Experience with HERA Joachim Keil / DESY On behalf of the HERA team Contents Introduction HERA II Luminosity Production Experiences with HERA Persistent
More informationOptics considerations for
Optics considerations for ERL x-ray x sources Georg H. Hoffstaetter* Physics Department Cornell University Ithaca / NY Georg.Hoffstaetter@cornell.edu 1. Overview of Parameters 2. Critical Topics 3. Phase
More informationLattice Design in Particle Accelerators
Lattice Design in Particle Accelerators Bernhard Holzer, DESY Historical note:... Particle acceleration where lattice design is not needed 4 N ntz e i N( θ ) = * 4 ( 8πε ) r K sin 0 ( θ / ) uo P Rutherford
More informationLattice Design of 2-loop Compact ERL. High Energy Accelerator Research Organization, KEK Miho Shimada and Yukinori Kobayashi
Lattice Design of 2-loop Compact ERL High Energy Accelerator Research Organization, KEK Miho Shimada and Yukinori Kobayashi Introduction Wepromote the construction of the compact Energy Recovery Linac(cERL)
More informationBeam Optics for Parity Experiments
Beam Optics for Parity Experiments Mark Pitt Virginia Tech (DHB) Electron beam optics in the injector, accelerator, and transport lines to the experimental halls has a significant impact on helicitycorrelated
More informationThe TESLA Dogbone Damping Ring
The TESLA Dogbone Damping Ring Winfried Decking for the TESLA Collaboration April 6 th 2004 Outline The Dogbone Issues: Kicker Design Dynamic Aperture Emittance Dilution due to Stray-Fields Collective
More informationEmittance preserving staging optics for PWFA and LWFA
Emittance preserving staging optics for PWFA and LWFA Physics and Applications of High Brightness Beams Havana, Cuba Carl Lindstrøm March 29, 2016 PhD Student University of Oslo / SLAC (FACET) Supervisor:
More informationSynchrotron Based Proton Drivers
Synchrotron Based Pron Drivers Weiren Chou Fermi National Accelerar Laborary P.O. Box 500, Batavia, IL 60510, USA Abstract. Pron drivers are pron sources that produce intense short pron bunches. They have
More informationA Luminosity Leveling Method for LHC Luminosity Upgrade using an Early Separation Scheme
LHC Project Note 03 May 007 guido.sterbini@cern.ch A Luminosity Leveling Method for LHC Luminosity Upgrade using an Early Separation Scheme G. Sterbini and J.-P. Koutchouk, CERN Keywords: LHC Luminosity
More informationLattices for Light Sources
Andreas Streun Swiss Light Source SLS, Paul Scherrer Institute, Villigen, Switzerland Contents: Global requirements: size, brightness, stability Lattice building blocks: magnets and other devices Emittance:
More informationSLS at the Paul Scherrer Institute (PSI), Villigen, Switzerland
SLS at the Paul Scherrer Institute (PSI), Villigen, Switzerland Michael Böge 1 SLS Team at PSI Michael Böge 2 Layout of the SLS Linac, Transferlines Booster Storage Ring (SR) Beamlines and Insertion Devices
More informationLongitudinal Top-up Injection for Small Aperture Storage Rings
Longitudinal Top-up Injection for Small Aperture Storage Rings M. Aiba, M. Böge, Á. Saá Hernández, F. Marcellini and A. Streun Paul Scherrer Institut Introduction Lower and lower horizontal emittances
More informationMedical Linac. Block diagram. Electron source. Bending magnet. Accelerating structure. Klystron or magnetron. Pulse modulator.
Block diagram Medical Linac Electron source Bending magnet Accelerating structure Pulse modulator Klystron or magnetron Treatment head 1 Medical Linac 2 Treatment Head 3 Important Accessories Wedges Dynamic
More informationX-band RF driven hard X-ray FELs. Yipeng Sun ICFA Workshop on Future Light Sources March 5-9, 2012
X-band RF driven hard X-ray FELs Yipeng Sun ICFA Workshop on Future Light Sources March 5-9, 2012 Motivations & Contents Motivations Develop more compact (hopefully cheaper) FEL drivers, L S C X-band (successful
More information