CAS CERN ACCELERATOR SCHOOL ADVANCED ACCELERATOR PHYSICS The Queen's ...

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CERN 87-03
21 April 1987
ORGANISATION EUROPÉENNE POUR LA RECHERCHE NUCLÉAIRE
CERN
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CAS
CERN ACCELERATOR SCHOOL
ADVANCED ACCELERATOR PHYSICS
The Queen's College, Oxford, England
16-27 September 1985
PROCEEDINGS
Editor: S. Turner
Vol.1
.GENEVA
1987
© Copyright CERN, Genève, 1987
Propriété littéraire et scientifique réservée pour Literary and scientific copyrights reserved in ail
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- iii -
ABSTRACT
This advanced course on general accelerator physics is the second of the biennial series given
by the CERN Accelerator School and follows on from the first basic course given at Gif-sur-Yvette,
Paris, in 1984 (CERN Yellow Report 85-19). Stress is placed on the mathematical tools of Hamiltonian
mechanics and the Vlasov and Fokker-Planck equations, which are widely used in accelerator theory.
The main topics treated in this present work include: nonlinear resonances, chromaticity, motion in
longitudinal phase space, growth and control of longitudinal and transverse beam emittance, space-
charge effects and polarization. The seminar programme treats some specific accelerator techniques,
devices, projects and future possibilities.
ADVANCED ACCELERATOR PHYSICS COURSE, OXFORD SEPTEMBER 1985
Time Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday Thursday Friday
16 September 17 September 18 September 19 September 20 September 21 September 22 September 23 September 24 September 25 September 26 September 27 September
R E A K F A ST (served 08.00 - 08.30) R E A K F A ST
09.00
Registration Non-Linear Non-Linear Landau Waves in Wake Fields Instabilities Instabilities Synchro- Diffusion
09.30 Resonances Resonances Damping Plasmas Betatron due to
Welcome Resonances R.F. Noise
and
Introduction
J. Mulvey C. Lashmore-
K. Johnsen E. Wilson E. Wilson H. Hereward Davies V.G. Vaccaro J.-L. Laclare O.-L. Laclare A. Piwinski G. Dome
10.00
C O F F EE C O F F EE
10.30
Hami Hon i an Chromaticity Chromat i city Beam-Beam Beam-Beam Betatron Space-Charge Beam Schottky Noise Beam
Dynamics Effect Effect and Coupling Dominated Break-up and Beam Loading
Beam with Beam Transport Transfer
Disruption Radiation Function
Diagnostics
J. Bell B. Montague G. Guignard L. Evans L. Evans
(Presented b. J. Gareyte) G. Guignard I. Hofmann J. LeDuff D. Boussard D. Boussard
11.30
Hamiltonian Hamiltonian Kinetic Hamiltonian Dynamics with Stochastic Stochastic Electron Intra-beam Seminar
Dynamics Treatment of Theory and Treatment of Radiation and Cooling Cooling Cooling and Multiple High Intensity
Longitudinal Vlasov Longitudinal Non-linear Scattering Neutron Beams
Mot i on Equation Motion Wigglers
C. Lashmore- FREE DAY FREE DAY
J. Bell G. Dome Davies G. Dome J. Jowett D. Mohl D. Mohl H. Poth A. Piwinski G. Rees
12.30
L U N CH L U C H
14.00
STUDY SESSI 0 N
15.00 Study Study Fi Im on
Seminar Discussion Discussion Discussion Discussion Session Session Polarization
and and and
RFQ V I S IT Discussion Discussion Discussion
Closing
M. Puglisi TO Remarks
16.00
T E A RUTHERFORD TEA K. Johnsen
16.30
TEA Seminar Seminar Seminar Seminar APPLETON Seminar Polarisation Seminar
17.00 in Electron
Particle S.C. R.F. High-Field Heavy Ions; LABORATORY Free-electron and Proton Linear
17.30 Tracking Systems Linacs The Present Laser Beams Colliders
Welcome and Future versus
Reception Storage Rings
H. Mais H. Piel J. LeDuff H. Gutbrod A. Renieri J. Buon U. Amaldi
18.00
E V E N I NG M E AL (start 19.00 prompt) E V E N I NG
20.00
Organ Recital Bingham String CocktaiIs
The Queen's Quartet +
College Chapel Holywell Music Banquet
M.S. Gautrey Rooms
CERN ACCELERATOR SCHOOL
Rutherford Appleton Laboratory &
Department of Nuclear Physics, Oxford
will jointly organize a course on
A D V A N C ED A C C E L E R A T OR
P H Y S I CS
16-27 SEPTEMBER 1985
at The Queen's College, Oxford, England
Lectures:
Hamiltonian Dynamics Kinetic Theory and Vlasov Equation
Non-linear Resonances Waves in Plasma
Chromaticity Landau Damping
Betatron Coupling with Radiation Dynamics with Radiation and Non-linear Wigglers
Synchro-Betatron Resonances Polarization in Electron and Proton Beams
Hamiltonian Treatment of Longitudinal Motion
Diffusion due to R.F. Noise
Seminars:
Beam Loading
Beam-Beam Effect RFQ
Beam Disruption Particle Tracking
Beam Break-up Superconducting Radiofrequency Systems
Space-Charge Dominated Beam Transport High-Field Linacs
Wake Fields Heavy Ions
Instabilities Free-electron Laser
Stochastic Cooling Linear Colliders versus Storage Rings
Electron Cooling High Intensity Neutron Beams
Intra-beam and Multiple Scattering Discussions and visit to
Schottky Noise and Beam Rutherford Appleton
Transfer Function Diagnostics Laboratory
General information Students should have a basic knowledge of accelerators. Persons wishing to attend this course can obtain
further information and application forms from the CERN Accelerator School, Mrs. S. von Wartburg,
LEP Division, CH 1211 Geneva 23. Application forms must be returned no later than 1st June 1985. The
registration fee of 970.- FS includes full board and lodging in The Queen's College, Oxford, England. All
participants will receive a copy of the proceedings. The number of participants is limited to 130.
Administration Head of School: K. Johnsen; Programme Committee: P. Bryant, J. Buon, K. Johnsen, W. Joho, R. Kohaupt,
J. Lawson, K. Nielsen, S. Tazzari;
Local Organizing Committee: P. Bryant, S. Collier, K. Johnsen, J. Maidment, J. Mulvey, S. von Wartburg.
- ix -
CONTENTS
Page No.
Foreword vi i
Opening address 1
Local coordinates for the beam and frequently used symbols 3
J.S. Bell
Hamiltonian mechanics 5
Introduction 5
Poisson brackets 8
Stationary and varying action 8
Poincaré invariant 10
Lagrange invariant 11
Synplectics 13
Liouville's theorem 14
Conserved quadratic form 15
Characteristic exponents 16
Canonical transformations 19
Point transformation 20
Change of independent variable 22
Scaling 23
Dynamical evolution as canonical transformation 24
Poincaré invariant 25
Lagrange invariant 25
Liouville invariant 27
One degree of freedom 29
Action and angle variables 30
Small deviations from closed orbit 31
Adiabatic invariance of J 35
Small canonical transformation 36
Canonical perturbation theory 37
E.J.N. Wilson
Nonlinear resonances 41
Introduction 41
The general form of the Hamiltonian 43
The magnetic vector potential for multipoles 45
Linear dynamics in action angle variables 46
Perturbation theory 52
Effect of nonlinearities far from a resonance 55
Resonances 56
The third-integer resonance 57
The trajectory of a third-integer resonance 59
The effect of an octupole 62
Phase-space topology with amplitude frequency variation 63
Amplitude growth on crossing a resonance 65
Synchrotron resonances 66
Beam lifetime due to magnet imperfections 68
The effect of two dimensions of transverse motion 69
Three dimensions of magnetic field 72
Conclusions 73
- X -
B. W. Montague
Chromatic effects and their first-order correction 75
Introduction 75
Basic ideas 76
Chromatic perturbation equations 80
Two dimensions 84
G. Guignavd
Chromaticity: nonlinear aberrations 91
Introduction 91
Description of the nonlinear perturbations 92
Perturbation theory in the canonical variables 96
Dynamic aperture and analytical approach 102
G. Dome
Theory of RF acceleration 110
Energy gain and transit time factor 110
Harmonic number 112
Finite difference equations 112
Differential equations for an arbitrary RF voltage 117
Hamiltonian with reduced variables 119
Small oscillations around the stable fixed point 123
Motion in the vicinity of the fixed points 124
Stationary bucket with a harmonic cavity 127
Formulae for a sinusoidal RF voltage 128
Adiabatic damping of phase oscillations 131
Back to finite difference equations. Stochasticity 136
Phase displacement acceleration 139
Linear accelerators 143
L. R. Evans and J. Gareyte
Beam-beam effects 159
Introduction 159
The beam-beam force 159
Experimental and numerical data from e+e" machines 165
Experimental data from hadron machines 171
Nonlinear beam-beam resonances 175
Beam disruption 184
Conclusions 185
A. Piwinski
Synchro-betatron resonances 187
Introduction 187
Dispersion in a cavity 188
Transverse fields with longitudinal variation 192
Beam-bean interaction with a crossing anqle 194
G. Guignard
Betatron coupling with radiation 203
Introduction 203
Perturbation treatment of linear betatron coupling 203
Amplitude variation due to radiation and acceleration 209
Equilibrium in the case of betatron coupling with radiation 213
Application to emittance control 217
C. H. Lashnore-Davies
Kinetic theory and the Vlasov equation 219
Introduction 219
The Vlasov equation 220
The effect of binary collisions 224
Fluid models 229
- xi -
C. N. Lashmore-Davies
Haves in plasmas 235
Introduction 235
Waves in a field-free plasma 236
Waves in a magnetized plasma 240
Low-frequency waves in a magnetized plasma 245
Raman scattering 247
H.G. Hereward
Landau damping 255
Spectrum of linear oscillations 255
Longitudinal instability 259
Nonlinear oscillations 261
J.L. Laclare
Bunched beam coherent instabilities 264
Introduction 264
Longitudinal instabilities 264
Transverse instabilities 306
Conclusion 325
J. Hofrnann
Space charge dominated beam transport 327
Introduction 327
Basic properties 327
Emittance and field energy 329
Application to emittance growth 332
L. Palumbo and V.G. Vocear o
Wake fields, impedances and Green's function 341
Longitudinal wake potential and impedance 341
Longitudinal impedance and wake potential for simple structures 344
General analysis 357
Circular accelerators 361
Transverse-wake potential and impedance 363
Remarks 368
Conclusions 369
G. Dôme
Diffusion due to RF noise 370
Statistical properties of random variables 370
Fokker-Planck equation 372
Differential equations for a stationary bucket with amplitude and phase noise 374
Computation of the coefficients k A in the Fokker-Planck equation 377
it 2
Case of a sinusoidal RF voltage 382
Finite difference equations 386
Diffusion equation 388
Contribution of RF noise to the finite beam lifetime in the SPS collider 392
A. Piwinski
Intra-beam scattering 402
Introduction 402
Calculation of rise times and damping times 403
Experimental results 411
- xii -
D. Bousscœd
Schottky noise and beam transfer function diagnostics 416
Schottky signals 417
Beam detectors 425
Observation of Schottky signals 440
Beam transfer functions 445
D. Möhl
Stochastic cooling 453
Introduction 453
Simplified theory, time-domain picture 455
A more detailed presentation of betatron cooling, frequency domain picture 478
Distribution function equations (Fokker-Planck) and momentum scalinq 510
H. Poth
Electron cooling 534
Introduction 534
What electron cooling is 534
Why electron cooling? 535
Ion-beam and storage-ring properties 535
How electron cooling works in principle 537
Introduction to electron cooling theory (for pedestrians) 538
Experimental realization of electron cooling 543
More on the theory of electron cooling 552
Recombination 555
Electron cooling experiments 557
Simulation of electron cooling in storage rings 561
Electron cooling diagnostics 562
Applications of electron cooling 564
Electron cooling projects 566
J. Jowett
Electron dynamics with radiation and nonlinear wigglers 570
Introduction 570
The dynamics of electrons in a storage ring 571
Normal modes and optical functions 579
Radiation damping 584
Quantum fluctuations and Fokker-Planck equations 587
Nonlinear wigglers 591
J. Le Duff
Beam break up 610
Experimental evidence 610
Transverse deflection of charge particles in radio-frequency fields 612
Deflecting modes in circular iris loaded waveguides 614
Regenerative beam break up 617
Cumulative beam break up 621
£>„ Boussard
Beam loading 626
Introduction 626
Single bunch passage in a cavity 627
Multiple bunch passages 629
Limiting case 6 = 0 630
Ü
The case of a travelling wave structure 633
Transient correction 635
RF drive generation 637
- xiii -
J. Buon
Polarization in electron and proton beams 647
Introduction 647
Generalities on polarization and spin motion 649
Acceleration of polarized protons in synchrotrons 661
Polarization of electrons in storage rings 671
H. Mais, G. Ripken, A. Wruliah and F. Schmidt
Particle tracking 690
Introduction 690
Hamiltoni an description of the proton motion 690
Dynamic aperture 693
Particle tracking 694
Qualitative theory of dynamical systems 696
Studies of chaotic behaviour in HERA caused by transverse magnetic multipole fields 699
Summary 704
M. Puglisi
The radiofrequency quadrupole linear accelerator 706
Introduction 706
The accelerating structure 706
Outline of the T-K expansion 709
The vane tips shaping 712
Physical considerations 717
The structure of an RFQ 720
Design and technical considerations 728
Recent developments 733
H. Piel
Fundamental features of superconducting cavities for high energy accelerators 736
Introduction 736
Some cavity fundamentals 737
Superconducting cavities 741
Cavity design 746
Anomalous losses 751
Cavities covered with superconducting thin films 761
Current accelerator projects and achievements 765
J. Le Duff
High field electron linacs 772
Introduction 772
Extrapolation of present technologies 772
RF compression scheme 775
Ultimate accelerating gradients in conventional structures 783
A survey of accelerating structures 785
RF power source: the lasertron 787
G. Dattoli, A. Renieri and A. Torre
Free electron lasers: a short review of the theory and experiments 792
Introduction 792
FEL: theory and design criteria 795
FEL storage ring operation 803
Single passage FEL operation 808
Conclusions 814
D.A. Gray and G.H. Rees
ISIS, the accelerator based neutron source at RAL 817
Introduction 817
Linac and synchrotron 817
Target station 819
Experimental facilities 821
High intensity performance of the ISIS synchrotron 822