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DESY Summer Student Lecture 31 st July 2002

An Introduction to the Physics and Technology of e+e- Linear Colliders Lecture 9: a) Beam Based Alignment Nick Walker (DESY). DESY Summer Student Lecture 31 st July 2002. USPAS, Santa Barbara, 16 th -27 th June, 2003. Emittance tuning in the LET. LET = L ow E mittance T ransport

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DESY Summer Student Lecture 31 st July 2002

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  1. An Introduction to thePhysics and Technologyof e+e- Linear CollidersLecture 9: a) Beam Based AlignmentNick Walker (DESY) DESY Summer Student Lecture31st July 2002 USPAS, Santa Barbara, 16th-27th June, 2003

  2. Emittance tuning in the LET • LET = Low Emittance Transport • Bunch compressor (DRMain Linac) • Main Linac • Beam Delivery System (BDS), inc. FFS • DR produces tiny vertical emittances (gey ~ 20nm) • LET must preserve this emittance! • strong wakefields (structure misalignment) • dispersion effects (quadrupole misalignment) • Tolerances too tight to be achieved by surveyor during installation  Need beam-based alignment mma!

  3. Basics (linear optics) thin-lens quad approximation: Dy’=-KY gij Yi Yj yj Ki linear system: just superimpose oscillations caused by quad kicks.

  4. Introduce matrix notation Original Equation Defining Response MatrixQ: Hence beam offset becomes G is lower diagonal:

  5. Dispersive Emittance Growth Consider effects of finite energy spread in beam dRMS chromatic response matrix: dispersivekicks latticechromaticity dispersive orbit:

  6. What do we measure? BPM readings contain additional errors: boffset static offsets of monitors wrt quad centres bnoise one-shot measurement noise (resolution sRES) random(can be averagedto zero) fixed fromshot to shot launch condition In principle: all BBA algorithms deal with boffset

  7. Scenario 1: Quad offsets, but BPMs aligned quad mover dipole corrector • Assuming: • a BPM adjacent to each quad • a ‘steerer’ at each quad steerer simply apply one to one steering to orbit

  8. Scenario 2: Quads aligned, BPMs offset one-to-one correction BAD! Resulting orbit not Dispersion Free emittance growth Need to find a steering algorithm which effectively puts BPMs on (some) reference line real world scenario: some mix of scenarios 1 and 2

  9. BBA • Dispersion Free Steering (DFS) • Find a set of steerer settings which minimise the dispersive orbit • in practise, find solution that minimises difference orbit when ‘energy’ is changed • Energy change: • true energy change (adjust linac phase) • scale quadrupole strengths • Ballistic Alignment • Turn off accelerator components in a given section, and use ‘ballistic beam’ to define reference line • measured BPM orbit immediately gives boffset wrt to this line

  10. DFS Problem: Note: taking difference orbit Dy removes boffset Solution (trivial): Unfortunately, not that easy because of noise sources:

  11. DFS example mm 300mm randomquadrupole errors 20% DE/E No BPM noise No beam jitter mm

  12. DFS example Simple solve In the absence of errors, works exactly • Resulting orbit is flat • Dispersion Free (perfect BBA) original quad errors fitter quad errors Now add 1mm random BPM noise to measured difference orbit

  13. DFS example Simple solve original quad errors fitter quad errors Fit is ill-conditioned!

  14. DFS example mm Solution is still Dispersion Free but several mm off axis! mm

  15. DFS: Problems • Fit is ill-conditioned • with BPM noise DF orbits have very large unrealistic amplitudes. • Need to constrain the absolute orbit minimise • Sensitive to initial launch conditions (steering, beam jitter) • need to be fitted out or averaged away

  16. DFS example Minimise absolute orbit now constrained remember sres = 1mm soffset = 300mm original quad errors fitter quad errors

  17. DFS example mm Solutions much better behaved! ! Wakefields ! mm Orbit notquite Dispersion Free, but very close

  18. DFS practicalities • Need to align linac in sections (bins), generally overlapping. • Changing energy by 20% • quad scaling: only measures dispersive kicks from quads. Other sources ignored (not measured) • Changing energy upstream of section using RF better, but beware of RF steering (see initial launch) • dealing with energy mismatched beam may cause problems in practise (apertures) • Initial launch conditions still a problem • coherent b-oscillation looks like dispersion to algorithm. • can be random jitter, or RF steering when energy is changed. • need good resolution BPMs to fit out the initial conditions. • Sensitive to model errors (M)

  19. Ballistic Alignment • Turn of all components in section to be aligned [magnets, and RF] • use ‘ballistic beam’ to define straight reference line (BPM offsets) • Linearly adjust BPM readings to arbitrarily zero last BPM • restore components, steer beam to adjusted ballistic line 62

  20. Ballistic Alignment 62

  21. Ballistic Alignment: Problems • Controlling the downstream beam during the ballistic measurement • large beta-beat • large coherent oscillation • Need to maintain energy match • scale downstream lattice while RF in ballistic section is off • use feedback to keep downstream orbit under control

  22. An Introduction to thePhysics and Technologyof e+e- Linear CollidersLecture 9: b) Lessons learnt from SLCNick Walker (DESY) DESY Summer Student Lecture31st July 2002 USPAS, Santa Barbara, 16th-27th June, 2003

  23. Lessons from the SLC • New Territory in Accelerator Design and Operation • Sophisticated on-line modeling of non-linear physics. • Correction techniques expanded from first-order (trajectory) to include second-order (emittance), and from hands-on by operators to fully automated control. • Slow and fast feedback theory and practice. D. Burke, SLAC

  24. The SLC 1980 1998 note: SLC was a single bunch machine (nb = 1) taken from SLC – The End Game by R. Assmann et al, proc. EPAC 2000

  25. SLC: lessons learnt • Control of wakefields in linac • orbit correction, closed (tuning) bumps • the need for continuous emittance measurement(automatic wire scanner profile monitors) • Orbit and energy feedback systems • many MANY feedback systems implemented over the life time of the machine • operator ‘tweaking’ replaced by feedback loop • Final focus optics and tuning • efficient algorithms for tuning (focusing) the beam size at the IP • removal (tuning) of optical aberrations using orthogonal knobs. • improvements in optics design • many many more! The SLC was an 10 year accelerator R&D project that also did some physics 

  26. The Alternatives 2003 Ecm=500 GeV

  27. Examples of LINAC technology 9 cell superconducting Niobium cavity for TESLA (1.3GHz) 11.4GHz structure for NLCTA (note older 1.8m structure)

  28. Competing Technologies: swings and roundabouts RF frequency higher gradient = short linac  higher rs = better efficiency  High rep. rate = GM suppression  smaller structuredimensions = high wakefields  Generation of high pulse peakRF power  CLIC(30GHz) NLC(11.4GHz) SLC(3GHz) long pulse low peak power  large structure dimensions = low WF  very long pulse train = feedback within train  SC gives high efficiency  Gradient limited <40 MV/m = longer linac  low rep. rate bad for GM suppression (ey dilution)  very large unconventional DR  TESLA (1.3GHz SC)

  29. An Introduction to thePhysics and Technologyof e+e- Linear CollidersLecture 9: c) SummaryNick Walker (DESY) DESY Summer Student Lecture31st July 2002 USPAS, Santa Barbara, 16th-27th June, 2003

  30. The Luminosity Issue • high RF-beam conversion efficiency hRF • high RF power PRF • small normalised vertical emittance en,y • strong focusing at IP (small by and hence smallsz) • could also allow higher beamstrahlung dBSif willing to live with the consequences • Valid for low beamstrahlung regime (<1)

  31. High Beamstrahlung Regime low beamstrahlung regime 1: high beamstrahlung regime 1: with

  32. Pinch Enhancement Trying to push hard on Dy to achieve larger HD leads to single-bunch kink instability  detrimental to luminosity

  33. power lost to structure beam loading The Linear Accelerator (LINAC) • Gradient given by shunt impedance: • PRFRF power /unit length • rlshunt impedance /unit length • The cavity Q defines the fill time: • vg = group velocity, • ls = structure length • For TW, t is the structureattenuation constant: • RF power lost along structure (TW): hRF would like RS to be as high as possible

  34. unloaded av. loaded The Linear Accelerator (LINAC) For constant gradient structures: unloaded structure voltage loaded structure voltage(steady state) optimum current (100% loading)

  35. The Linear Accelerator (LINAC) Single bunch beam loading: the Longitudinal wakefield NLC X-band structure:

  36. wakefield RMS DE/E RF f = 15.5º <Ez> Total fmin = 15.5º The Linear Accelerator (LINAC) Single bunch beam loading Compensation using RF phase

  37. Transverse Wakes: The Emittance Killer! Bunch current also generates transverse deflecting modes when bunches are not on cavity axis Fields build up resonantly: latter bunches are kicked transversely  multi- and single-bunch beam breakup (MBBU, SBBU)

  38. Damped & Detuned Structures Slight random detuning between cells causes HOMs to decohere. Will recohere later: needs to be damped (HOM dampers)

  39. tail head Single bunch wakefields Effect of coherent betatron oscillation - head resonantly drives the tail Cancel using BNS damping:

  40. Wakefields (alignment tolerances) • higher frequency = stronger wakefields • higher gradients • stronger focusing (smaller b) • smaller bunch charge

  41. Damping Rings initial emittance(~0.01m for e+) equilibriumemittance final emittance damping time

  42. Bunch Compression • bunch length from ring ~ few mm • required at IP 100-300 mm long.phasespace dispersive section

  43. The linear bunch compressor see lecture 6 initial (uncorrelated) momentum spread: duinitial bunch length sz,0compression ration Fc=sz,0/szbeam energy ERF induced (correlated) momentum spread: dcRF voltage VRFRF wavelength lRF= 2p / kRFlongitudinal dispersion: R56 conservation of longitudinal emittance RF cavity

  44. The linear bunch compressor chicane (dispersive section) Two stage compression used to reduce final energy spread COMP #1 LINAC COMP #2 F2 E0 F1 DE

  45. Final Focusing chromatic correction

  46. Synchrotron Radiation effects FD chromaticity + dipole SR sets limits on minimum bend length

  47. Final Focusing: Fundamental limits Already mentioned that At high-energies, additional limits set by so-called Oide Effect:synchrotron radiation in the final focusing quadrupoles leads to a beamsize growth at the IP independent of E! minimum beam size: occurs when F is a function of the focusing optics: typically F ~ 7(minimum value ~0.1)

  48. sing1e quad 100nm offset 100nm RMS random offsets LINAC quadrupole stability for uncorrelated offsets Dividing by and taking average values: take NQ = 400, ey ~ 610-14 m, b ~ 100 m, k1 ~ 0.03 m-1  ~25 nm

  49. Beam-Beam orbit feedback see lecture 8 use strong beam-beam kick to keep beams colliding Generally, orbit control (feedback) will be used extensively in LC

  50. g = 0.01 g = 0.1 g = 0.5 g = 1.0 f / frep Beam based feedback: bandwidth f/frep Good rule of thumb: attenuate noise with f<frep/20

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