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Linear Collider Parameters

Linear Collider Parameters. International Linear Collider School May 21 st , 2006. Outline. Luminosity and beam parameters Introduction Luminosity expressions IP parameters Beamstrahlung Disruption Spot size limitations Particle sources Emittance generation

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Linear Collider Parameters

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  1. Linear Collider Parameters International Linear Collider School May 21st, 2006

  2. Outline • Luminosity and beam parameters • Introduction • Luminosity expressions • IP parameters • Beamstrahlung • Disruption • Spot size limitations • Particle sources • Emittance generation • Damping rings, bunch compression, and Linac emittance limits • Final focusing system • RF system parameters and efficiency  to be covered by Chris Adolphsen

  3. Schematic of the ILC

  4. SLC: The 1st Linear Collider Built to study the Z0and demonstrate linear colliderfeasibility Energy = 92 GeV Luminosity = 3e30 Had all the featuresof a 2nd gen. LCexcept both e+and e- shared thesame linac Much more than a 10% prototype

  5. SLC luminosity:Many Lessons Learned

  6. Luminosity versus SLC

  7. SLC, E-158 Experimental Basis for the ILC Design Bunch Compression SLC, FFTB, ASSET, E-158 SLC and FEL’s SLC and(ATF2 in the future) ePreservation BDS & IR TESLA Test Facility (SMTF & STF in the future) Linac rf system ATF, 3rd Gen Light Sources, SLC Damping Rings e+ / e- Sources

  8. Luminosity: Aiming for 2x1034 Collider luminosity (cm-2 s-1)isapproximately given by where: nb = bunches / trainN = particles per bunchfrep = repetition frequencyA = beam cross-section at IPHD = beam-beam enhancement factor For a Gaussian beam distributionwhere Sx = sqrt(sx12 + sx22):

  9. Luminosity • frep * nb tends to be low in a linear collider • Fortunately the beam-beam tune shift limit is much looser in a linear collider than a storage rings  achieve luminosity with spot size and bunch charge • Small spots mean small emittances and small betas:sx = sqrt(bxex)

  10. Interjection – Phase Space Beta function b characterize optics Emittance eis phase space volume of the beam – optics analogyis the wavelength Tilt is parameterized with a Beam size: (e b)1/2 Divergence: (e /b)1/2 Squeeze on beam size  increase angular divergence Beam emittance is not conserved during acceleration  normalized emittance should be ge

  11. Linear Collider Luminosity • Convert luminosity expression using beam power • Pbeam = Ecms * eN * nb * frep • Required to have large beam powers • Further constrained by IP effects • Beamstrahlung – synchrotron radiation due to strong beam fields • Disruption – beam distortion due to strong beam fields at the IP • Hourglass – b≥ sz • For flat beams (sx >> sy)where d ~ N2/sx2sz

  12. (8 Cavities per Cryomodule) Main Linac RF System ~90% eff. ~95% eff. ~65% eff. Cavity losses are very small but cryo-system efficiency ~0.2%  small losses have impact

  13. Beam Power Issues • Beam power depends upon linac design, operating limitations, and collider AC power consumption limitations • Typical AC  beam efficiencies are ~20% (inc. cooling) 11 MW beam power implies ~100 MW AC power • In practice there are many other requirements • ILC site power consumption is closer to 200 ~ 250 MW • SC cavities dissipatelittle power but still needto be filled  65% eff. • Ac  rf power efficiency depends on technologybut is typically ~50%plus ~ 10% for overhead • Covered by C. Adolphsen generatorvoltage RF on cavity voltage beam on beaminduced voltage

  14. Beam Parameters • Requirements: • High luminosity – set by physics needs • Low backgrounds (small IP effects) • Forced to high beam power and small vertical spots • Details of technology determine other limitations • Rf cavities and power sources  10 mA beam current • Damping rings  beam emittances and number of bunches • Bunch compressors  IP bunch length • Cryogenic systems  duty cycle • Extensive cost optimization is required to balance systems • Linear collider will push many technological and beam-physics limits • Need to have operational flexibility to overcome unexpected problems

  15. ILC Parameters Parameter range established to allow for operational optimization

  16. IP Parameters • IP parameters determine basic beam structure • Charge per bunch • Beam power • IP spot sizes • All parameters are linked

  17. Linear Collider Parameters • Model for linear collider design! Bob Palmer 1990

  18. Beam-Beam Tune Shifts • Fields from charge particles focus (or defocus) each other as they pass through each other in IP • Effect is known as the beam-beam tune shift in a storage ring xx,y and is typically limited to ~ 0.05 to prevent the beam spot sizes from increasing as the beam circulates • In ILC, the ‘ring tune shift’ is ~2 (thin lens calculation) • Ideally in single-pass collider the tune-shift is not a limitation • In practice it is still a limit but is much looser • The analogous effect is referred to as the disruption in an LC

  19. IP Beam Fields (1) • Fields from charge particles focus (or defocus) each other as they pass through each other in IP • Fields from relativistic beam are radial – spread as 1/g: v ~ clinear charge density = l a

  20. IP Beam Fields (2) • Fields in Gaussian beams peak ~ sand then decay as 1/r (in a roundGaussian beam) • Peak field  • Beam fields are very strong • Linear colliders are designed with ‘flat’ beams to minimize the IP fields for a given luminosity • Luminosity is inversely proportional to cross-sectional area • Fields are inversely proportional to surface area • Flat beams are naturally generated in damping rings and thus this is an ‘easy’ optimization • With asymmetric Gaussian beams:

  21. IP Beam Fields (3) • F = e(Er + cBq) • E and B cancel at as 1/g2 in co-propagating • E and B add in counter-propagating beams  F ~ 2eEr • Fields are extremely strong at IP ~ few V / Angstrom or kT [kilo-Tesla] • Main effects: beam disruption and synchrotron radiation • Focusing at IP is given by dF / dr normalize by charge and mass  K [m-2] • Now: • Finally with asymmetric Gaussian beams: a2  2sx,y(sx + sy)

  22. IP Beam Fields • Two main effects: • Beamstrahlung – Synchrotron radiation of particles in the strong fields of the opposing beam; many % of the beam energy can be radiated • Pair production – Intense fields can convert beamstrahlung photons into e+/e- pairs • Disruption – fields of the opposing beam will distort the beam during the collision • Pinch effect luminosity enhancement where mutual focusing of the oppositely charged beams increases density in collision • Beam-beam deflections  small offsets between the beam are amplified into large angular kicks which can be measures and used to stabilize the collision • Single bunch kink  when disruption is large enough, end up with a two-stream instability which can reduce luminosity

  23. Beamstrahlung • The IP fields cause synchrotron radiation • Generates potential backgrounds • Degrades the luminosity spectrum • Effect is described with three parameters: • Average energy loss: d • Number of photons: ng • Quantum parameter: Y • Simplistically, ng describes the spectrum close to the center-of-mass energy while d describes the tails

  24. Simple Beamstrahlung • Beam particles radiate synchrotron radiation in strong fieldswhere • For nominal ILC parameters at 250 GeV and using the peak B field ~60 GeV radiated in collision or 25% of energy • Need to do the calculation properly averaging over the beam but scaling is clear USR ~ g2sz N2 / sx2

  25. Quantum Effects • Assumed classical synchrotron radiation formulation but at high-energy and high-fields quantum effects can be important • The critical photon energy is: • Effects are parameterized with Upsilon:TeV linear collider designs operate withY << 1 but, above 1 ~ 2 TeV, upsilonis usually chosen to be greater 1

  26. Beamstrahlung Formula • Approximate formulas can be written which describe the process over the usual range of LC parameters • See: P. Chen, “Differential Luminosity under Multi-Photon Beamstrahlung”, Phys. Rev. D, 46: 1186 (1992). K. Yokoya, P. Chen, “Beam-beam phenomena in linear colliders,” Lecture Notes Physics, 400: 415 (1992). P. Chen, “Disruption effects from the collision of quasi-flat beams,” PAC 93.

  27. Pair Production (1) • The beamstrahlung photons can create e+/e- pairs • Incoherent pair production – arises from photons scattering off of beam particles • Multiple channels but typically relatively few pairs ~105 • Coherent pair production – arises from photon scattering off collective fields of the beam • With Y ~ 1, as many pairs as beam particles

  28. Pair Production (2) • Pairs are a significant source of background • Relatively low energy particles are given large transverse deflections by the beam fields • Can be partly controlled with strong solenoidal field at the IP but need to be careful with detector design to constrain the particles and secondary interactions

  29. Disruption (1) • Strong fields will distort the opposing beam • Normalized beam-beam focusing force at the IP: • Disruption parameter defined using thin lens approximation and comparing focal to bunch length • Assume a rectangular distribution  number of oscillations in opposing bunch:

  30. Luminosity Enhancement • Mutual focusing of oppositely charged beams can increase the collision density • HD is small~1.5 with flatbeams • Increased Dymakes lumisensitive tooffsets From Yokoya & Chen Dy

  31. Luminosity with Offsets • Disruption forces help stabilize the collisions tooffsets for lowDy but thesingle-bunchkink instabilityreducesluminosityat high Dy > 15 HD = L/L0 Dy / sy

  32. Luminosity Enhancement • Many simulations have been written to model IP environment: • CAIN – Yokoya and Chen • GuineaPig – Shulte • An empirical expression was fit to simulation results • Depends on disruption and weakly on depth of focus (hour-glass effect) • Expression is valid over typical LC parameters • Needs to supported with detailed simulations

  33. Hourglass Effect • Hourglass limits by ~ sz From Nick Walker for TESLA

  34. Single Bunch Kink (1) • Single bunch kink is a two-stream instability • Small offsets are amplified by very strong beam-beam forces • Potential limitation at high disruption parameters • Why high disruption? • Luminosity expression can be re-written in terms of Dy • If there is a practical limit on the maximum disruption  luminosity can be increased by shortening the bunch • Hard to avoid larger beamstrahlung

  35. Single Bunch Kink (2) Single bunch kink due to 1% initial offset between beams Dy = 12 Dy = 24

  36. Single Bunch Kink Movie

  37. ILC Parameters Parameter range established to allow for operational optimization

  38. Schematic of the ILC

  39. Polarized Electron Source • Polarized electron beam generated from a polarized laser on a strained GaAs photocathode • Technology is robust • Demonstrated for years on SLC and E-158 at SLAC • Laser system has new requirements but is not thought to be a significant technical limitation • Options for new technology in the form of polarized rf guns • Requires more robust photocathode material • Gains in operational simplicity but not large cost savings UNLESS the rf gun can replace the damping rings • Damping rings have multiple functions • Damp incoming phase space • Provide a stable platform and damping incoming transients • Allow for feed-forward to pre-set linac systems

  40. Tune-up dump (diagnostics section) SHB Buncher |---- RT Pre-Accelerator----| 12 MeV / m Laser Diagnostics Laser Gun Gun 12 MeV 71 MeV 120 keV Klystron 10 MW Spare Klystron 10 MW ILC Electron Source

  41. Polarized Photo-cathodes

  42. GaAsP 30 A Strained GaAs 40 A Active Region 1000 A GaAs0.64P0.36 Buffer GaAsP 25mm Strained GaAs GaAs(1-x)Px Graded Layer 25mm GaAsP Strained GaAs GaAs Substrate Polarized Photo-Cathode R&D • Strained superlattices are yields ~90% polarization • Further optimization possible for ILC bunch train • Develop GaN as a more robust alternate

  43. Positron Source • Large number of positrons required per second • 60 times more than in SLC • Pulsed damage to the target • Average heating of the target • Radiation damping to the target • Difficult complex system SLC e+ target Beam direction

  44. Target and Capture Structures

  45. ILC Positron Source • Three options considered for ILC • Thick 4 rl WRe target with ~6 GeV e- beam • Conventional technology but very high radiation loads • Thin Ti target with 10 MeV photon beam • Photon beam generated by passing 150 GeV e- thru undulator • Allows for e+ polarization as well • Thin target using Compton scattered laser beam • Requires very powerful laser systems but would have benefits of independence from e- beam and possible polarization • Capture systems are the same in all cases • Chose undulator-based source as baseline • Many advantages – only problem is that it couples e+ source to the electron beam and constrains timing systems and beam operations

  46. Beam Delivery System Positron Linac IP 150 GeV 100 GeV 250 GeV Helical Undulator In By-Pass Line Photon Collimators e- Dump e- Dump Photon Dump e- DR e- source e+ pre-accelerator ~5GeV Photon Target Adiabatic Matching Device Auxiliary e- Source e+ DR Adiabatic Matching Device e- Target Undulator-Based Positrons • 200 meters of helical undulator in electron beam line • Photons impinge on 0.5 rl Ti target • Captured in normal conducting structures • High radiation environment with large beam losses does not work for superconducting structures • Not much head-room on e+ production rates

  47. Damping Rings • Damping rings have more accelerator physics than the rest of the collider • Required to: • Damp beam emittances and incoming transients • Provide a stable platform for downstream systems • Have excellent availability ~99% (best of 3rd generation SRS) • Mixed experience with SLC damping rings: • Referred to as the “The source of all Evil” • Collective instabilities; Dynamic aperture; Stability • Damping ring designs based on KEK ATF, 3rd generation SRS, and high luminosity factories • Experimental results provide confidence in design

  48. KEK ATF Damping Ring • Probably world’s largest linear collider test facility World’s lowest emittance beam: ey = 4 pm-rad below X-band LC requirements Used to verify X-band DR concepts Detailed measurements of emittance tuning, lattice properties, IBS, ions, collective effects, and instrumentation 1.3 GeV Damping Ring and S-band linac Commissioning started in 1997

  49. Damping Ring Emittances (1) • See M. Sand, “Physics of Electron Storage Rings,” SLAC-121 (1972). • Two competing processes: radiation damping and quantum excitation • Radiation damping: • Longitudinal phase space • Higher energy particles radiate more energy than low energy particles in the bends • Transverse phase space • Radiation is emitted in a narrow cone centered on the instantaneous direction of motion • Transverse momentum is radiated away • Energy is restored by the RF cavities longitudinally • Combined effect of radiation and RF is a loss in transverse momentum

  50. Damping Ring Emittances (2) • Quantum excitation • Radiation is emitted in discrete quanta • Number and energy distribution etc. of photons obeystatistical laws • Radiation process can be modeled as a series of “kicks” that excite longitudinal and transverse oscillations Start to oscillate about nominal trajectory Low E Trajectory NominalTrajectory DE = 0

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