1. Tor Raubenheimer Linear Collider Parameters International Linear Collider School May 21 st, 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 1 st Linear Collider Built to study the Z 0 and demonstrate linear collider feasibility Energy = 92 GeV Luminosity = 3e30 Had all the features of a 2nd gen. LC except both e+ and e- shared the same linac Much more than a 10% prototype

5. SLC luminosity: Many Lessons Learned

6. Luminosity versus SLC

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

8. Luminosity: Aiming for 2x10 34 Collider luminosity (cm -2 s -1 ) is approximately given by where: n b = bunches / train N = particles per bunch f rep = repetition frequency A= beam cross-section at IP H D = beam-beam enhancement factor For a Gaussian beam distribution where  x = sqrt(  x1 2 +  x2 2 ):

9. Luminosity f rep * n b 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:  x = sqrt(  x  x )

10. Interjection – Phase Space Beta function  characterize optics Emittance  is phase space volume of the beam – optics analogy is the wavelength Tilt is parameterized with  Beam size: (   Divergence: (  ) 1/2 Squeeze on beam size  increase angular divergence Beam emittance is not conserved during acceleration  normalized emittance should be 

11. Linear Collider Luminosity Convert luminosity expression using beam power –P beam = E cms * eN * n b * f rep –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 –  ≥  z For flat beams (  x >>  y ) where  ~ N 2 /  x 2  z

12. Main Linac RF System (8 Cavities per Cryomodule) ~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 dissipate little power but still need to be filled  65% eff. –Ac  rf power efficiency depends on technology but is typically ~50% plus ~ 10% for overhead Covered by C. Adolphsen generator voltage cavity voltage beam induced voltage beam on RF on

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 nomlow Nlrg Ylow PHigh L N  10 10 21222 nbnb 28205640282013302820  x,y  m, nm 9.6, 4010,3012,8010,3510,30  x,y cm, mm2, 0.41.2, 0.21, 0.41, 0.2  x,y nm543, 5.7495, 3.5495, 8452, 3.8452, 3.5 DyDy 18.51028.62722  BS %2.21.82.45.77 zz mm 300150500200150 P beam MW11 5.311 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  x,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/  : a v ~ c linear charge density =

20. IP Beam Fields (2) Fields in Gaussian beams peak ~  and then decay as 1/r (in a round Gaussian 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(E r + cB  ) –E and B cancel at as 1/  2 in co-propagating –E and B add in counter-propagating beams  F ~ 2eE r 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: a 2  2  x,y (  x +  y )

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:  –Number of photons: n  –Quantum parameter: Y –Simplistically, n  describes the spectrum close to the center-of- mass energy while  describes the tails

24. Simple Beamstrahlung Beam particles radiate synchrotron radiation in strong fields where 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 U SR ~  2  z N 2 /  x 2

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 with Y << 1 but, above 1 ~ 2 TeV, upsilon is 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 ~10 5 –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 –H D is small ~1.5 with flat beams Increased D y makes lumi sensitive to offsets From Yokoya & Chen Dy

31. Luminosity with Offsets Disruption forces help stabilize the collisions to offsets for low D y but the single-bunch kink instability reduces luminosity at high D y > 15  y /  y H D = L/L 0

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  y ~  z 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 D y –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 D y = 12 D y = 24

36. Single Bunch Kink Movie

37. ILC Parameters nomlow Nlrg Ylow PHigh L N  10 10 21222 nbnb 28205640282013302820  x,y  m, nm 9.6, 4010,3012,8010,3510,30  x,y cm, mm2, 0.41.2, 0.21, 0.41, 0.2  x,y nm543, 5.7495, 3.5495, 8452, 3.8452, 3.5 DyDy 18.51028.62722  BS %2.21.82.45.77 zz mm 300150500200150 P beam MW11 5.311 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. ILC Electron Source

41. Polarized Photo-cathodes

42. 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 Strained GaAs GaAsP Strained GaAs GaAsP Strained GaAs GaAsP 30 A 40 A GaAs Substrate GaAs (1-x) P x Graded Layer GaAs 0.64 P 0.36 Buffer Active Region 25  m 1000 A

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. 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 e- source e - DR e - Dump Photon Dump e + DR Auxiliary e - Source Photon Collimators Adiabatic Matching Device e + pre-accelerator ~5GeV 150 GeV100 GeV Helical Undulator In By-Pass Line Photon Target 250 GeV Positron Linac IP Beam Delivery System e- Target Adiabatic Matching Device e - Dump

47. Damping Rings Damping rings have more accelerator physics than the rest of the collider Required to: 1.Damp beam emittances and incoming transients 2.Provide a stable platform for downstream systems 3.Have excellent availability ~99% (best of 3 rd 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, 3 rd generation SRS, and high luminosity factories –Experimental results provide confidence in design

48. KEK ATF Damping Ring World’s lowest emittance beam:  y = 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 Probably world’s largest linear collider test facility

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 obey statistical laws –Radiation process can be modeled as a series of “kicks” that excite longitudinal and transverse oscillations Nominal Trajectory  E = 0 Low E Trajectory Start to oscillate about nominal trajectory

51. Damping Ring Emittances (3) Quantum excitation occurs in the horizontal plane Two effects determine the vertical emittance: –Opening angle of the SR – typically limits at about 10% of design emittance –Alignment errors which couple the horizontal to the vertical Vertical bending due to orbit errors Skew quadrupole fields due to quadrupole rotations or vertical sextupole misalignments Tolerances are very tight – frequently a few microns Combined effect of radiation damping and excitation:  inj = injected emittance  equ = equilibrium emittance  = radiation damping time

52. Issues in the Damping Rings Emittance tuning and error correction –Orbit correction and component stabilization Injection/extraction of individual bunches –Kicker rise/fall time – very large rings to store 3000 bunches Dynamic aperture –Long wigglers needed if the ring is too big Single-bunch intensity –Tune shift by self-Coulomb force (space charge) Instabilities (mainly average current) –Electron cloud instability –Fast ion instability –Classical collective instabilities Rings operate in a new regime with fast damping and very small beam emittances

53. Bunch Compressors Bunch lengths in damping rings are ~1cm –Seen that for high luminosity, would like short bunches at the IP Compress bunches in magnetic bunch compressors after the damping rings –Three problems: Magnetic bunch compressors operate by bending the beam  synchrotron radiation can dilute the beam emittances –Normalized emittance growth scales as  6 in transport line Longitudinal phase space is conserved  shortening the bunch length will increase the energy spread –Large energy spread in the linacs makes preserving the beam emittance more difficult  ~ (  E/E) 2 Longitudinal nonlinearities make compressing by more than 10~20x difficult in any single stage

54. Bunch Compressors Magnetic bunch compression  z z z RF Accelerating Voltage Path Length-Energy Dependent Beamline V = V 0 sin(  ) z0z0 zz  z = R 56  Under- compression Over- compression

55. ILC BC Solution Want capability of compressing from 6mm  150  m Factor of 40 too large for a simple single-stage system –Dual stage system: Compress just after damping ring at 5 GeV by ~6x Compress again at ~15 GeV point by another factor of ~8x Provides large operating range while limiting the energy spread in the linacs  less emittance dilution than in a single-stage Bunch compressor system also includes: –Transverse and longitudinal collimation –Spin rotation –Skew correction to correct errors from damping ring or in the spin rotation system –Extensive diagnostics before launching the beam into the linac

56. Linac Beam Dynamics Main issues in the linac are: –Short-range wakefields –Dispersive emittance dilutions Superconducting linac has relatively loose tolerances for wakefield dilutions –Cavity alignment at the 300  m level Need to be careful on alignment at the low energy ends of the linac due to the dispersive dilutions –Must align the quadrupoles at the 25  m level to avoid dispersive dilutions:  ~ (  E/E) 2 –Requires beam-based alignment techniques

57. Linac Parameter Trades Damping Ring (sources) IR (IP) Beam extraction Linac (relaxed within limits) From Nick Walker, Snowmass 2005

58. Beam Delivery System Requirements: –Focus beams down to very small spot sizes –Collect out-going disrupted beam and transport to the dump –Collimate the incoming beams to limit beam halo –Provide diagnostics and optimize the system and determine the luminosity spectrum for the detector –Switch between IPs

59. Beam Delivery System Layout 2mrad collim & FF 20mrad collim & FF BDS designed up to 1TeV w. fixed geometry FF with local chrom.corr.  -spoilers survivable up to 2 bunches E-coll after  -coll for clean collimation

60. Collimation System and MPS Collimation system must remove beam tails Extremely dense beams are very difficult to collimate and stop – Machine Protection System is a challenge Collimation system becomes long and difficult with tight tolerances if the beam size is increased sufficiently to prevent damage

61. IP Switchyard to tune-up dump to IPs MPS betatron collimators skew correction 4-wire 2D  diagnostics Energy diag. chicane kicker (comb w. bends), septum polarimeter chicane  collim. High bandwidth horiz. bend.sys. EBSY Recent modifications: –sacrificial MPS betatron collimation at entry –septum & tune-up line is being redesigned, to be released soon 1  m beam at laser wires with DR emitt.  y =2e-8m at 1TeV ISR in 11mrad bend: E-collim. tapered spoilers

62. IR Design (1) 20(14)mrad IR –Self shielded compact quads successfully tested –Focus on 14mrad alternative to push the technology ILC crab cavity: –collaboration of Fermilab, UK (Daresbury, et al), SLAC. –Based on 3.9GHz deflecting cavity designed at Fermilab. Design is being verified and preparing for production Omega3P Mesh 3.9 GHz deflecting cavity, early 13 & 3 cell models and recent 9cell design Fermilab BNL

63. IR (2) Small and large crossing angle designs Pairs induced background similar in both cases Losses in extraction & background harder in 2mrad but 2 mrad easier for detector Pairs induced backgriund in SiD

64. Parameter Tables Most of the parameter relations can be put into an Excel spreadsheet –Makes it simple to compare different scenarios Posted publicly at www-project.slac.stanford.edu/ilc/temp/ILC_parms.xls

65. Summary Basic beam parameters are determined from the luminosity requirements –ILC design then follows trying to meet those requirements Constrains arise from: –IP physics (luminosity, beamstrahlung, disruption, depth of focus) –Damping rings, bunch compressor and positron source –Rf acceleration – topic of Chris Adolphsen’s talk Details will be discussed in all the subsequent talks –Looks like a great program! –Thanks to the organizers! Join the ILC accelerator effort – an accelerator for the future