1. F. Willeke, Snowmass 20011 Luminosity Limitations of e-p Colliders Extrapolation from HERA Experience Examples for IR Layout LINAC-Ring Limitations HERA Limitations

2. F. Willeke, Snowmass 20012 HERA Luminosity 2001 PARAMETERS N p number of protons per bunch = 1 x 10 11 N e number of leptons per bunch = 3 x 10 10 n b number of bunches = 174 f 0 revolution frequency = 47.3kHz  x,y,p,e hor./vert. beam dimensions of leptons & protons = 114  m/ 30  m  half crossing angle = 0 L luminosity = 7 x 10 31 cm -2 sec -1

3. F. Willeke, Snowmass 20013 HERA Luminosity Constraints & Limitations Limitations: N p /  N proton beam brightness = 1 x 10 11 / 4  m (injector, ibs, bb-e) I e total lepton beam current = 60mA (rf power, bb-p)  p proton relativistic factor = 981 (max field, circumference)  x,y p hor.& vert. Betafunctions at the IP = 2.45m/0.18m (ir layout,  p ) Constraints:  mr (beam-beam tracking Sen‘95) =>  set 0(head on coll.)  x,yp =~  x,ye (Brinkmann, Willeke PAC’93)  e not (yet) limiting L = 7 x 10 31 cm -2 sec -1 To what extend are these fundamental?

4. F. Willeke, Snowmass 20014 Proton Beam Brightness Limitations Present design N p /  N =1 x 10 11 / 4 x 10 -6 m Laslett Tuneshift in DESY III Booster Synchrotron 50MeV (kin.energy) injection  sc ~ R N p / (  N    B ) = 0.6 @ 1.3 10 11 &  N =2  m Can be overcome by smaller ring are higher injection energy in the booster No principal limitation `just´ costs Example : DESYIII Inj. Energy from 50MeV  120MeV @ 10M$

5. F. Willeke, Snowmass 20015 Proton Beam Brightness Limitations:IBS Scaling from HERA

6. F. Willeke, Snowmass 20016

7. 7 Scaling IBS Increasing N p /  N increases growth time:  larger  s  Larger  s  larger  * (hourglass effect)  Luminosity almost independent of N p /  N Possible Cure: More RF Voltage  ibs ~U RF 0.25 however  e ~ U RF 0.25 L / L0 = (  e /  e ) 2 = (U RF / U RF0 ) 1/2 (expensive) HERA Experience: Running with 2x nominal  e still ok but effect already noticeable (increased backgrounds)  s ~  N 1.42 ~  s 1.52 ~U RF 1/4

8. F. Willeke, Snowmass 20018 Cooling Bunched Beam Stochastic Cooling at High Energy  Not very promising perspective Bunched e-Beam Cooling: -May be cost effective way to provide bright beams -Doesn‘t look promising for high energies -May work for ions  See K.Balewski‘s presentation

9. F. Willeke, Snowmass 20019 Lepton Beam-Beam Effect This is already a rather large value which potentially limits the proton beam brigthness. What are the margins?  beam-beam experiments  ey =0.045

10. F. Willeke, Snowmass 200110 Too Strong Beam-Beam Force on e? No reduction of L s by the second experiment No reduction of L s by a larger  -funktionen LsLs I ppb So far no reduction of L s by the bunch current

11. F. Willeke, Snowmass 200111 Where are the Beam-Beam Limits? Upgrade and Ip=140mA: emittance starts to grow

12. F. Willeke, Snowmass 200112 Conclusion of Proton Beam Brightness Limitation For a machine with the circumfrence and the energy range of HERA there is no large increase factor in p beam brightness possible. A factor of > 2 might be compatible with lepton beam beam effect and controlling IBS Lepton Beam-Beam Effect: Could be mitigated By smaller beta, however: D.A. limitations present HERA optics DA=~15-20  x

13. F. Willeke, Snowmass 200113 Electron Beam Current Limitations RF RF installation costs, operation costs Not fundamental Now: RF power 12 MW, R S 1.5GW  60mA @ 27.5GeV Cost example: prov RF to increase I by factor 1.6  5M$ Vacuum costs, not fundamental SR losses 5.2MW @ 1000W/m (~B-Factories ) Presumably no big current increase factor reasonable! (factor 2-3?) costs! Feedback System: designed for 60mA, upgrade no technical problem Proton Beam Beam Effect (stability, background, lifetime concerns)  b =96ns, unproblematic For IR design & paras. Resonances  px =1.4 x 10 -3 limit? f: fill factor

14. F. Willeke, Snowmass 200114 L s is independent of e-current T p depends on e- current Tails depend on e-current Too Strong Beam-Beam Force on p? 16mA73mA Corresponding e-current after upgrade

15. F. Willeke, Snowmass 200115 Conclusions: Electron Beam Current Limitations Educated guess: Besides COSTS, the beam current is limited by IR design considerations and beam-beam effects. For HERA, the e-beam current could be increased by a factor ~2 if costs could be disregarded

16. F. Willeke, Snowmass 200116 Limitations to Focussing Chromatic effects  Dynamic Aperture Limitations Hourglass Effect Interaction Region Layout and IR Magnet Design: Need e & p lenses close to IP Crossing angle  separate quickly beam dynamics, geometry Magnetic Separation Concern about SR

17. F. Willeke, Snowmass 200117 Lumi Reduction by Hourglass Effect e p Length 19cm: 12cm: Luminosity ( ) 20cm bunch length: 6cm 30cm

18. F. Willeke, Snowmass 200118 New HERA Inter Action Region (==>see M. Seidel) strong magnetic combined function separation Half Quadrupoles Superconducting Separator/Quads p-focusing Half Quadrupoles Superconducting Separator/Quads p-focusing sc p-beam e-beam e-focusing DF p-focusing D-F-D-F

19. F. Willeke, Snowmass 200119 Superconducting Magnets in the Detectors

20. F. Willeke, Snowmass 200120 Ring Linac Collider Become interesting at Lepton Energies beyond capability of Storage Rings E e >100GeV N p 10 -6 m  p 10cm P e 250GeV L= 4.8 x 10 30 cm -2 sec -1 10 11  N 1066  * 26.6MW E e N p 10 -6 m  p 10cm P e 250GeV L= 4.8 x 10 30 cm -2 sec -1 10 11  N 1066  * 26.6MW E e High Energy bunched beam Cooling! Energy Recovery

21. F. Willeke, Snowmass 200121 THERA LINAC-Ring Lattice (proposed) small crossing angle protons focussed by 2 electron low beta triplets,  *=10cm  max 8km protons deflected from e-orbit by a long off-center quadrupole electron orbit straight energy range E p /E e : 4/1 - 1/1 Proton Optics 1TeV Electron Optics 250GeV-800GeV

22. F. Willeke, Snowmass 200122 Conclusions Ring-Ring HERA L=~10 32 cm -2 sec -1 New Collider in the range of HERA Energies: L=10 33 cm -2 sec -1 is an ambitious goal and may be considered as a target for new designs Ring-LINAC L>10 31 cm -2 sec -1 :only feasible witg bunched beam cooling