USPAS Accelerator Physics 2015 at Old Dominion University

Dive into the world of collider physics with insights on colliders, luminosity, event rates, crabbing, and more from the USPAS Accelerator Physics 2015 at Old Dominion University. Explore the fundamentals of colliders, their optimization, and the significance of probing small entities. Uncover how accelerators enhance statistical resolution and the intricate processes involved in interaction rates. Join Todd Satogata, Vasiliy Morozov, and Alex Castilla on this enlightening journey through the realms of accelerator physics.

• USPAS
• Accelerator Physics
• Collider
• Luminosity
• Crabbing

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1. USPAS Accelerator Physics 2015 Old Dominion University Colliders, Luminosity, & Crabbing Todd Satogata (Jefferson Lab) / satogata@jlab.org Vasiliy Morozov (Jefferson Lab) / morozov@jlab.org Alex Castilla (ODU) / acast020@odu.edu http://www.toddsatogata.net/2015-USPAS A. Castilla / January 2015 USPAS Accelerator Physics 1

2. Outline Colliders Why and where? Issues Accelerator Physics of Colliders Event rate Luminosity Looking at the luminosity Fixed target Colliders: Gaussian bunches, head-on Optimization knobs and complications Hourglass effect Crossing angle Crabbing A. Castilla / January 2015 USPAS Accelerator Physics 2

3. Colliders Where? STAR detector at RHIC, J.G. Cramer UW Colloquium 2002. Butchered slide from Steve Myers IPAC2012 New Orleans. A. Castilla / January 2015 USPAS Accelerator Physics 3

4. Colliders (2) Because they are super cool! Why? www.businessinsider.com Laurent Egli. True! But also: 2+ ?1+ ?2 2 ???= ?1+ ?2 Fixed target (?2= 0) ???= ?1+ ?2 Colliding beams (?1= ?2) 2?2+ 2?1? ???= A. Castilla / January 2015 USPAS Accelerator Physics 4

5. Probing small things SUSY?? ?? Higher energy higher resolution 1 ??? 125 G?? Weak nuclear force Proton and neutron Quarks, muon Nuclear states transitions ? =? 1 ??? ? 1 ??? Electron Transitions in the inner-shell atomic states 1 ??? Atomic states transitions 1 ?? Lattice vibration in solids (phonons) 1 ??? A. Castilla / January 2015 USPAS Accelerator Physics 5

6. Accelerator Basics of Colliders More events in time better statistic/resolution of the processes. ?? ??= ? ?? ?? ?? interactions per second, - - ?? interaction cross section (machine independent), - ? luminosity, relativistic invariant, independent of the interaction and very important- measurable. A. Castilla / January 2015 USPAS Accelerator Physics 6

7. Accelerator Basics of Colliders (2) *F. Zimmermann, SLAC Summer Institute (2012). A. Castilla / January 2015 USPAS Accelerator Physics 7

8. Shining Beam on a Fixed Target The interaction rate will be a function of: ?? ??= (????) ?? - ?? interaction cross section. ??= ????? - ? beam particles flux. ? - ?? target density. ? ? = ????? - ? target size. A. Castilla / January 2015 USPAS Accelerator Physics 8

9. Shining Beam on a Beam (Collider) The interaction rate will be a function of: ?? ??= (????) ?? ??= ????? - Then: ? ?????/? ? target = - ? bunch frequency. moving beam! - ?? number of particles per bunch. - ? beam transverse profile. A. Castilla / January 2015 USPAS Accelerator Physics 9

10. Collider Luminosity ?2 ?1 Per bunch crossing: = ? ?1?2 ?0 ????????0[?1?,?,?, ?0 ?2 ?,?,?,?0] Where ?0= ??. And ? is the kinematic factor 2?2. 2 ?1 ?2 ?1 ?2 Head-on collisions ( ?1= ?2), then ? = 2. For uncorrelated distributions: ? ?,?,?,?0 = ??? ??? ??? ?0 A. Castilla / January 2015 USPAS Accelerator Physics 10

11. Luminosity of Gaussian Bunches For two bunches with ?1 and ?2 particles respectively: ?2 ?1 ?0 1? ? = Where ? ?? are the rms horizontal/vertical beam sizes. No offset and head-on collision. https://en.wikipedia.org/wiki/Multiv ariate_normal_distribution A. Castilla / January 2015 USPAS Accelerator Physics 11

12. Luminosity of Gaussian Bunches (2) For two beams: = 2 ?1?2 ? ?? ????????0[ ?1?? ?1?? ?1?? ?0 ?2?? ?2?? ?2?? + ?0] The Gaussian distributions can be written: ?2 ( (? ?0)2 2??2) ; ( 2???2), ??? ?0 = 1 1 ???? = ??? 2?? ?? 2?? where ? = ?,? and ? = 1,2 indicates the bunch number. A. Castilla / January 2015 USPAS Accelerator Physics 12

13. Luminosity of Gaussian Bunches (3) Normal distributions are 0K for bunches in equilibrium. Not Gaussian? (most likely) numerical integration. Simplest case: Identical bunches: ?1?= ?2?, ?1?= ?2?, and ?1?= ?2? Even ?1? ?2? and ?1? ?2? can be easily calculated (we will keep ?1? ?2?). We will also consider no dispersion at the collision point. Let s try a bit of real-time math! A. Castilla / January 2015 USPAS Accelerator Physics 13

14. Luminosity of Gaussian Bunches (4) What happens to the bunch s shape here? ?2 ?1 1? ? = Where at the IP: Is this Again, for identical optimizable ? 2 ??,? ? and = ? beams, no crossing angle, ??,? = ?? no dispersion, no off-set. =?1?2??? 4? ?? ?? Then =?1?2??? 4????? A. Castilla / January 2015 USPAS Accelerator Physics 14

15. Turning Knobs for Luminosity Not head-on collisions (crossing angle ??). Beam deformations at IP (hour-glass effects). Desired or non-desired offsets. Dispersion at IP. More a complication rather than a knob? injector and beam-beam Strong coupling, etc. ?????? ? ? ? ? ?(??,?,? ,??) Reduction factor: hourglass effect, crossing angle = ?? total beam current energy and ? A. Castilla / January 2015 USPAS Accelerator Physics 15

16. Hourglass Effect ?-functions dependent on ?, usually: 2 ? ?(?) ? 1 + ? Then ???????? = ? ? : 2 ? (?) ? 1 + ? Results important if ?? ? . *Werner Herr, CAS-Lectures, Bulgaria (2010). A. Castilla / January 2015 USPAS Accelerator Physics 16

17. Hourglass Effect (2) So the luminosity reduction factor: 2 ? ?? ?? ?? ? ?? ?? 0 = ? ???? ?? = 0 ?? (??,?,? ,??) Enigmatic dependency mentioned before! A. Castilla / January 2015 USPAS Accelerator Physics 17

18. A Bit More Interesting Case (Crossing Angle) x s ?2 ?1 ?? 2 ?? 2 Reduce parasitic collisions. Physical space for magnets. Better detector resolution. A. Castilla / January 2015 USPAS Accelerator Physics 18

19. Rotating Reference Frames (for each bunch) x ?1 s ?? 2 ?? 2 ?1 ?2 ?2 ?1= ?cos?? 2+ ?sin?? 2 , ?1= ?cos?? 2 ?sin?? 2 . ?2= ? cos?? 2+ ?sin?? 2 , ?2= ?cos?? 2 ? sin?? 2 . A. Castilla / January 2015 USPAS Accelerator Physics 19

20. For the Distributions in the New Systems For two beams: = 2 ?1?2 ? ?? ????????0[ ?1??1?1??1?1??1 ?0 ?2??2?2??2?2??2+ ?0] Now we will use: ?2 ?? ? ? ? ? ??? ??2+??+?= ?? With some approximations: then: 2 fairly small (mrad ~10 2deg), ??2~tan ??2~ ??2 sin A. Castilla / January 2015 USPAS Accelerator Physics 20

21. For the Distributions in the New Systems (2) ?? Some more approximations since 2 is small: ??2~tan ??2~ ??2; sin ?? discarding ???sin? is ?? ??? tan 2 ; ? + ? 4 ?? ??sin? ?? ?? 2. 2 2 And so the result is slightly different: ?1?2??? 1 = ?? 2 4?? ?? ?(??,?,? ,??) ?? ??tan?? 1+ 2 A. Castilla / January 2015 USPAS Accelerator Physics 21

22. Crossing Angle w/o Correction ?? IP A. Castilla / January 2015 USPAS Accelerator Physics 22

23. The Crabbing Concept *R. Palmer, SLAC-PUB-4707 (1988). . A. Castilla / January 2015 USPAS Accelerator Physics 23

24. RF Transverse Deflection ??? cos?? + ???? sin?? ??= ?? ? ? ?? ? A. Castilla / January 2015 USPAS Accelerator Physics 24

25. RF Transverse Deflection(special case) ??? cos?? + ???? sin?? ??= ?? ? ? ?? ? A. Castilla / January 2015 USPAS Accelerator Physics 25

26. Local Crab Crossing Correction ?? IP A. Castilla / January 2015 USPAS Accelerator Physics 26

27. Jefferson Labs Medium Energy Electron-Ion Collider A. Castilla / January 2015 USPAS Accelerator Physics 27

28. The MEIC at JLab Deep inelastic ?? ?? scattering. Y. Zhang, et al. arXiv:1209.0757v2 (2012). A. Accardi, et al. arXiv:1110.1031v1 (2011). ( ? = 20 70 ???)and~???? ?? ?? ? luminosity. A. Castilla / January 2015 USPAS Accelerator Physics 28

29. The MEIC Layout Ions IP ?1?2??? 1 Electrons = ?? 2 4?? ?? ?? ??tan?? 1+ 2 Electrons Ions IP s V. S. Morozov , MEIC study group (2013). A. Castilla / January 2015 USPAS Accelerator Physics 29

30. The MEIC Luminosity Approach Short bunches for both species. Small transverse emittance. Ultrahigh collision frequency CW beams. Staged electron cooling. Small final focusing ? . Large beam-beam tune shift. Crab crossing. A. Castilla / January 2015 USPAS Accelerator Physics 30

31. MEIC Crabbing Requirements High repetition. Big crossing angle. ? ? ???tan?? 2 ??= ? ?? ??? ?? Parameter Units GeV MHz mrad cm m MV Electron 5 Proton 60 Beam energy ?? Bunch frequency ?? Crossing angle ?? Betatron function at the IP ?? Betatron fn. at the crab cavity ?? Integrated kicking voltage ?? 750.0 50 10 ? 300 1.35 1400 8 A. Castilla / January 2015 USPAS Accelerator Physics 31

32. Transverse Kick (e.g. 750 MHz SRFD) ??? cos?? + ???? sin?? ??= ?? ? ? ?? ?2 = 0.2 ?? Electric Field Magnetic Field ??= ?? ??? = 1 ?? ??,? = 0.2 ?? ??,? = 0.4 ?? A. Castilla / January 2015 USPAS Accelerator Physics 32

33. Most of the Content Borrowed from W. Herr Concepts of luminosity for particle colliders CAS-Lectures, Varna, Bulgaria 2010. F. Zimmermann LHC: The machine , SLAC Summer Institute 2012. J. G. Cramer Surprises from RHIC UW Phys. Dept. Colloquium 2002. And many more A. Castilla / January 2015 USPAS Accelerator Physics 33