1. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Studies of Machine protection for a Crab Cavity in the LHC Bruce Yee Rendón Departamento de Física Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional Unidad Zacatenco 1

2. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Scheme  Introduction.  Machine protection studies.  Results.  Future work. 2

3. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Introduction 3

4. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón LHC 4

5. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón In Table 1 shown relevant optics parameter for the Nominal and Upgrade scheme in the LHC. Table 1. Optics parameters for the Nominal and Upgrade (ATS scheme [1]) under study. 5 ParameterSymbolNominal SchemeUpgrade Scheme EnergyE [TeV]77 Protons per bunchN b [10 11 ]1.151.7 rms bunch lengthσ z [cm]7.55 Beta function at IP5/IP1 β * [cm]5015 Emittanceε[10 -6 mrad]3.75 Full crossing angleθ[μrad]285580 LHC parameters

6. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Luminosity 6 The Luminosity in the nominal LHC is 10 34 cm -2 s -1. Figure 1: The Crossing angle scheme.

7. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Crab Cavities A device called “crab cavity” (CC) applies a tiny sideways kick to each particle bunch, in order to changed its dynamics to achieve a head-on collision at the IP. For the HL-LHC the luminosity will increase by factor of 5 (with respect to the nominal) [2]. 7 IP5 Left CCs Right CCs Figure 3: The CC´s effect in the beam at collision point in the LCC scheme. Figure 2 : The CC scheme at IP5 for the Upgrade.

8. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Machine protection studies 8

9. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón LHC safe operation The Stored energy in the LHC beam at 7 TeV is 350 MJ [3]. 5% of a single beam can quench the superconducting magnets [3]. The safe beam extraction is in 3 turns [4]. The CC ´s effect in the beam loss, when the CC presents or not a failure [5]. 9

10. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Collimation´s tools SixTrack simulates the track of large numbers of particles, taking in account the interaction of beam with the collimators [6]. Local Loss Maps shows the particles losses (in the collimators, cold and warm magnets) around the lattice [7]. Absorbed particles in the collimators. Lost particles around the ring (not in the collimators). 10

11. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Beam distribution In general, halos distributions are using to made collimation studies. A double and triple Gaussian distributions were used in order to simulate a more realistic beam profile [8,9,10]. 11 Figure 4 : The typical beam distribution using for machine protection studies.

12. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Double Gaussian distribution 12 Tails. Core. Around 2 millions of particles generated. Figure 5 : The beam profile obtained by using the CMS measurements. The sigma of the tails is 1.8 times than the core [8]. 10 1 10 -1 10 -2 10 -3 10 -4 10 -5

13. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Triple Gaussian distribution 13 Figure 6 : The beam profile obtained by apply Abel transformation to the scrapping measurements of collimation team at injection energy at LHC [9,10]. Core. A 1 =0.53 σ 1 =0.66 Tails. Around 1 millions of particles generated. A 2 =0.16 σ 2 =1.32 A 3 =0.005 σ 3 =1.996

14. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Simulation cases 14

15. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Free turns 15 Turns Voltage Phase Figure 7 : Here we show the way that the amplitude of voltage and phase are change as a function of the number of the turns. In the Free turns (FT) the voltage and phase of the CC remain zero. V 0 t1 T1 ϕ inicial

16. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Normal operation 16 Turns Voltage Adiabatic Ramping up Phase Figure 8 : In the Normal operation (NO) represent the ideal performance of the CC.

17. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Voltage failure 17 Turns Voltage Adiabatic Ramping up Phase establish “steady-state” conditions with crab cavity and collimator before simulating a crab- cavity failure Figure 9 : In the Voltage failure (VF) just the voltage drops to zero, in contrast the phase remains like in the normal operation scheme [5, 9,10].

18. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Phase failure 18 Turns Voltage Adiabatic Ramping up Phase Turns establish “steady-state” conditions with crab cavity and collimator before simulating a crab-cavity failure Figure 10 : In analogy with the VF case, in the Phase failure (PF) case just the phase change 90 degrees with respect to its initial phase [5, 11,12].

19. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Results 19

20. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Distribution of the turns in the simulation 20 CaseFree turnsRamping up turns Plateau turns Ramping down turns Final value voltage Final value phase FT200000Remains equals NO1101890Remains equals VF1101691,3 or 50 Remains equals PF1101691,3 or 5Remains equals π/2 T he numbers of turns for the tracking are 200 turns. The collimators are turn on in since the first turn. Table 2. This Table illustrates the distribution of the turns for the different case and shows the finals value of voltage and phase.

21. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Nominal 21

22. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón LLM for the Nominal LHC 22 Figure 11 : The LLM for a phase failure of 90° in 5 turns, for a simple and double Gaussian distribution increase the beam size by factor of three to overpopulated the tails.

23. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Absorbed particle in the Nominal LHC 23 Figure 12 : The percentage of the particle absorbed for the failures in voltage and phase using a double Gaussian (beam size increase by a factor of 1.5). ( 1x10 6 particles, double Gaussian with 1.5 σ x,y )

24. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón 24 Lost particle in the PF case at Nominal LHC ( 1x10 6 particles, double Gaussian with 1.5 σ x,y ) Figure 13 : The percentage of the particle total for the failures in phase using a double Gaussian (beam size increase by a factor of 1.5).

25. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón ATS 25

26. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Results with out CC in the ATS scheme Here is presents the percentage of lost and absorbed particles using a Double Gaussian (Table 3). Table 3. The percentage of particles lost, absorbed and impact real for the ATS lattice, without CC. The total of particles generated around 1 million. 26 DistributionLost particles [%]Absorbed Particles [%] Double Gaussian ( 1.0 σ x,y )0.171.81 Double Gaussian ( 1.5 σ x,y )1.113.66

27. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón CC voltage correctors 27 The equation of the CC left voltage: (1) The equation of the right CC voltage: (2) where δ is the kick of the correctors, E s is the beam energy, q charge of particle, c is the speed of the light, ω is the frequency of the CC, σt is the rms bunch length and n cc the number of CC.

28. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón CC voltage analytic formula 28 The equation of the CC left voltage: (3) The equation of the right CC voltage [12]: (4) (5.1) with (5.2) where β * is the beta function at IP, β left/right cc is the beta function in the left/right cc, Θ crossing angel, Δφ left/right is the difference of phase advance between the IP and the CC left/right, Δφ cc is the difference of phase advance between the left and right CC and R 2,2 is the element (2,2) of the transport matrix from left and right CC.

29. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Voltage Here is presents the value of voltage using de formulas (1) to (5.2). Table 4. The value of voltage for a CC of 400 MHz for the ATS lattice. 29 Voltage of Corrector (MeV)Analytic Voltage (MeV) V leftCC =9.3465V leftCC =10.129 V rightCC =10.867a) V rightCC =11.782* b) V rightCC = 11.778** *Equation (4). **Equations (5.1) & (5.2).

30. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón X Orbit 30 Figure 14 : The superposition of the Orbit X, using the voltage of the orbit corrector and the two initial formula in the region from S.DS.L5.B1/E.DS.R5.B1.. 6E-5 4E-5 2E-5 0.0 -2E-5 -4E-5 -6E-5 X(m) X Orbit IP5 3CCs 6117 6317 6517 6717 6917 7117 Ct(m)

31. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón X orbit 31 Figure 15 : The Orbit X using the voltage calculate by formulas 3 and 4 from S.DS.L5.B1/E.DS.R5.B1. 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 X(σ) 6117 6317 6517 6717 6917 7117 Ct(m) X Orbit IP5 3CCs

32. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón X-Ct Voltage Failure 32 IP5 Right CCLeft CC IP5Free turns Linear fit Effect of the ramping up Figure 16 : The effect of the CC in the X coordinate close to IP5 is shown for a tracking of one particle 200 turns. The plots consists in the superposition of the CC´s operation cases, failures in voltage, and a linear fit w.r.t. the normal operation case. The fit give us a slope of 274 μ rad, close to the half of the crossing angle..

33. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón X-Ct Voltage Failure 33 IP5 Right CCLeft CC Free turns Linear fit Effect of the ramping up Free turns Normal operation Failure starts Figure 17: A close up when the failure starts of the Figure16. The effect of the voltage failure for the different cases are shown and compare between them.

34. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón X-Ct Phase Failure 34 Figure 18: In analogy with the voltage failure (Figure 17), the effect of the phase failure for the different cases are shown and compare between them. Normal operation Failure starts Free turns Failure starts Free turns Normal operation

35. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón X-Ct Voltage and Phase Failure 35 Figure 19 : The superposition between the failures of voltage and phase in five turns, using the free turns and normal operation case like baseline. The effect produces for the phase change is larger than the voltage. The square of the voltage failure cover the circles of the phase failures before the failures appears. Failure starts Free turns Normal operation

36. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón 36 Figure 20 : The LLM for a phase failure of 90° in 5 turns, for a double Gaussian distribution increase the beam size by factor of 1.5 to overpopulated the tails. ( 1 million particles) LLM for the ATS LHC

37. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón 37 Figure 21 : The LLM for a phase failure of 90° in 5 turns, for a double Gaussian distribution increase the beam size by factor of 1.5 in the Nominal and ATS scheme.. ( 1 million particles) Comparisons

38. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Future Work 38

39. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Activities Implement the correct aperture model of the full ring and settings for the ATS lattice (Collimation team help). Consider different distributions which can describe better the tails (using a Triple Gaussian from halo scraping measurements) Study more realistic case of failure in voltage and phase (the way that voltage or phase change). 39

40. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Acknowledgements I want to say thank to A. Marsili, F. Burkart, R. de Maria, T. Baer, R. Tomas, J. Barranco, R. Calaga, F. Zimmermann, R. Lopez; US-LARP, CONACYT. 40

41. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón References 41 [1] R. De Maria et al, “A proposal for the optics and layout of the HL-LHC with Crab-cavities”, IPAC´11, THPZ013, 2011. [2] O. Brunning et al., “The Large Hadron Collider”, Progress in Particle and Nuclear Physics,2012. [3] R. Schmidt et al., PAC07, 2007. [4] J. Wenninger, “Machine Protection Specifications”, LHC-CC10, 2010. [5] T. Baer et al, “Beam losses due to abrupt Crab Cavities failures in the LHC”, IPAC´11, TUPZ009, 2011. [6] F. Schmidt. “SixTrack, User’s Reference Manual”. CERN SL/94-56 AP.

42. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón References 42 [7] LHC Collimation Project, http://lhc-collimation-project.web.cern.ch/lhc- collimation-project/code-tracking-2009.htmhttp://lhc-collimation-project.web.cern.ch/lhc- collimation-project/code-tracking-2009.htm [8] The CMS Collaboration, “Absolute Calibration of the CMS Luminosity”, CMS PAS EWK-11-001, 2011. [9] F. Burkart et al, “Absolute Calibration of the CMS Luminosity”, IPAC´11, THPZ030, 2011. [10] B. Yee Rendon, “Abel transformation report”, personal note, 2012. [11] R. Calaga et al., “Beam Losses due to Abrupt Crab Cavity Failures in the LHC, PAC´11, MOODN4,2011. [12] Y. Sun et al, “Beam Dynamics aspects of Crab Cavities in the CERN Large Hadron Collider”, Phys. Rev. ST Accel. Beams, vol 12, no.10, 2009.

43. 2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón Thanks for your attention 43