Studies of Machine protection for a Crab Cavity in the LHC

1. 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

2. Scheme • Introduction. • Machine protection studies. • Results. • Future work.

3. Introduction

4. LHC

5. LHC parameters 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.

6. Luminosity The Luminosity in the nominal LHC is 1034 cm-2 s-1. Figure 1: The Crossing angle scheme.

7. 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]. Right CCs Left CCs Figure 3: The CC´s effect in the beam at collision point in the LCC scheme. IP5 Figure 2 : The CC scheme at IP5 for the Upgrade.

8. Machine protection studies

9. 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].

10. 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).

11. 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]. Figure 4 : The typical beam distribution using for machine protection studies.

12. Double Gaussian distribution 101 10-1 10-2 10-3 10-4 10-5 Core. Tails. 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].

13. Triple Gaussian distribution Core. A1=0.53 σ1=0.66 Tails. Around 1 millions of particles generated. A2=0.16 σ2=1.32 A3=0.005 σ3=1.996 Figure 6 : The beam profile obtained by apply Abel transformation to the scrapping measurements of collimation team at injection energy at LHC [9,10].

14. Simulation cases

15. Free turns Voltage V 0 t1 Turns Phase ϕinicial T1 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.

16. Normal operation Voltage Adiabatic Ramping up Turns Phase Turns Figure 8 : In the Normal operation (NO) represent the ideal performance of the CC.

17. Voltage failure establish “steady-state” conditions with crab cavity and collimator before simulating a crab-cavity failure Voltage Adiabatic Ramping up Turns Phase Turns 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. Phase failure establish “steady-state” conditions with crab cavity and collimator before simulating a crab-cavity failure Voltage Adiabatic Ramping up Turns Phase Turns 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. Results

20. Distribution of the turns in the simulation • The 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. Nominal

22. LLM for the Nominal LHC 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. Absorbed particle in the Nominal LHC ( 1x106 particles, double Gaussian with 1.5 σx,y) 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).

24. Lost particle in the PF case at Nominal LHC ( 1x106 particles, double Gaussian with 1.5 σx,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. ATS

26. 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.

27. CC voltage correctors The equation of the CC left voltage: (1) The equation of the right CC voltage: (2) where δ is the kick of the correctors, Es 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 ncc the number of CC.

28. CC voltage analytic formula 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, βleft/rightcc is the beta function in the left/right cc, Θ crossing angel, Δφleft/right is the difference of phase advance between the IP and the CCleft/right, Δφcc is the difference of phase advance between the left and right CC and R2,2 is the element (2,2) of the transport matrix from left and right CC.

29. 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. *Equation (4). **Equations (5.1) & (5.2).

30. X Orbit X Orbit 6E-5 4E-5 2E-5 0.0 -2E-5 -4E-5 -6E-5 3CCs X(m) IP5 • 6317 6517 6717 6917 7117 • Ct(m) 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. .

31. X orbit X Orbit 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 IP5 3CCs X(σ) • 6317 6517 6717 6917 7117 • Ct(m) Figure 15 : The Orbit X using the voltage calculate by formulas 3 and 4 from S.DS.L5.B1/E.DS.R5.B1 .

32. X-Ct Voltage Failure Linear fit Effect of the ramping up Left CC Right CC IP5 Free turns IP5 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. X-Ct Voltage Failure Normal operation Failure starts Linear fit Effect of the ramping up Left CC Right CC IP5 Free turns Free turns 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. X-Ct Phase Failure Normal operation Normal operation Failure starts Failure starts Free turns Free turns 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.

35. X-Ct Voltage and Phase Failure Normal operation Failure starts Free turns 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.

36. LLM for the ATS LHC ( 1 million particles) 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.

37. Comparisons ( 1 million particles) 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..

38. Future Work

39. 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).

40. 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.

41. References [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. References [7] LHC Collimation Project, http://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. Thanks for your attention