6D weak-strong beam-beam simulations with SixTrack: theory and simulations

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1 6D weak-strong beam-beam simulations with SixTrack: theory and simulations Javier Barranco Garcia Ackowledgements: T. Pieloni, R. De Maria, D. Banfi, R. Tomas, A. Valishev, K. Ohmi,... HSC Meeting 13/08/14

2 Brief history of BB studies with SixTrack The weak-strong 6D with crossing angle formalism was first formulated by K. Hirata. Implemented in SixTrack (~2002) by L.A.H. Leunissen based on Hirata's BBC code. However there is no record of any LHC studies using 6D BB lens. In the HL-LHC era the larger crossing angles there is need of evaluating correctly this effect. Some time spent understanding the implementation plus debugging (for example answering ICE action still open).

3 W-S BB interactions with Crossing Angle: Bibliography Don't be afraid of beam-beam interactions with a large crossing angle, K. Hirata. SLAC-PUB A symplectic beam-beam interaction with energy change, K. Hirata, H. Moshammer and F. Ruggiero, KEK preprint A (1992) and Part. Accel. 40, (1993). Synchro-Beam interaction, K. Hirata, H. Moshammer, F. Ruggiero and M. Bassetti, CERN SL-AP/90-02 (1990) and Proc. Workshop on Beam Dynamics Issues of High-Luminosity Asymmetric Collider Rings, Berkeley, 1990, ed. A.M. Sessler (AIP Conf. Proc. 214, New York, 1990), pp Analysis of Beam-Beam Interactions with a Large Crossing Angle, K. Hirata, Phys. Rev. Lett. 74, Six-dimensional beam-beam kick including coupled motion, L. H. A. Leunissen, F. Schmidt, and G. Ripken, Phys. Rev. ST Accel. Beams 3, (2000).

4 Why? How? To simulate the bunch length effect in a collision with crossing angle there is the mapping, called synchro-beam mapping (SBM), which is symplectic in a six-dimensional sense but is formulated only for the head-on collision. There is a Lorentz transformation that transforms the collision with an angle to a head-on collision between bunches tilted horizontally.

5 W-S 6D Formalism The à la Hirata implementation is a 6D symplectic beam-beam mapping. It consists of 3 consecutive maps. CP Virtual Drift Mapping from IP to CP (including Lorentz boost) CP Synchro-beam Mapping Inverse Virtual Drift Mapping from CP to IP (including anti-lorentz boost) The whole map expresses the collision effect at the CP in terms of the canonical variables defined at the IP. Full article:

6 W-S 6D Formalism: Weak Beam Lorentz Boost of the weak beam. Since s= 0 is not always transformed to s = 0, a transformation ~x (s ) ~x (0 )has to be performed in addition. More details in the bibliography.

7 W-S 6D Formalism: Strong Beam Strong beam moments rotation by crossing plane α and crossing angle ϕ (i.e.θ/2). An additional variable ϕ2 was added to decouple the weak and strong beam rotation. Strong beam moments has to be transported to the collision point for each slice (similarly is done the particles in the weak beam)

8 W-S 6D Formalism: Synchro-Beam Mapping This map shows the coupling between transverse and longitudinal motions due to a BB interaction with crossing angle.

9 W-S 6D Formalism: Crossing Angle* It is a transformation from Cartesian to accelerator coordinates. It is a rotation in X-Z plane by an angle Φ/2 and a boost to the direction of the rotated X. STRONG Boost WEAK X Θ/2 Θ/2 Z * Don't be afraid of beam-beam interactions with a large crossing angle, K. Hirata, SLAC-PUB-6375.

10 W-S 6D Formalism: Lorentz Boost In the boosted frame there are now head on collisions with a longitudinal tilt of the strong beam. STRONG Z* X* WEAK

11 W-S 6D Formalism: Crossing Plane Hirata's BBC included only purely horizontal crossings. SixTrack allows to define arbitrary crossing planes*. IP1 crossing plane Y ~ X Arbitrary crossing plane α X IP5 crossing plane * Six-dimensional beam-beam kick including coupled motion, L.H.A. Leunissen et al., PRSTAB

12 Crossing angle: Strong beam model Original SixTrack input for 6D beam-beam lens allowed to define in the input half crossing angle (θ/2) and crossing plane angle (α). However the θ/2 was common for weak and strong beam so not possible to perform simulations with the strong beam crabbed. The crabbing of the weak beam is done by the CC element. Nslices θ/2[rad] bb_ho5b1_0 bb_ho1b1_ e e 3 IP5 α[rad] Horizontal Crossing IP5 Vertical Crossing IP1 IP1 Weak beam

13 Crossing angle: Strong beam model Possibility of reverting the sign of the crossing angle. Nslices bb_ho5b1_0 bb_ho1b1_0 5 5 θ/2[rad] 0.295e e 3 IP5 α[rad] Horizontal Crossing IP1 Vertical Crossing IP5 IP1 Weak beam

14 Crossing angle: Strong beam model An additional variable θ2/2 controlling the strong beam crabbing has been added in the BEAM block of the fort.3 input. Nslices θ/2[rad] bb_ho5b1_ e 3 bb_ho1b1_ e 3 IP5 α[rad] θ2/2[rad] IP1 Crab Crossing IP5 Crab Crossing IP1 Weak beam

15 W-S 6D Checks: Synchro-Betatron Resonances The inclusion of the bunch length effect in the beam-beam simulations excite synchro-betatron resonances. Qx±2Qs

16 LHC flag option for W-S studies The LHC flag used to provide with the other beam with the correct optics when they are not symmetric. From the manual, For the LHC with its anti symmetric IR the separation of the beams in one plane can be calculated by the β function of the other plane. For flat beams (not anti-symmetric optics) the separation can be loaded from the fort.2 file. (0 = off; 1 = anti-symmetric;2 = load from file). In the sixdeskenv environment used to automatize the Dynamic Aperture studies currently it is hard coded to lhc=1. Since flat optics will become common studies, the reponsibles might want to include as another input.

17 BB Elements round optics β*=15 cm Long Range elements anti-symmetric lhc =1

18 BB Elements flat optics β*=7.5/30 cm Long Range elements non-anti-symmetric lhc =2

19 LHC flag option: LHC β*=55 cm optics Hour glass effect negligible for these optics. Perfect agreement simulations and analytical formula. β*xy > 7* σz Converging for #slices 7

20 LHC flag option: HLLHC β*=15 cm optics Hour glass effect might start to play a role for these optics. Mismatch between simulations and analytical formula for small crossing angles. β*xy = 2* σz

21 LHC flag option: HLLHC β*=15 cm optics Benchmark against Ohmi's 6D BB W-S code (also based on Hirata's formalism) provided with a result not matching for small xsing angles with our previous assumptions. Still something wrong?

22 6D BB lens: lhc parameter This is fine for 4D as both HO and LR info is read from fort.2. However when doing 6D the HO is wrongly calculated for lhc=1 and 2. Example: flat optics 30/7.5 cm. LR have to be read from fort.2 but this overwrites the 6D slicing done by SixTrack internally. Anti-symmetric switches hor ver Missing second order moments for 6D slicing.

23 LHC flag option: HLLHC β*=7.5/30 cm optics Very good agreement versus S. Valishev analytical formulae (including hourglass and crossing angle) and SixTrack with the new lhc=2 implementation for 6D elements.

24 Crossing angle sign: Strong beam model It was raised a concern regarding of the different crossing sign in the 6D BB formalism. The difference of tuneshift found for low amplitude particles is ~10-11 SixTrack MADX

25 Crossing Angle Definition crossing angle definition +/- beam 1 strong/weak beam plot tracked particle position at slices of strong beam? Clarify with a plot the convention we use. Plot weak beam versus slices position. Weak beam

26 ICE Pending Actions related to SixTrack BB From Meeting Action 14 (FS and beam-beam team): Possibility to make some tracking with SIXTRACK when betax* betay*, called flat beams. It is worth mentioning that 3 cases might be referred to as flat beams: betax* betay* (the case of interest here), epsx epsy and flat longitudinal distribution. In the case of betax* betay*, the output of MADX is fine (it is well computed) but the problem is then the data transfer between MADX and SIXTRACK => Not all the parameters (betas, sizes, intensities) are transferred. For the other two "flat" cases it should be fine. => Done (EmmanuelL) but to be redone as it seems there are some issues (see beam-beam meeting on 11/12/2013). Emmanuel L. included the option of lhc=2 to read from MADX the separations and beam sizes for the case betax* betay*. The modification worked fine for the 4D case but not for 6D where the slicing process did not take into account correctly the hour glass effect. Now corrected and new released needed simulate flat beams. - Action 15 (FS and beam-beam team): 6D beam-beam lens (in fact it is 4D + time dependence) => We need this even if the strong beam is a single particle. There is a lens in SIXTRACK but it is not debugged. For instance it is not clear if the crossing angle is defined for the strong or the weak beam. The crossing angle input for the 6D BB lens is defined in the fort.3 file was used by both the weak (Lorentz boost) and strong beams (slicing process). Now two independent angles (Φ weak beam and Φ2 strong beam) - Action 16 (FS and beam-beam team): Effect of the 6D beam-beam lens on the strong beam => Both the divergence effect of the strong beam and crab tilt. See BB Meeting 28-June-2013.

27 LHC Simulation Results From T. Pieloni talk at HSC meeting 16/04/14.

28 LHC Simulation Results From T. Pieloni talk at HSC meeting 16/04/14.

29 HL-LHC Baseline Studies For the HL-LHC nominal parameters not enough DA is granted for good beam stability. Machines errors effect on the DA are masked by BB effect. D. Banfi et al., WEAK-STRONG BEAM-BEAM SIMULATIONS FOR HL-LHC, IPAC14.

30 HL-LHC Baseline Studies D. Banfi et al., WEAK-STRONG BEAM-BEAM SIMULATIONS FOR HL-LHC, IPAC14.

31 HL-LHC Baseline Studies First time ever DA studies in a β* leveling scenario. DA always largely above the 6σ for the nominal parameters. Margin for increasing intensity, reducing crossing angle, reducing CC voltage,... D. Banfi et al., WEAK-STRONG BEAM-BEAM SIMULATIONS FOR HL-LHC, IPAC14.

32 New features CC RF Curvature A LHC RF 200 MHz (6 MV) is a option currently under study. Allowing longer bunches with larger intensity from the SPS. However longer bunches will see the RF curvature effect from the CC reducing the ΔQbb. On going work with R. Tomas. Next results to be presented at Chamonix.

33 SixTrack BB documentation SixTrack Beam-Beam wiki section has been updated with 4D and 6D BB lens explanations (source code and variables explanation). It can be found here, In addition we are agreed with optics experts to modify the input of the BB is given to SixTrack, i.e. there will be an new input file with a full set of second order moments to characterize the head on elements differently from MADX. This will provide more flexibility of having different optics b1/b2, dispersion effects, etc.

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