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RF Quadrupole Structures for Transverse Landau Damping in Circular Accelerators

This study explores the use of RF quadrupole structures for transverse Landau damping in circular accelerators. The working principle, numerical simulations, and experimental studies are presented, along with a summary and outlook. The potential advantages of RF quadrupoles over traditional octupoles are discussed.

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RF Quadrupole Structures for Transverse Landau Damping in Circular Accelerators

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  1. RF Quadrupole Structures forTransverse Landau Dampingin Circular Accelerators IPAC’17, Copenhagen, Denmark17. May 2017 M. Schenk, X. Buffat, L. R. Carver, A. Grudiev, K. Li, A. Maillard, E. Métral, K. Papke Acknowledgements G. Arduini, H. Bartosik, R. De Maria, S. Fartoukh, Y. Papaphilippou, G. Rumolo, E. Shaposhnikova,LHC OP team

  2. Contents • Introduction • Working principle • Numerical simulations • Experimental studies • Summary and outlook M. Schenk et al. 17.05.2017

  3. Contents • Introduction • Working principle • Numerical simulations • Experimental studies • Summary and outlook M. Schenk et al.

  4. Collective instabilities … and a way around them Source particleinteracts electro-magnetically with the accelerator structure / impedance Wake kicks can drive (head-tail) instabilities characterised by the complex coherent tune shift ΔQc and a mode pattern 1 2 • Creates wake fieldthat acts back on trailing particles (witnesses) Problem:Collective instabilities(Impedance-driven) 15 20 source witness v ≈ c wake field Head-tail ampl. [a.u.] 0 Bunch centroid [µm] 0 -20 -15 0 -0.1 0.1 0.2 -0.2 0 2·105 4·105 6·105 z [m] • We want to generate a large enough incoherent tune spread ΔQ 1 Time [turns] This increases the stable area in the complex tune space 2 A solution:Landau damping unstable Re (ΔQc) Tune distribution -Im(ΔQc) With large enough spread, the instability can be suppressed 3 ΔQc stable 0 Q0 0 Tune Q Re(ΔQc) M. Schenk et al.

  5. How to generate tune spread? Magnetic octupoles 1 Betatron detuning with transverseamplitude RF quadrupole[1-3] 2 Betatron detuning with longitudinal amplitude Not to be confused with the RFQ used in Linacs! M. Schenk et al. 17.05.2017

  6. Potential advantages of an RF quadrupole LHC nominal at 7 TeV 2 LHC Landau octupoles (≈ 56 m) 1 1/γ RF quadrupole (≈ 1 m) 1/γ2 7 • ΔJx,y << ΔJz(LHC nom., 7 TeV: factor 104 – 105)[1,4] • Jzprovides much larger handle for detuning 1 m of RF quadrupole produces same RMS tune spread as max. LHC octupoles (@7 TeV) 1 • Octupoles: affected by adiabatic damping& higher beam rigidity(1/γ2) • RF quadrupole: only affected by higher beam rigidity (1/γ)(thanks to longitudinal blow up[5]) Higher energy machines 2 • Potentially more violent instabilities • Smaller transverse emittance makes octupoles less effective Higher intensity / higher brightness beams 3 • E.g. halo cleaning: can decrease octupole detuning efficiency, while the RF quadrupole isunaffected Manipulations in the transverse planes 4 M. Schenk et al.

  7. Basic working principle of an RF quadrupole J. Scott Berg and F. Ruggiero developed basic stability diagram theory for detuning with Jz[6] RF-modulated quadrupole kick 1 • Theory is approximate and does not include all the beam dynamics • Asymmetry in the two planes can be reduced with a two-family scheme(see [7] for details) At present best addressed with tracking simulations b(2) [T/m m] denotestheintegratedquadrupolargradient Translates into a betatron detuning(assume ϕ0 = 0) 2 -Im(ΔQc) [a.u.] unstable unstable stable stable 2nd order:Detuning with longitudinal action Re(ΔQc) [a.u.] M. Schenk et al.

  8. Add a ‘side note’: RF quadrupole has been studied to increase TMCI (strong head-tail) threshold. Not further pursued due to high required strength -> problem of resonances a.o. Here: For Landau damping of weak head-tail modes, we operate in a different regime (put pictures). M. Schenk et al.

  9. Contents • Introduction • Working principle • Numerical simulations • Experimental studies • Summary and outlook M. Schenk et al. 17.05.2017

  10. The PyHEADTAIL model[8] • Interaction point • Wake field kicks • Chromaticity • Octupoles, RF quadrupole • Electron cloud (PyECLOUD) • … 4 Linear periodic maps for transverse tracking from one IP to the next 3 15 Wake field 20 Data acquisition 5 y 0 7 0 Head-tail ampl. [a.u.] Bunch centroid [µm] 100’000s turns … -20 z • Initialise bunch • Typically 106macroparticles • Various distributions possible: Gaussian, matched to rf bucket, waterbag, … 2 -15 0 -0.1 0.1 0.2 -0.2 0 2·105 4·105 6·105 z [m] Time [turns] x Once per turn: Apply (non-)linear synchrotron motion 6 CourtesyK. Li Divide ring into segments separated by interaction points (IP) 1 Wake kicks M. Schenk et al.

  11. Numerical proof of concept (I) PyHEADTAIL Stability diagram theory LHC experiment[9] Excellent agreement between experiment, tracking, and theory • Solid understanding of the involved mechanisms • Landau damping from octupoles responsible for mitigation • PyHEADTAIL models the machine accurately (a.o. reliable impedance model) and reproduces observations, in particular the Landau damping mechanism Ideal study case to address the stabilising effect of an RF quadrupole 2 0 Bunch centroid [a.u.] -2 • Same m = -1 instability • Rise time • τ≈ 4.5 s at Ioct = -10 A • τ≈ 12.8 s at Ioct = -15 A • Ioct= -17.5 ± 2.5 A • Circulant matrix model (BimBim[10]) to solve eigenvalue equation • Again m = -1 instability • Ioct = -17.5 ± 1 A • LHC at 3.5 TeV, single bunch • Head-tail instability m = -1 • Rise time τ≈ 10 s at Ioct = -10 A • Cured with octupoles Ioct = -15 ± 5 A 0 1.2·106 4·105 8·105 Turn M. Schenk et al.

  12. Numerical proof of concept (II) RF quadrupoles Magnetic octupoles Factor 10 difference in required active lengths for this particular instability. Expected to become even better at higher energies. What happens if we replace octupoles with RF quadrupoles? • As expected from theory, the RF quadrupole mitigates the instability, similarly to octupoles • Strength can be achieved with a single cavity • Active length ≈ 0.15 m • Landau octupole current of -17.5 ± 2.5 A is required for stabilisation • Corresponds to active length ≈ 1.5 m(LHC octupoles at max. strength) M. Schenk et al.

  13. HL-LHC PyHEADTAIL study: Synergy between octupoles and RF quadrupole • Q’ = 10 • HL-LHC, single nominal bunch, 7 TeV[11] • Working point Q’ = 10 • Head-tail mode (0, 2) – as observed in the LHC • Without RF quadrupole: LHC Landau octupole currentIoct= (170 ± 10) A is required for stabilisation(accounting for impedance only) Landau octupoles (≈ 17 m) (170 ± 10) A RF quadrupole (≈ 0.5 m) • An RF quadrupole can significantly decrease the required octupole current • It can also stabilise the beam alone, here with 2-3 cavities • Factor 34 difference in active lengths M. Schenk et al.

  14. Contents • Introduction • Working principle • Numerical simulations • Experimental studies • Summary and outlook M. Schenk et al.

  15. Experimental studies • Direct experimental validation of RF quadrupole simulations isnot possible at present as no such cavity has been built yet • But: Stabilisingmechanism canbe verified using second order chromaticity Q’’ • How? Linear synchrotron motion RF quadrupole Chromaticity RF-modulated quadrupole kick leads to betatron detuning Betatron detuning from relative momentum error RF quadrupole Q’’ term leads to • Q’’ can be introduced in the LHC by powering the main sextupole magnets in a specific configuration[12] • This has limitations and does not offer the same flexibility as an RF quadrupole • Magnitude and range depend on the machine lattice • It can in general not be a fully independent knob due to optics constraints • It also creates detuning with transverse action ΔQ(Jx, Jy) Q’’ M. Schenk et al.

  16. PyHEADTAILwith detailed impedance and MAD-X optics model at Ioct = 0 A Experimental studies[12,13] • Goal: Stabilisesingle bunches at 6.5 TeV with Q’’ • PyHEADTAIL predictions: Q’’ creates large areas of stability interleaved with two unstable bands (different head-tail modes!) • ExperimentProcedure:Introduce Q’’ and reduce the Landau octupole current to determine the single bunch stability threshold • Two different working points: • (a) Qx’’ = 0 / Qy’’ = 0 (@Ioct= 0 A) • Bunches go unstable at Ioct= 80 A[14]meas. vs.Ioct= 105 ± 5 A sim. • (b) Qx’’ ≈ -40’000 / Qy’’ ≈ -40’000 (@Ioct= 0 A) • Octupoles are reduced to Ioct = 0 A, with 3 out of 4 bunches in the machine stable • One bunch goes unstable in the horizontal plane when reducing from Ioct = 36 A to 0 A • This is explained by the unstable band located next to the working point. • Measurements and simulations show excellent agreement on the unstable modes for both cases. Horizontal Vertical Stable Unstable (b) (b) +35 -20 (a) (a) PyHEADTAIL(Horizontal) Measurements(Horizontal) M. Schenk et al.

  17. PyHEADTAILwith detailed impedance and MAD-X optics model at Ioct = 0 A Experimental studies[12,13] • Goal: Stabilisesingle bunches at 6.5 TeV with Q’’ • PyHEADTAIL predictions: Q’’ creates large areas of stability interleaved with two unstable bands (different head-tail modes!) • ExperimentProcedure:Introduce Q’’ and reduce the Landau octupole current to determine the single bunch stability threshold • Two different working points: • (a) Qx’’ = 0 / Qy’’ = 0 (@Ioct= 0 A) • Bunches go unstable at Ioct= 80 A[14]meas. vs.Ioct= 105 ± 5 A sim. • (b) Qx’’ ≈ -40’000 / Qy’’ ≈ -40’000 (@Ioct= 0 A) • Octupoles are reduced to Ioct = 0 A, with 3 out of 4 bunches in the machine stable • One bunch goes unstable in the horizontal plane when reducing from Ioct = 36 A to 0 A • This is explained by the unstable band located next to the working point. • Measurements and simulations show excellent agreement on the unstable modes for both cases. Horizontal Vertical Stable Unstable (b) (b) • Experiments confirm that detuning with longitudinal action contributes to beam stability • Details of the experimental observations are reproduced with PyHEADTAIL • The relevant effects are accurately modelled • Gives confidence for the RF quadrupole simulations • Q’’ / RF quadrupole has two effects on beam dynamics(see [7,13] for more details) • Stabilisation from incoherent tune spread • Change of the unstable mode (effective impedance), like from a first order chromaticity +35 -20 (a) (a) PyHEADTAIL(Horizontal) Measurements(Horizontal) M. Schenk et al.

  18. Summary and outlook • PyHEADTAIL simulations show that the RF quadrupole works successfully and effectively either in combination with Landau octupoles or on its own • Detuning with longitudinal action offers several advantages over conventional methods • Large handle for tune spread since ΔJz >>ΔJx,y(compact RF quadrupole, saving space for other components) • This is true in particular at high energies and for low transverse emittance beams • It is not affected by manipulations in the transverse planes • Experimental tests with Q’’ in the LHC demonstrate that the stabilising mechanism works and that PyHEADTAIL accurately models the involved effects • Outlook, add here: • DA studies (oct. vs. RF quadrupole) • Theorywork • Maybe: Comp RF quad / Q’’ / Oct. ? M. Schenk et al.

  19. References (I) [1] A. Grudiev, Radio frequency quadrupole for Landau damping in accelerators, Phys. Rev. ST Accelerators and Beams 17, 011001, 2014. [2] A. Grudiev, K. Li, and M. Schenk, Radio Frequency Quadrupole for Landau Damping in Accelerators: Analytical and Numerical Study, Proceedingsof HB2014, paper WEO4AB01, East-Lansing (USA), 2014. [3] M. Schenk et al., Use of RF Quadrupole Structures to Enhance Stability in Accelerator Rings, Proceedings of HB2016, paper THPM7X01, Malmö (Sweden), 2016. [4] O. Brüninget al., LHC Design Report, CERN Yellow Reports: Monographs, Geneva, Switzerland, 2004. [5] F. Baudrenghien and T. Mastoridis, Longitudinal emittance blowup in the Large Hadron Collider, NIM A 726, pp. 181-190, 2013. [6] J. Scott Berg and F. Ruggiero, Stability Diagrams for Landau Damping, LHC Project Report 121, 1997. [7] M. Schenk et al., RF Quadrupole Structures for Transverse Landau Damping in Circular Accelerators, presented at IPAC’17, Copenagen (Denmark), paper THPVA026, 2017. [8]E.Métralet al., Beam instabilities in hadron synchrotrons, IEEE Transactions on Nuclear Science 63, no. 2, pp. 1001-1050, 2016. [9] E. Métral, B. Salvant, N. Mounet, Stabilization of the LHC single-bunch transverse instability at high-energy by Landau octupoles, 13.09.2011. M. Schenk et al.

  20. References (II) [10] X. Buffat, Transverse beams stability studies at the Large Hadron Collider, PhD Thesis No. 6321, EPFL, Switzerland, 2015. [11] O. Brüning and L. Rossi (Edts.), The High Luminosity Large Hadron Collider, Advanced Series on Directions in High Energy Physics Vol. 24, 2015. [12] L. R. Carver et al., MD1831: Single bunch instabilities with Q’’ and non-linear corrections, CERN MD Note, Feb. 2017. [13] M. Schenk et al., Practical Stabilisation of Transverse Collective Instabilities with Second Order Chromaticity in the LHC, presented at IPAC’17, Copenagen (Denmark), paper SUSPSIK059, 2017. [14] L. R. Carver et al., Current status of instability threshold measurements in the LHC at 6.5 TeV, Proceedings of IPAC16, Busan (Korea), 2016. M. Schenk et al.

  21. Backup M. Schenk et al.

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