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Augmentation de la luminosité du LHC: les défis en physique des accélérateurs

Augmentation de la luminosité du LHC: les défis en physique des accélérateurs. Barbara Dalena A. Chancé , O. Gabouev , J. Payet CEA R. De Maria, S. Fartoukh CERN. Contents. The project Hi- Lumi Optics design

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Augmentation de la luminosité du LHC: les défis en physique des accélérateurs

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  1. Augmentation de la luminosité du LHC: les défis en physique des accélérateurs Barbara Dalena A. Chancé, O. Gabouev, J. Payet CEA R. De Maria, S. Fartoukh CERN

  2. Contents Barbara Dalena, Roscoff • The project Hi-Lumi • Optics design • IR1/5 Matching Section (MS) layout for crab cavity operation • Non linear fringe field effects of large aperture magnets • Scaled Q4 MQYY quadrupole example • Outlook

  3. Hi-Lumi LHC Goal: integrated luminosity ~250 fb-1 per year • Luminosity Leveling • Hardware changes (Nb3Sn superconducting technology, • crab cavities) • New Optics Scheme Barbara Dalena, Roscoff

  4. HiLumi Working Packages CEA-Irfu SACM/LEDA • WP2.Task 2: Optics & Layout • Optics option with 170 T/m triplet gradient and 120 mm aperture • IR1/5 Matching Section (MS) layout for crab cavity operation • WP2.Task 3: Tracking • Field quality of HL-LHC magnets • Non linear fringe field effect of large aperture magnets Barbara Dalena, Roscoff

  5. Optics & Layout Barbara Dalena, Roscoff

  6. Optimization for crab cavity operation Reduce the voltage of the crab cavity: V  1/(*crab)1/2 D2 CRAB Q4 Q5 Q6 Q7 • increasing the beta • functionat the CRAB • using • MS quadrupole types • MS quadrupole positions Barbara Dalena, Roscoff

  7. Proposed IR1/IR5 matching section layout D2 CRAB Q4 Q5 Q6 Q7 baseline Q7+ D2 CRAB Q4 Q5 Q6 Q7 v1 22.3 m 22.1 m 22.1 m 5.595 m new proposed Q7+ D2 CRAB Q4 Q5 Q6 Q7 v2 15.05 m 15.2 m 36.6 m Barbara Dalena, Roscoff

  8. Optics Collision * = 15 cm (ATS) baseline proposed v1 proposed v2 Injection * = 3 m • Collision: •  increase at the crab cavity location of a factor ~2 in v1 and v2 • Injection: • v2 optimizes  in Q6 Barbara Dalena, Roscoff

  9. Apertures • Collision: • v1 and v2 are similar • matchingquadrupoles apertures more close to the limit (green line) • Injection: • v2 improves apertures in Q6 Barbara Dalena, Roscoff

  10. Gain Crab cavity voltage gain Few changes in the interaction region layout  a lot of benefits: • Possibility to reduce the crab voltage of ~20-30% •  Possibility to squeeze to very low * (non ATS) • Possibility to reduce * at injection • Compatible with new optics scheme (ATS) • Drawbacks: • Less flexibility toward high * at injection • Matching section apertures a bit more close to the limit Barbara Dalena, Roscoff

  11. Non linear fringe field effect Barbara Dalena, Roscoff

  12. Non linear fringe field effect The HL-LHC project relies on large aperture quadrupoles and dipole (mainly inner triplet and D1)  the beam is much more sensitive to non-linear perturbations in this region. Analytical evaluations of detuning with amplitude and chromatic effects show that the effect is small, but not negligible  Tracking simulations of long-term behavior needed. A.V. Bogomyagkov et al., WEPEA049, IPAC’13 Courtesy of M. Segreti (CEA SACM/LEAS) Example: Q4 MQYY G=120 T/m @1.9 K  = 90 mm, L = 3.5 m • Non linearity's: • main field fringe • higher order multipoles Barbara Dalena, Roscoff

  13. Symplectic integrator of z-dependent Hamiltonian • ;;; •  is the independent variable with d =dz • (z,pz) is the fourth canonical pairs, needed to have the explicit dependence onz The solution of the equation of motion (Transfer Map) for this Hamiltonian using Lie algebra formalism is: The transfer map M(σ) can be replaced by a product of symplectic maps which approximates it (symplectic integration). Reference: Y. Wu, E. Forest and D. S. Robin, Phys. Rev. E 68, 046502, 2003 Barbara Dalena, Roscoff

  14. From 3D magnetic field data to tracking Harmonic analysis Fourier integrals Interpolation • B Field map • Cartesian • coordinates • Harmonics Gradient extraction Fourier Transform Inverse FT Frequency resolution (step in z dependent) Lie Tracking • Vector Potential A Stage M2 Oleg Gabouev Barbara Dalena, Roscoff

  15. Fringe field effect of a single quadrupole • Fringe field effects of Q4 design 2 order of magnitude less than simple test quadrupole Barbara Dalena, Roscoff

  16. Lie vs Runge Kutta 4 (Q4 design) • small residual linear part • dependence on the high harmonics at large amplitudes • Long term effects ? To be evaluated with SixTrack… Barbara Dalena, Roscoff

  17. Conclusion & Outlook • Options for the optics of the high luminosity matching sections for crab cavity operation are studied • crab cavity voltage gain ~20% • injection optics with high * (6 m) more difficult • Non linear fringe field effects for the high apertures quadrupole of the interaction region is studied • the effect is of the order 10-8rad for a single quadrupole, long term effect ? To be evaluated with SixTrack... • comparison with octupole-like kicks Barbara Dalena, Roscoff

  18. Optics design IP5 • Baseline optics with a new triplet of gradient 170 T/m (=120mm) compatible with the ATS scheme • Problem: • match with LHC ATS scheme • not easy due to several • constraints • Solution: • definition of a tools to choose • the optimal initial conditions Triplet Matching section Q4/5/6 L*=23 m LFFS=268m Barbara Dalena, Roscoff

  19. Chromatic correction Barbara Dalena, Roscoff

  20. Application If Ax , Ay and Az are non zero and K split as: The second order integrator writes Explicit dependence on z using The number of iterations needed can be reduced choosing a Gauge transformation, so that Ax=0 or Ay=0 Barbara Dalena, Roscoff

  21. Transfer map The seconds half iterations for K1, K2 and K3 are missing in the table. K1 K2 K3 K4 Barbara Dalena, Roscoff

  22. Computation of the vector potential in cartesian coordinates • The three components of the quadrupole vector potential can be written as expansions of normal (s) and skew (c ) multipoles • Each of the multipole can be expanded in terms of homogenous polynomials in x,y and z-dependent coefficients (called generalized gradients) if if References: A. J. Dragt, www.physics.umd.edu/dsat Task.2.3 meeting 07/06/2013

  23. The generalized gradients The z-dependent coefficients can be calculated using the multipoles expansion of the magnetic field: where: is the derivative of the modified Bessel function Task.2.3 meeting 07/06/2013

  24. Field harmonics Q4 scaled version Courtesy of M. Segreti (CEA SACM/LEAS) Barbara Dalena, Roscoff

  25. Field reconstruction Barbara Dalena, Roscoff

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