The HiLumi LHC Design Study is included in the High Luminosity LHC project and is partly funded by the European Commission within the Framework Programme 7 Capacities Specific Programme, Grant Agreement 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 I. I. Optics design IR1/5 Matching Section (MS) layout for crab cavity operation II. II.Non linear fringe field effects of large aperture magnets Scaled Q4 MQYY quadrupole example Outlook Barbara Dalena, Roscoff2 15/10/2013

Barbara Dalena, Roscoff3 Hi-Lumi LHC Goal: integrated luminosity ~250 fb -1 per year Luminosity Leveling Hardware changes (Nb 3 Sn superconducting technology, crab cavities) New Optics Scheme

15/10/2013 Barbara Dalena, Roscoff4 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

15/10/2013 Barbara Dalena, Roscoff5 I.Optics & Layout

Optimization for crab cavity operation Barbara Dalena, Roscoff6 D2CRABQ4Q5Q6Q7 LHCHL-LHC baseline Q4 MQY, G=160 K  = 70 mm, L = 3.4 m MQYY, G=120 K  = 90 mm, L = 3.5 m Q5 MQML, G=160 K  = 56 mm, L = 4.8 m MQYL, G=160 K  = 70 mm, L = 4.8 m Q6 MQML, G=160 K  = 56 mm, L = 4.8 m MQML, G=160 K  = 56 mm, L = 4.8 m Q7 2  MQM, G=200 K  = 56 mm, L = 3.4 m 2  MQM, G=200 K  = 56 mm, L = 3.4 m  increasing the beta function at the CRAB using MS quadrupole types MS quadrupole positions Reduce the voltage of the crab cavity: V  1/(  *  crab ) 1/2 15/10/2013

Barbara Dalena, Roscoff7 Proposed IR1/IR5 matching section layout 15/10/2013 D2CRABQ4Q5Q6Q7 D2CRABQ4Q5Q6Q7 new Q m baseline proposed D2CRABQ4Q5Q6Q7 Q m m 15.2 m 36.6 m 22.3 m v1 v2

15/10/2013 Barbara Dalena, Roscoff8 Optics proposed v1proposed v2baseline Collision  * = 15 cm (ATS) Injection  * = 3 m Collision:  increase at the crab cavity location of a factor ~2 in v1 and v2 Injection: v2 optimizes  in Q6

15/10/2013 Barbara Dalena, Roscoff9 Apertures Injection: v2 improves apertures in Q6 Collision: v1 and v2 are similar matching quadrupoles apertures more close to the limit (green line)

15/10/2013 Barbara Dalena, Roscoff10 Gain  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 Few changes in the interaction region layout  a lot of benefits: Side, IR and beam Baseline [MV] Proposed [MV] v1 v2 Proposed non ATS [MV] v1 v2 H L/R 5 b 110.8/ / /8.89.2/ /9.4 H L/R 5 b 212.0/ / /8.99.4/ /8.8 V L/R 1 b 111.8/ / /8.99.3/ /8.6 V L/R 1 b 210.8/ / /8.79.3/ /9.3 Crab cavity voltage gain

15/10/2013 Barbara Dalena, Roscoff11 II.Non linear fringe field effect

15/10/2013 Barbara Dalena, Roscoff12 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 Example: Q4 MQYY G=120 K  = 90 mm, L = 3.5 m Non linearity's: main field fringe higher order multipoles Courtesy of M. Segreti (CEA SACM/LEAS)

Barbara Dalena, Roscoff13 Symplectic integrator of z-dependent Hamiltonian Reference: Y. Wu, E. Forest and D. S. Robin, Phys. Rev. E 68, , 2003 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). 15/10/2013

Barbara Dalena, Roscoff14 From 3D magnetic field data to tracking Harmonic analysis Fourier integrals Interpolation Gradient extraction Fourier Transform Inverse FT Frequency resolution (step in z dependent) B Field map Cartesian coordinates B Field map Cartesian coordinates Harmonics Vector Potential A Lie Tracking Stage M2 Oleg Gabouev

Barbara Dalena, Roscoff 15 15/10/2013 Fringe field effect of a single quadrupole Fringe field effects of Q4 design 2 order of magnitude less than simple test quadrupole

15/10/2013 Barbara Dalena, Roscoff16 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…

Conclusion & Outlook Barbara Dalena, Roscoff 17 15/10/2013 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 rad for a single quadrupole, long term effect ? To be evaluated with SixTrack... comparison with octupole-like kicks

15/10/2013 Barbara Dalena, Roscoff19 Optics design IP5 L*=23 m L FFS =268m Triplet Matching section Q4/5/6 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

15/10/2013 Barbara Dalena, Roscoff20 Chromatic correction

Application Barbara Dalena, Roscoff21 If A x, A y and A z are non zero and K split as: The second order integrator writes using Explicit dependence on z  The number of iterations needed can be reduced choosing a Gauge transformation, so that A x =0 or A y =0 15/10/2013

Barbara Dalena, Roscoff22 Transfer map x pxpx y pypy l  z pzpz K1K1 K2K2 K3K3 K4K4 The seconds half iterations for K 1, K 2 and K 3 are missing in the table. 15/10/2013

Task.2.3 meeting 07/06/ Computation of the vector potential in cartesian coordinates References: A. J. Dragt, if

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

15/10/2013 Barbara Dalena, Roscoff25 Field harmonics harmonicsIntegral at R=30 mm 2-1, ,71327e ,5493e ,93321e ,60133e ,26182e ,63571e -5 Q4 scaled version Courtesy of M. Segreti (CEA SACM/LEAS)

15/10/2013 Barbara Dalena, Roscoff26 Field reconstruction