Modelling and measurements of bunch profiles at the LHC FB Stefania Papadopoulou, Fanouria Antoniou, Yannis Papaphilippou 24/6/16

Contents Beam profiles at FB -The q Gaussian distribution function -LHC beam profiles SIRE code -IBS effect at FB, comparison with MADX

The q Gaussian distribution The emittance evolution at LHC FB energy is dominated by the IBS effect. In the case of LHC, the interplay between IBS and a series of other effects, can enhance the tails of the beam distributions, which may become non-Gaussian. In many cases, the bunch profiles in the LHC, appear to have heavier tails than a normal distribution. In order to describe them more accurately, the q-Gaussian function, is used. This distribution has a probability density function given by: 3 parameters In the heavy tail domain (1 < q < 3) for q =1 Gaussian function

Beam profiles at FB low frequency excitation (MD453), Miriam

Beam profiles at FB B1 B2 G.Trad Fit parameters for B1 6/11/15 00:00 Gaussian; s 0.33 q Gaussian; s and q 0.33 and 1.15 Fit parameters for B2 6/11/15 00:00 Gaussian; s 0.33 q Gaussian; s and q 0.33 and 1 G.Trad low frequency excitation (MD453), Miriam

Beam profiles at FB B1 B2 G.Trad Fit parameters for B1 6/11/15 00:00 Gaussian; s 0.33 q Gaussian; s and q 0.33 and 1.15 Fit parameters for B2 6/11/15 00:00 Gaussian; s 0.33 q Gaussian; s and q 0.33 and 1 G.Trad low frequency excitation (MD453), Miriam

Beam profiles at FB B1 B2 G.Trad Fit parameters for B1 6/11/15 01:00 Gaussian; s 0.34 q Gaussian; s and q 0.34 and 1 Fit parameters for B1 6/11/15 01:00 Gaussian; s 0.34 q Gaussian; s and q 0.34 and 1 G.Trad low frequency excitation (MD453), Miriam

Beam profiles at FB Tune scans Fill4785, Gianni and Annalisa Forbidden by e-cloud + Q’ + octupoles Forbidden by Q’ + octupoles Can give stability issues if coupling is not fully corrected Nominal 2015 Tune scans Fill4785, Gianni and Annalisa

Beam profiles at FB Tune scans Fill4785, Gianni and Annalisa Forbidden by e-cloud + Q’ + octupoles Forbidden by Q’ + octupoles Can give stability issues if coupling is not fully corrected Nominal 2015 Tune scans Fill4785, Gianni and Annalisa

Beam profiles at FB Tune scans Fill4785, Gianni and Annalisa

Beam profiles at FB Tune scans Fill4785, Gianni and Annalisa

Beam profiles at FB Tune scans Fill4785, Gianni and Annalisa

developed by A. Vivoli and M. Martini and revised by Fanouria SIRE Software for IBS and Radiation Effects (a Monte Carlo multiparticle simulation code) developed by A. Vivoli and M. Martini and revised by Fanouria Inputs -The optics along a lattice (MADX twiss file). -The parameters file. -The particles distribution (default: Gaussian distribution). Computing IBS (and Radiation Effects) -Particles are tracked from point to point in the lattice by their invariants. -At each point of the lattice the scattering routine is called. -6-dim coordinates of particles are calculated. -Particles of the beam are grouped in cells. -The intrabeam collisions between pairs of macro-particles are iteratively computed, the momentum of particles is changed because of scattering. -Invariants of particles are recalculated. -Radiation damping and excitation effects are evaluated at the end of every loop. Outputs -The beam distribution is updated and the rms beam emittances are recomputed, giving finally the evolution of the emittance and particle distribution in time. The analytical models that describe the IBS effect assume Gaussian beam distributions. In the case of non-Gaussian beam distributions no theoretical models exist. SIRE calculates IBS for any distribution.

SIRE Parameters file Fastrun NIBSruns nturnstostudy ncellx ncellz ncells numpart The Fastrun is applied in order to speed up the simulation. -the IBS is applied in oneturn and the growth rate per particle is calculated -the emittance per particle is recalculated based on the exponential IBS growth in a specific timestep. -continue tracking with the interpolated distribution Number of timesteps that the time is divided to calculate IBS Number of turns (total time) Number of cells in each plane Number of macroparticles

SIRE Parameters file Fastrun NIBSruns nturnstostudy ncellx ncellz ncells numpart The Fastrun is applied in order to speed up the simulation. -the IBS is applied in oneturn and the growth rate per particle is calculated -the emittance per particle is recalculated based on the exponential IBS growth in a specific timestep. -continue tracking with the interpolated distribution Number of timesteps that the time is divided to calculate IBS Number of turns (total time) Number of cells in each plane Number of macroparticles In order to avoid combinations which give very small #macroparticles/cell, it was observed (by Fanouria) that 5macroparticles/cell is the optimal minimum number.

SIRE Parameters file scanning tested Parameters (at injection) Nominal Fastrun NIBSruns nturnstostudy ncellx ncellz ncells numpart The Fastrun is applied in order to speed up the simulation. -the IBS is applied in oneturn and the growth rate per particle is calculated -the emittance per particle is recalculated based on the exponential IBS growth in a specific timestep. -continue tracking with the interpolated distribution Number of timesteps that the time is divided to calculate IBS Number of turns (total time) Number of cells in each plane Number of macroparticles scanning In order to avoid combinations which give very small #macroparticles/cell, it was observed (by Fanouria) that 5macroparticles/cell is the optimal minimum number. tested Parameters (at injection) Nominal HiLumi ex,y [mm] 3.5 2 4s bunch length [ns] 1.2 1 Bunch population [1011] 2.3 lattice recurrences Elements of the lattice with twiss functions differing of less than prec.% are considered equal

Scanning ncells and #mp 30min at FB, full optics Scanning ncells and #mp Nominal HiLumi

Reduced lattice As the LHC has a large number of elements (more than 11000), the computational time that SIRE needs to track the distribution for all of them along the ring is very long. The IBS growth rates were calculated for the LHC’s full optics, using the IBS module of the MADX, based on the B-M formalism. The optimal minimum number of IBS kick points around the lattice, without affecting the overall effect, are identified. Finally, the reduced lattice used in SIRE has only 92 points (much lower computational time). so

30min at FB, reduced lattice Scanning ncells and #mp Nominal HiLumi

30min at FB, reduced lattice Choose the optimal case of ncells and #mp, for both nominal and HiLumi parameters. Parameters Nominal HiLumi #mp/cell 5 #mp 135000 160000 ncellx·ncelly·ncells 27000 31950 SIRE runs many times (cause there are random generators) then the mean values are compared with the B-M result from MADX.

30min at FB, reduced lattice Optimal case parameters Nominal +2% +3% HiLumi +16% +12%

Summary and next steps Non-Gaussian beam profiles with heavy tails use of the q-Gaussian distribution function. The benchmarking with B-M (MADX) is very good for the 30min at FB. SIRE: IBS tends to develop tails of the particle distribution. Use q Gaussian as an input distribution in SIRE. At the LHC FT , the IBS effect becomes weaker while SR damping becomes more pronounced. After the longitudinal beam manipulations during the energy ramp, the longitudinal bunch profiles arrive at FT with a clearly non-Gaussian shape interplay between IBS and SR in this regime, the impact on the evolution of the bunch characteristics and finally on the luminosity. Acquire beam profiles more regularly.

J. D Bjorken, S. K. Mtingwa, Intrabeam Scattering, Part. Accel. Vol J.D Bjorken, S.K. Mtingwa, Intrabeam Scattering, Part. Accel. Vol. 13, p. 115-143 (1983). M. Martini, A. Vivoli, “INTRA-BEAM SCATTERING IN THE CLIC DAMPING RINGS”, CERN-ATS-2010-094, 2010. M. Martini, A. Vivoli, “Effect of intrabeam scattering and synchrotron radiation damping when reducing transverse emittances to augment the LHC luminosity”, sLHC Project Report 0032, 2010. E. M. F. Curado and C. Tsallis, “Generalized statistical mechanics: connection with thermodynamics”, 1992 J. Phys. A: Math. Gen. 25 1019. W. Thistleton, J.A. Marsh, K. Nelson, C. Tsallis, “Generalized Box-Mller Method for Generating q-Gaussian Random Deviates”, 2006. A. Piwinski, Proc. 9th Int. Conf. on High Energy Accelerators, Stanford, 1974. P. Zenkevich, O. Boine-Frankenheim, A. Bolshakov, Last advances in analysis of intrabeam scattering in the hadron storage rings, Nucl. Instr. and Meth. A 577 p. 110-116 (2007). F. Antoniou, F. Zimmermann, Revision of Intrabeam Scattering with Non-Ultrarelativistic Corrections and Vertical Dispersion for MAD-X“, CERN-ATS-2012-066. MAD-X homepage, URL http://mad.web.cern.ch/mad . M. Kuhn, Emittance Preservation at the LHC, Master Thesis, University of Hamburg/CERN, Geneva, Switzerland 2013.

Thank you!

30min at FB, reduced lattice Optimal case parameters Nominal +2% +3% HiLumi +12% +16%

Beam profiles at FB t=0 t=22min Juan Juan wait for the next fill with nominal bunches and acquire new data. If they keep the bunches some time in the machine it would be possible to see the evolution of the profile at flat bottom. I took measurements of the nominal bunch in Beam 1 every 5 seconds. Each measurement contains 100 traces acquired every 100 turns, so you can average them to get a smoother profile. The files are standard HDF5 files. Juan Juan

Beam profiles at FB nominal bunches log G.Trad Fit parameters t=0 Gaussian; s 0.28 q Gaussian; s and q 0.27 and 1.31 G.Trad

Fits(HB2) Growth time [h] 1 70.028 2 48.295 3 4.036 4 6.078 5 4.378 6 14.077 7 10.965 8 8.503 9 7.698 10 8.075

Fits(HB1) Growth time [h] 1 6.085 2 20.94 3 13.144 4 22.651 5 -139.353 6 24.798 7 23.915 8 65.694 9 15.446 10 165.508

Beam profiles at FB G.Trad low frequency excitation (MD453), Miriam Fit parameters for B1 5/11/15 23:00 Gaussian; s 0.35 q Gaussian; s and q 0.34 and 1.14 Fit parameters for B2 5/11/15 23:00 Gaussian; s 0.34 q Gaussian; s and q 0.34 and 1 G.Trad low frequency excitation (MD453), Miriam

Beam profiles at FB G.Trad low frequency excitation (MD453), Miriam Fit parameters for B1 5/11/15 23:00 Gaussian; s 0.35 q Gaussian; s and q 0.34 and 1.14 Fit parameters for B2 5/11/15 23:00 Gaussian; s 0.34 q Gaussian; s and q 0.34 and 1 G.Trad low frequency excitation (MD453), Miriam

Nominal Fit parameters t=0 t=30min Gaussian; s 0.337 0.339 q Gaussian; s and q 0.293 and 2.16 0.295 and 2.19 (+1.4%) Nominal

Nominal Fit parameters t=0 t=30min Gaussian; s 0.337 0.339 q Gaussian; s and q 0.293 and 2.16 0.295 and 2.19 (+1.4%) Nominal

HiLumi Fit parameters t=0 t=30min Gaussian; s 0.334 0.352 q Gaussian; s and q 0.291 and 2.17 0.304 and 2.26 (+4%)

Why non Gaussian if SIRE has this distribution as default? Parameters LHC CLIC DRs #mp <160000 200000 ncellx·ncelly·ncells <27000

Nominal 3qgauss:(1-a/b+a/b.*exp((x.^2/2).*(-1+q).*b)).^(1/2+1/(1-q)) Fit parameters t=0 t=30min Gaussian; s 0.328 0.336 q Gaussian; s and q 0.289 and 2.14 0.294 and 2.17 (+1.4%) Nominal 3qgauss:(1-a/b+a/b.*exp((x.^2/2).*(-1+q).*b)).^(1/2+1/(1-q))

HiLumi Fit parameters t=0 t=30min Gaussian; s 0.322 0.346 q Gaussian; s and q 0.287 and 2.12 0.303 and 2.27 (+7.1%)

Nominal horiz. t=0 t=30min

Nominal longit. t=0 t=30min