Macroparticle simulation of IBS in Super B T
Macroparticle simulation of IBS in Super. B T. Demma (INFN-LNF) In collaboration with: M. Boscolo (INFN-LNF) A. Chao, M. T. F. Pivi (SLAC).
Plan of Talk • Introduction • Conventional calculation of IBS • Multi-particles codes structure • Growth rates estimates and comparison with conventional theories • Bunch distribution evolution • Parallel implementation • Conclusions and outlook 2
IBS Calculations procedure 1. 2. 3. 4. Evaluate equilibrium emittances ei and radiation damping times ti at low bunch charge Evaluate the IBS growth rates 1/Ti(ei) for the given emittances, averaged around the lattice, using K. Bane approximation* Calculate the "new equilibrium" emittance from: • For the vertical emittance use* : • where r varies from 0 ( y generated from dispersion) to 1 ( y generated from betatron coupling) Iterate from step 2 * K. Kubo, S. K. Mtingwa, A. Wolski, "Intrabeam Scattering Formulas for High Energy Beams, " Phys. Rev. ST Accel. Beams 8, 081001 (2005) 3
IBS in Super. B LER (lattice V 12) h=2. 412 nm @N=6. 5 e 10 z=4. 97 mm v=5. 812 pm @N=6. 5 e 10 Effect is reasonably small. Nonetheless, there are some interesting questions to answer: • What will be the impact of IBS during the damping process? • Could IBS affect the beam distribution, perhaps generating tails? @N=6. 5 e 10 4
Intra-Beam Scattering (IBS) Simulation Algorithm IBS applied at each element of the Ring lattice • Lattice read from MAD (X or 8) files containing Twiss functions and transport matrices • At each element in the ring, the IBS scattering routine is called: – Particles of the beam are grouped in cells. – Particles inside a cell are coupled – Momentum of particles is changed because of scattering. – Invariants and corresponding growth rate are recalculated. • Particles are transported to the next element. • Radiation damping and excitation effects are evaluated at each turn. Dec 1, 2011 IBS coll. meeting T. Demma, M. Boscolo, M. Biagini (INFN), M. Pivi , A. Chao (SLAC) 5
Zenkevich-Bolshakov Algorithm For two particles colliding with each other, the changes in momentum for particle 1 can be expressed as: with the equivalent polar angle eff and the azimuthal angle distributing uniformly in [0; 2 ], the invariant changes caused by the equivalent random process are the same as that of the IBS in the time interval ts 6
Radiation Damping and Quantum Excitation • Normalized coordinates are defined by Twiss (B) and Dispersion (H) matrix : • Synchrotron Radiation is taken into account with the following map: • Switch back to physical coordinates by: 7
Intrabeam Scattering in Super. B LER Parameter Energy Bunch population Circumference Emittances (H/V) Bunch Length Momentum spread Damping times (H/V/L) N. of macroparticles N. of grid cells Bane Piwinski IBS-Track Unit Ge. V 1010 m nm/pm mm % ms - Value 4. 18 6. 5 1257 1. 8/4. 5 3. 99 0. 0667 40/40/20 105 64 x 64 Bane Piwinski IBS-Track 8
Emittance Evolution in Super. B LER • Super. B V 12 LER Nb= 2 x 1010 - 12 x 1010 F=10 tx = 10 -1 x 40 ms ty = 10 -1 x 40 ms ts = 10 -1 x 20 ms 9
Bunch-slice parallel decomposition Computation in parallel - pipeline Each processor deals with the bunch-slice, then send information to the next in the pipeline. The last processor print out the beam information. At each turn, 1 processor gathers all particles and compute Radiation Damping and Quantum Excitation. M. Pivi (SLAC) 10
IBS – Super. B LER (using C-MAD) C-MAD parallel code (M. Pivi SLAC) for beam collective effects: • IBS • Electron cloud instability Benchmark: Super. B lattice ~1800 IPs IBS-Track CMAD Dec 1, 2011 z=5. 0*10 -3 m dp=6. 3*10 -4 ppb= 5. 7 1012 Macro. Particle. Number=3 x 105 Grid size = 10 y x 10 x # bunch slices = 64 # processors for this run = 64 M. Pivi (SLAC), T. Demma (INFN)11
CPU timing studies: Super. B LER 1 turn CPU Time [sec] Gain N. of Processors 400 1 1 250 1. 6 2 200 2 4 46 8. 7 16 24 16. 3 32 16 25 64 • Gain not linear: bunch slice decomposition not balanced • Gain @ 64 CPU is only 25 but total execution time is well below 1 min. . • Still working on routines optimization M. Pivi (SLAC) 12
Emittance Evolution in Super. B LER M. Pivi (SLAC), T. Demma (INFN)13
IBS Distribution study Parameter c 2799 Confidence Z 1857. 56 <1 e-6 X 1455. 68 <1 e-6 Y 778. 228 0. 6920 M. Pivi (SLAC), T. Demma (INFN)14
SIRE: IBS Distribution study: CLIC DR Parameter c 2999 Confidence p/p 3048. 7 <1 e-15 X 1441. 7 <1 e-15 Y 1466. 9 <1 e-15 Parameter A. Vivoli (CERN) Value Eq. x (m rad) 2. 001 e-10 Eq. y (m rad) 2. 064 e-12 Eq. d 1. 992 e-3 Eq. z (m) 1. 687 e-3 15
Super. B Damping Ring Energy (Ge. V) 1 Circumference (m) 51. 1 Equilibrium horizontal emittance (nm) 23 Equilibrium vertical emittance, k=. 01 (nm) 0. 2 betatron damping time (ms) 7. 3 Equilibrium energy spread 6. 2 10 -4 Momentum compaction 5. 7 10 -3 RF frequency 475 RF voltage (MV) 0. 5 Bunch length (low current, mm) 4. 8 A damping ring at 1 Ge. V is used to reduce the positron beam injected emittance 5/29/11 16 M. Preger 16
IBS in Super. B Damping Ring ex (m) Injection ez (m) 1100 e-9 1. 5 e-4 Extraction w/ IBS 25 e-9 3. 3 e-6 Extraction w/o IBS 23 e-9 2. 97 e-6 Only 1 IP per tun is conidered 17
The SLS lattice Picture shows the interpolated beta and h functions. In particular: Sqrt[betax] (magenta), Sqrt[betay] (blue), 20*hx (gold), 105*hy (green). 18 Parameter Value Energy [Ge. V] 2. 411 Circumference [m] 288 Energy loss/turn [Me. V] 0. 54 RF voltage [MV] 2. 1 Mom. Comp. factor 6. 05 e-4 Damping times h/v/l [ms] 8. 59/8. 55/4. 26 Hor. emittance [nm rad] 5. 6 Vert. emittance [pm rad] 2 Bunch length [mm] 3. 8 Energy spread [%] 0. 086 F. Antoniou (CERN) 18
IBS effect: 1 Turn w/ Vertical Dispersion Effect of vertical dispersion has been successfully included!!! MAD-X files including vertical dispersion in Super. B are already available…. 19
Summary • Interesting aspects of the IBS such as its impact on damping process and on generation of non Gaussian tails may be investigated with a multiparticle algorithm. • Two codes implementing the Zenkevich-Bolshakov algorithm to investigate IBS effects have been developed: – Benchmarking with conventional IBS theories gave good results –Evolution of the particle distribution shows deviations from Gaussian behaviour due to IBS effect (SIRE-CERN, CLIC-DR). • Parallel implementation of the algorithm is ready : –IBS routines included in CMAD (thanks to M. Pivi). • Comparison of the code results with measurements at SLS and/or Cesr-TA would provide the possibility of • Benchmarking with real data • Tuning code parameters (number of cells, number of interactions, etc. ) • Revision of theory or theory parameters (Coulomb log, approximations used, etc. ) 20
SPARES 21
Differential equation system for x and z Radial and longitudinal emittance growths can be predicted by a model that takes the form of a coupled differential equations: Bane Model N number of particles per bunch a and b coefficients characterizing IBS obtained once by fitting the tracking simulation data for a chosen benchmark case Obtained by fitting the zero bunch intensity case (IBS =0) 22
Summary plots: Super. B parameters Equilibrium horizontal emittance vs bunch current Equilibrium longitudinal emittance vs bunch current 23
Summary plots: DAFNE parameters Macro. Particle. Number=40000 z=12. 0*10 -3 dp=4. 8*10 -4 NTurn=1000 (≈10 damping times) tx = 1000 -1 * 0. 042 ex=(5. 63*10 -4)/g ty = 1000 -1 * 0. 037 ey=(3. 56*10 -5)/g ts = 1000 -1 * 0. 017 24
SIRE: SLS simulations 1/Tx (s-1) 1/Ty (s-1) 1/Tz (s-1) MADX (B-M) 20 37 59 SIRE (compressed) 15. 6 24. 5 47. 2 SIRE (not compressed) 14. 4 23. 4 42. 2 A. Vivoli, F. Antoniou 25
SIRE: IBS Distribution study D: IBS Parameter c 237 Confidence Sample % P/P 38. 81 0. 39 26 X 36. 73 0. 48 25 Y 46. 83 0. 13 22 Parameter Value ap 5. 281 e+7 bp 1. 568 ax 3. 840 e+10 bx 1. 280 ay 4. 557 e+12 by 1. 196 A. Vivoli 26
Bjorken-Mtingwa 27
Piwinski 28
Bane’s high energy approximation • Bjorken-Mtingwa solution at high energies • Changing the integration variable of B-M to λ’=λσH 2/γ 2 Approximations a, b<<1 (if the beam cooler longitudinally than transversally ) The second term in the braces small compared to the first one and can be dropped Drop-off diagonal terms (let ζ=0) and then all matrices will be diagonal 29
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