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Multi-particle simulation code for IBS

This article presents a multi-particle simulation code for investigating Intra-Beam Scattering (IBS) effects in the CLIC damping rings. It compares the results of the simulations with conventional IBS theories and discusses the growth of emittance with and without IBS.

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Multi-particle simulation code for IBS

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  1. Multi-particle simulation code for IBS A. Vivoli*, M. Martini Thanks to : Y. Papaphilippou * E-mail : Alessandro.Vivoli@cern.ch

  2. CONTENTS • Introduction • Conventional Calculation of IBS • SIRE structure • Comparison with conventional theories • Results of simulations • Conclusions A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  3. Introduction: Motion in the DR The motion of the particles in the CLIC damping rings can be expressed through 3 invariants (and 3 phases). Transversal invariants: Longitudinal invariant: Emittance: A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  4. Introduction: Intra-Beam Scattering in DR IBS is the effect due to multiple Coulomb scattering between charged particles in the beam: P1’ P1 P2’ P2 Evolution of the emittance: WITH IBS IBS Growth Times IBS Radiation Damping Quantum Excitation NO IBS Tk contain the effect of all the scattering processes in the beam at a certain time. Energy [GeV] A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  5. Introduction: Conventionaltheories of IBS Conventional IBS theories in Accelerator Physics (Bjorken-Mtingwa, Piwinski) derive Tk by the formula: The particle distribution is inserted from outside the theory. The integral is too complicate. In practise, the integral has been solved only for Gaussian particles distribution. In this case the formulas for the growth times reduce to: Growth rates are calculated at different points of the lattice and then averaged over the ring: s1 s6 s2 s5 s4 s3 A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  6. IBS studies for the CLIC Damping Rings Goals: Follow the evolution of the particle distribution in the DR (we are not sure itremainsGaussian). Calculate IBS effect for anyparticle distribution (in case itdoesn’tremainGaussian). Development development of a tracking code computing the combined effect of radiation damping, quantum excitation and IBS during the cooling time in the CLIC DR. (Software for IBS and Radiation Effects) A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  7. Software for IBS and Radiation Effects s1 s6 • The lattice is read from a MADX file containing the Twiss functions. • Particles are tracked from point to point in the lattice by their invariats (no phase tracking up to now). • At each point of the lattice the scattering routine is called. s2 s5 s4 s3 • 6-dim Coordinates of particles are calculated. • Particles of the beam are grouped in cells. • 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. • A routine has also been implemented in order to speed up the calculation of IBS effect. A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  8. Zenkevich-Bolshakov algorithm (from MOCAC) Relativistic Center of Mass Frame: Laboratory Frame: (P.R. Zenkevich, O. Boine-Frenkenheim, A. E. Bolshakov, A new algorithm for the kinetic analysis of inta-beam scattering in storage rings, NIM A, 2005) Radiation damping and quantum excitation are calculated with the formula: A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  9. Lattice Recurrences Elements of the lattice with twiss functions differing of less than 10% are considered equal. Lattice: First reduction: + 3 X + + 3 X + ( ) Second reduction: + 2 X + 3 X + + CLIC DR LATTICE: 14400 elements 420 elements A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  10. SIRE: Benchmarking (Gaussian Distribution) Arc cell of the CLIC DR (old parameters) A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  11. SIRE: Benchmarking (Gaussian Distribution) on LHC A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  12. SIRE: Benchmarking (Gaussian Distribution) on CLIC DRs Intrinsic random oscillations in SIRE A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  13. SIRE: CLIC Damping Rings Simulation Simulation of the CLIC Damping Rings: IBS ON IBS ON IBS OFF IBS OFF Beam parameters A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  14. Conclusions • A new code to investigate IBS effect in the CLIC damping rings is being developed: • Benchmarking with conventional IBS theories gave good results after some parameters training. • Calculation of the evolution of emittances gives reliable results. • Refinement of quantum excitation routine will be implemented in order to give reliable particle distribution evolution. • Vertical dispersion will be added soon. Simulations of the CLIC DR damping will continue. A. Vivoli, M. Martini, Multi-particle simulation code for IBS

  15. THANKS. The End A. Vivoli, M. Martini, Multi-particle simulation code for IBS

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