In this benchmarking study, two contemporary codes, DIMAD and PLACET, are compared. We consider the 20 mrad post-collision line of the Compact Linear Collider (CLIC) and perform tracking studies of heavily disrupted post-collision electron beams. We successfully find that the two codes provide an equivalent description of the beam transport from the interaction point to the final dump

Ahmed, I

Elsener, K

Ferrari, A

Latina, A

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CERN-OPEN-2009-01324/02/2009CERN – EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHC L I C  I CLIC-Note-770BENCHMARKING OF THE PLACET AND DIMAD TRACKING CODES USING THE CLIC POST-COLLISION LINEIjaz AhmedNational Centre for Physics, Islamabad PakistanKonrad ElsenerCERN, Geneva, SwitzerlandArnaud FerrariUppsala University, SwedenAndrea LatinaFermilab, USAAbstractIn this benchmarking study, two contemporary codes, DIMAD and PLACET, are compared. We consider the 20 mrad post-collision line of the Compact Linear Collider (CLIC) and perform tracking studies of heavily disrupted post-collision electron beams. We successfully find that the two codes provide an equivalent description of the beam transport from the interaction point to the final dump.Geneva, Switzerland(24 February 2009)IntroductionAt the Compact Linear Collider CLIC [1], the beams must be focused to extremely small spot sizes in order to achieve high charge densities and, in turn, to reach the desired luminosity. This leads  to  a  large  angular  divergence  and an  energy spread  that  almost  reaches 100% for  the disrupted beam, as well as to the emission of beamstrahlung photons and coherently produced electron-positron pairs. A careful design of the post-collision extraction line was performed in [2] to transport these outgoing beams from the interaction point to their dumps with small, controlled losses, in order to avoid irradiation of the detector by back-scattered secondary particles. For design purposes, it is essential to have a reliable simulation program for particle tracking. In this study, we present a comparison between two codes, DIMAD [3] and PLACET [4], using the present version of the CLIC post-collision line for benchmarking purposes.  DIMAD is a charged particle optics code used for the design of particle beam lines, circular accelerators and storage  rings.  It  uses  the  second order  matrix  formalism  of  TRANSPORT [5].  The  present version of the code ensures that the matrix treatment is correct to all orders for energy deviations. This is important, as the CLIC disrupted beams downstream of the interaction point can have a very  large  energy  spread.  PLACET  is  a  program  used  to  simulate  the  dynamics,  including wakefields, of a beam in the main accelerating or decelerating part of a linac. It allows for the investigation  of  single-  and  multi-bunch  effects,  the  simulation  of  normal  RF  cavities  with relatively  low  group  velocities,  as  well  as  transfer  structures  specific  to  CLIC.  Recent improvements include the possibility to simulate bunch compressors, ground motion, and the use of  parallel  computer  systems.  It  also  simulates  beam transport  and  orbit  correction in  linear colliders, from the damping ring to the interaction point and beyond. It is a fully programmable and  modular  software,  thanks  to  a  Tcl/Tk  interface  and  external  modulars  based  on  shared libraries.Tracking study along the CLIC post-collision line, with a comparison between DIMAD and PLACETFor this benchmarking study, we use the nominal beam parameters for CLIC at 1.5 TeV. The particle distributions for the disrupted beam at the interaction point were obtained with GUINEA-PIG [6] and then transported, with DIMAD or PLACET, along the CLIC 20 mrad extraction line. The beam line used for the code comparison is shown in Figure 1. It consists of eight vertical bending dipole magnets,  which aim at separating the charged beams from the beamstrahlung photons. The disrupted beam and the particles of the coherent pairs with the same charge receive a downward bend, while the particles of the coherent pairs with the opposite charge receive an upward bend. Three collimators are sandwiched between the first four bending magnets, in order to reduce the losses in the magnets as well as the maximum beam size near the intermediate dump, which is located 50 m from the interaction point and absorbs the particles of the coherent pairs with the wrong charge while letting other beams (including the beamstrahlung photons) pass through. The vertical magnetic chicane starts 20 m after the interaction point and the total length of the post-collision beam line is about 150 m. - 2 -Figure 1: Schematic layout of the CLIC post­collision line, where each bend is provided by four dipole magnets.The first section of the CLIC post-collision line consists of four sector bend magnets spaced by 1.5 m, with a length of 4 m and a field of 1 T each. A vertical bending angle of 0.8 mrad by magnet allows the separation of the main disrupted beam from the beamstrahlung photons and the wrong-sign charged particles of the coherent pairs, which are stopped in the intermediate dump. The disrupted beam and the beamstrahlung photons then pass through the second section of the post-collision line, which consists of four bending magnets, again with a length of 4 m and a field of (about) 1 T each. Downstream, there is a long field free region of 75 m from the end of the second set of magnets to the final dump. There, the disrupted beam and the beamstrahlung photons travel parallel  towards the final dump. In addition, this  long drift space allows non-colliding  beams  to  grow  naturally  before  reaching  the  dump.  Some  of  the  most  relevant geometrical characteristics of the eight bending magnets are shown in Table 1 and Table 2.Magnet 1 Magnet 2 Magnet 3 Magnet 4Length (m) 4 4 4 4Width (m) 0.414 0.682 0.946 1.208Height (m) 0.833 1.451 2.065 2.677Gap width (m) 0.167 0.230 0.288 0.344Gap height (m) 0.26 0.61 0.96 1.31Table 1: First set of four magnets, starting 20 m from the interaction point.Table 2: Second set of four magnets, just after the intermediate dump.- 3 -Magnet 5 Magnet 6 Magnet 7 Magnet 8Length (m) 4 4 4 4Width (m) 1.87 1.87 1.87 1.87Height (m) 1.51 1.51 1.51 1.51Gap width (m) 0.45 0.45 0.45 0.45Gap height (m) 1.0 1.0 1.0 1.0Tracking off-momentum particlesWe  first  compare  the  trajectories  of  four  particles  through  the  extraction  line  lattice.  The synchrotron  radiation  is  switched-off  and  the  particle-matter  interactions  are  not  taken  into account,  because  our  aim  is  only  to  compare  the  tracking  procedures  of  both  codes.  The transverse  coordinates  of  the  four  particles  are  assumed  to  be  (x=0,  x'=0,  y=0,  y'=0)  at  the collision point of  two electron beams and four  different  values  of the  energy deviation   is assigned to the tracked particles: =0, =-0.333, =-0.800, =-0.933. The first one is a reference particle with the nominal energy and follows a (centered) reference path while going through the beam-line elements. The other three particles with lower energies follow different trajectories as they pass through the magnetic chicane. The vertical position of the four particles is shown in Figure 3 for both codes, as a function of the longitudinal position. For all energies, there is a perfect agreement between DIMAD and PLACET, except for a few points. In each sector bend, DIMAD  provides  three  identical  values  of  a  particular  variable  at  a  given  position,  while PLACET returns two different distributions of the vertical offset at the same position. Note that the paths are slightly different when synchrotron radiation is considered in the simulations, which is however beyond the scope of this note.Figure 3: Trajectories of four particles with different energies along the CLIC 20 mrad extraction line, as computed by DIMAD and PLACET.Another way of comparing DIMAD and PLACET is to consider 1000 particles with the same « ideal »  transverse  coordinates,  but  with  a  wider  range  of  energies.  In  that  case,  a  good agreement is obtained between the two codes for the vertical position of all particles after the first and second magnets, as shown in Figure 4 and Figure 5.- 4 -Figure 4: Vertical offset of the ideal beam just after passing through the first magnet of the extraction line.Figure 5: Vertical offset of the ideal beam just after passing through the second magnet of the extraction line.Disrupted beam tracking in the 20 mrad CLIC extraction lineA disrupted beam with 200,000 electrons, generated using GUINEA-PIG, was then transported through the CLIC post-collision extraction line. Note that the beam losses occuring during the transport of the disrupted beams from the interaction point to the final dump concerns almost exclusively particles with a  large  energy deviation.  The transverse distributions of the  CLIC disrupted beam at  the  final  dump are  shown in  Figure  6,  as  taken  from both  tracking code outputs. Again, a good agreement is obtained. The double peak shape of the x’ distribution is characteristic for collision with flat beams. - 5 -Figure 6: Transverse distributions of the disrupted beam at the final dump of the CLIC post-collision line.As for  the  energy spectrum of the  disrupted beam, as  obtained from DIMAD and PLACET outputs, it is shown in Figure 7. The low energy tails result from the emission of beamstrahlung photons during the bunch crossing, which can further convert into e+e- coherent pairs. Additional scatter plots are also included in Figure 8, showing the transverse coordinates at the dump as a function of the energy, for all particles tracked with DIMAD and PLACET. Again, a very good agreement is obtained between the codes.ConclusionWe have performed a detailed benchmarking study of two particle tracking codes, DIMAD and PLACET. For this purpose, we have considered the CLIC post-collision extraction line with a crossing  angle  of  20  mrad.  We  have  performed  tracking  studies  of  disrupted  post-collision electron beams and found that both programs give an equivalent description of the beam transport in all parts of the post-collision lines. - 6 -Figure 7: Energy spectrum of the disrupted beam at the final dump. Figure 8: Scatter plots of the transverse distributions (position and angle) of the heavily disrupted beam at the end of the CLIC extraction line as a function of the energy of the tracked particle.- 7 -AcknowledgementsThis  work  was  financially  supported  by  the  National  Centre  for  Physics  (NCP)  and  the Commission of the European Communities under the 6th Framework Programme "Structuring the European Research Area", contract number RIDS011899. We would like to thank Erik Adli, Daniel Schulte, Frank Stulle, Javier Resta Lopez and Mike Salt for the useful discussions and assistance regarding this study. I. Ahmed is grateful to Prof. Hafeez R. Hoorani and Hans Braun for  facilitating  financial  matters  and  providing  several  opportunities  in  attending  the  CLIC relevant workshops and the CERN Accelerator School (CAS). References[1] http://clicstudy.web.cern.ch/CLICStudy/[2] A. Ferrari, CERN-OPEN-2008-018; CLIC-Note-739.[3] R. Servranckx, K. Brown, L. Schachinger, D. Douglas, Users Guide to the Program DIMAD, SLAC-0285 (1990)[4] D. Schulte, et al., Simulation Package based on PLACET, PAC2001, Chicago (2001).[5] K. L. Brown, D.C. Carey, Ch. Iselin and F. Rothacker, “TRANSPORT”, a computer program for  designing charged particle  beam transport  systems,  SLAC 91 (1973 Rev.),  NAL 91 and CERN 8004.[6] D. Schulte. TESLA-97-08 (1996)- 8 -

Benchmarking of the Placet and Dimad tracking codes using the CLIC Post-Collision line

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