Particle Beamline Simulation Code Comparison by Tracking of Single Muons

MICE, the international Muon Ionization Cooling Experiment, is a project to design, construct, operate and test a cell of a muon ionisation cooling channel that may be used for a future Muon Collider or Neutrino Factory.<br>The object of the MICE experiment is to take a beam of muons created from protons from the ISIS accelerator hitting a titanium target and to show that it is possible to create a narrow intense beam, using detector techniques from particle physics.<br>Initially the detailed design of the MICE Muon Beamline used two separate simulation codes:The established Graphic Turtle code[1] was fast - one could see the effect of changes with a turn-around time of a couple of minutes - but limited in its handling of magnet fringe-fields and of scattering processes, an issue with a beamline the majority of which had the particles travelling through air.G4beamline[2] could model an extended set of physical processes, including scattering in a range of materials and had the ability to track particles through user-supplied field maps, and the output would be passed into the nascent g4mice code for modelling the MICE Cooling Channel. However, it was hugely more resource hungry.Ideally these would have complemented each other - interactively identify a promising layout in Graphic Turtle, and then confirm it by running a set of G4beamline simulations overnight. In practice the detailed design of the beamline was hampered by discrepancies between the outputs of the simulation codes, with a mismatch of up to a factor of two between the emittances of the output beams for the same magnet settings[3, 4]. MICE therefore undertook an extensive code comparison activity, to understand the differences both between the software and between their input decks.<br>The exercise found issues with both codes: G4beamline bugs relating to fringe fields and field-map handling were fixed in G4beamline 1.14<i>pre</i> and later[5].Kevin Tilley noticed that the discrepancy was reduced when Turtle was run in 1^st rather than 3^rd order, and I therefore proposed comparing the trajectories of single particles modelled with Graphic Turtle against 1^st[5] and 3^rd order[6] simulations of a single quadrupole implemented in Microsoft Excel. Restricting the particle trajectories to a single plane, either <em>y</em>=0 or <em>x</em>=0, allowed the cross-terms to be left out. A couple of the cases, B and H, allowed further simplification and were also calculated to 3^rd order [7],[8] with pencil and four-figure tables[9], as a crude check of the Excel implementation.This initial 2-<em>d</em> simplification confirmed an issue within Graphic Turtle, and the 3^rd-order tracking in quadrupoles was fixed in the 14^th January 2008 release[10].Material<br><em>NextTTlvG4BL_4.xls</em> (15/11/2007): Comparison of beams simulated with G4beamline and Graphic Turtle for MICE Muon Beamline<br><em>SingleMuonTracking.zip</em> (10/05/2019): Tracks with Graphic Turtle (22-Mar-2005 release) to 1^st and 3^rd order (and with MAD-X)<br><em>TTLvG4BL_Single.xls</em> (13/12/2007): Single particle tracks spreadsheet, collating tracks from <em>SingleMuonTracking.zip</em>This item forms part of the MICE Miscellaneous data, DOI: 10.17633/rd.brunel.5024885 ( <em>Construction/Beamline/Other/ParticleBeamlineSimulationCodeComparisonByTrackingOfSingleMuons.zip</em> ).AcknowledgementsKevin Tilley oversaw the comparison activity and first identified Turtle's 3^rd order calculations as a possible source of the discrepancy.<br>Henry Nebrensky thought of comparing individual particle trajectories; ran the single-particle Turtle simulations, and collated the results.<br>Richard Fenning repeated some cases for us using MAD-X.Henry Nebrensky and Kevin Tilley ran the Turtle simulations for the beamline comparison (NextTTlvG4BL_4.xls), while Tom Roberts and Kenny Walaron ran the G4beamline simulations.DisclaimerThis data is provided in the form of spreadsheets and text files as saved to disk over a decade ago (datestamps listed above, or embedded in zip archive).<br>References1. PSI Graphic Turtle Framework by U. Rohrer based on a CERN-SLAC-FERMILAB version by K.L. Brown <em>et al.</em>, http://aea.web.psi.ch/Urs_Rohrer/MyWeb/turtle.htm<br>2. G4beamline: http://g4beamline.muonsinc.com/3. K. Tilley: "Status of Beamline Design" at <em><em><em>MICE Collaboration Meeting CM17<em><em>, CERN, Geneva, Switzerland, 22^nd-25^th February 2007. https://indico.cern.ch/event/7432/contributions/2086077/</em></em></em></em></em>4. H. Nebrensky and K. Tilley: "Status of Beamline Optics" at <em><em><em>18^th MICE Collaboration Meeting<em>, Rutherford-Appleton Laboratory, Chilton, UK, 13^th-16^th June 2007. http://mice.iit.edu/cm/cm18/cm18_nebrensky_beamline.ppt [ BURA ]</em></em></em></em>5. H. Nebrensky: "Simulation comparison / tools / issues" at <em><em>MICE Beamline Design and Commissioning Review<em>, Imperial College, London, UK, 16^th November 2007. http://mice.iit.edu/tb/Reviews/Beamline/2007-11-16/br07_nebrensky_simulation.ppt [ BURA ]</em></em></em>6. H. Nebrensky: "Code Comparison – Single Particles" at <em>MICE Beamline Optics group meeting</em> 19^th December 2007. [ BURA ]7. D.L. Smith: “Focusing Properties of Electric and Magnetic Quadrupole Lenses” <em>Nuclear Instruments and Methods</em> <strong>79</strong>(1) pp.144-164 DOI: 10.1016/0029-554X(70)90020-0 (1970)8. G.E. Lee-Whiting: “Comparison of calculated third-order aberrations of a magnetic quadrupole lens” <em>Nuclear Instruments and Methods</em> <strong>99</strong>(3) pp.609-610 DOI: 10.1016/0029-554X(72)90675-1 (1972)9. C. Godfrey and A.W. Siddons: "<em>Four-Figure Tables</em>" (2^nd Ed., revised) Cambridge University Press ISBN: 0-521-05097-9 (1980)<br>10. U. Rohrer: "<em>Re: Graphic Turtle - 3rd order quadrupoles</em>", Personal Communication, 16^th January 2008<br><br>