1 / 36

Recent developments of the HEADTAIL code

Recent developments of the HEADTAIL code. G. Rumolo , G. Arduini , E. Benedetto , E. Métral , D. Quatraro , B. Salvant , D. Schulte, R. Tomás, F. Zimmermann CERN/GSI Meeting, GSI, Darmstadt, 18-19/02.2009. Overview. Description of the HEADTAIL code

novia
Download Presentation

Recent developments of the HEADTAIL code

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Recentdevelopments of the HEADTAIL code G. Rumolo, G. Arduini, E. Benedetto, E. Métral, D. Quatraro, B. Salvant, D. Schulte, R. Tomás, F. Zimmermann CERN/GSI Meeting, GSI, Darmstadt, 18-19/02.2009 Giovanni Rumolo

  2. Overview • Description of the HEADTAIL code • history and model • features and motivationsforupgrades • Upgrades and applications • Transverseplane • Transport based on maps • Selection of interaction/observationpoints • Application • Longitudinal plane: • Bunchflatteningwithdouble rfsystemorrfdipolekick • Bunchlengtheningandmicrowaveinstability • Acceleratingbucket and transitioncrossing • Outlook Giovanni Rumolo

  3. Localized impedance source "Electroncloudsimulations: beaminstabilities and wakefields" G. Rumolo and F. Zimmermann, PRST-AB 5, 121002 (2002) Thecollectiveinteractionislumped in oneormorepointsalongthe ring (kick points), wherethesubsequentslices of a bunch (macroparticles) interactwith an electroncloud (macroelectrons) or an impedance (wake) Giovanni Rumolo

  4. Bunch macroparticles are transported across different interaction points through the sector matrices At each interaction point macroparticles in each slice receive the kick from the wakes of the preceding slices Slicing is refreshed at each turn taking into account the longitudinal motion i 1 2 Ns Slice i Slice Ns Slice 2 Longitudinal Wi = WL(iDz) Slice 1 i-1 Ns-1 ΣWkNi-k ΣWkNi-k W0N1 W1N1+W0N2 K=0 K=1 Energy loss Giovanni Rumolo

  5. Bunch macroparticles are transported across different interaction points through the sector matrices At each interaction point macroparticles in each slice receive the kick from the wakes of the preceding slices Slicing is refreshed at each turn taking into account the longitudinal motion i 1 2 Ns Slice i Transverse (x) dipolar: Wid = Wdx(iDz) quadrupolar: Wiq = Wqx(iDz) xicentroid of slice i x position of particle Slice Ns Slice 2 Slice 1 i-1 Ns-1 ΣNk(Wkdxk+Wkqx) ΣNk(Wkdxk+Wkqx) N1(W1dx1+W1qx) K=1 K=1 Giovanni Rumolo

  6. Bunch macroparticles are transported across different interaction points through the sector matrices At each interaction point macroparticles in each slice interact with the electron cloud, as it was modified by the interaction with the preceding slices Slicing is updated i 1 2 Ns Slice i Slice Ns Slice 2 Slice 1 Electrons step 0 Electrons step 1 Electrons step i-1 Electrons step Ns-1 … … Giovanni Rumolo

  7. What the HEADTAIL model includes (I) • Synchrotron motionincluded • Single bunchwithlongitdinaldistributionthatcanbeGaussianor uniform (barrierbucket, 2002). Longitudinal dynamicsissolved in a linear, sinusoidal (2004) voltageor no bucket ( debunching). • Chromaticity and detuningwithamplitude • Dispersion at the kick section(s). • Electroncloudkick(s): • Soft Gaussianapproachwith finite sizeelectrons (usedtill 2001, obsolete) • PIC module on a gridinsidethebeampipe (2001) • PIC solverwith optional conductingboundaryconditions(GR, D. Schulte, E. Benedetto, 2003) • Uniform or 1-2 stripesinitiale-distributions (GR, E. Benedetto, 2005) • Kicks canbegiven at locationswithdifferent betafunctions(2004) • Electronscanmove in fieldfreespaceor in certainmagneticfieldconfigurations, likedipole, solenoid, combinedfunctionmagnet (2002) Giovanni Rumolo

  8. What the HEADTAIL model includes (II) • Short range wake field due to a broad band impedance • or to classicalthickresistive wall. • x,ycomponents (driving and detuning) of thewakescanbeweightedbytheYokoyacoefficientsto includetheeffect offlatchamber. • Spacecharge: eachbunchparticlecanreceive a transverse kick proportional to thelocalbunchdensityaroundthelocalcentroid. • Linear couplingbetweentransverse planes Giovanni Rumolo

  9. Outputs of HEADTAIL (I) • The main direct output files of HEADTAIL give: • Bunch centroid positions, rms-sizes and emittances (horizontal, vertical and longitudinal) as a function of time • Slice by slice centroid positions and rms-sizes. Coherent intra-bunch patterns can be resolved using this information. • Transverse and longitudinal phase space of the bunch with a sub-sample of macroparticles and bunch longitudinal distributions • Off line analysis of the HEADTAIL output allows evaluating tune shifts, growth rates, mode spectra (B. Salvant) • Instability thresholds can be determined through massive simulation campaigns with different bunch intensities Giovanni Rumolo

  10. Outputs of HEADTAIL (II)  Instabilitythresholdsare inferred by HEADTAIL tracking when unstable coherent motion of the bunch centroid with exponential growth suddenly appears for a tiny change of bunch current. • Advantages of HEADTAIL wrt analytical formulae that can be used to determine the instability thresholds: • It allows for simulations with several types of impedance and with dipole and quadrupole components of the wake • It allows for simulations in non-ideal conditions (correct longitudinal motion, chromaticity, amplitude detuning, linear coupling, space charge) • It gives as an output the full bunch dynamics in the unstable regime. Giovanni Rumolo

  11. Predictions of tune shifts and instability thresholds (design of new machines) Lattice MAD-X HEADTAIL Comparison with beam-based measurements of collective effects (PSB, PS, SPS, LHC) Bench measurements Z-Base RESWALL Gdfidl Particle Studio Other EM codes… HFSS Giovanni Rumolo

  12. Recent upgrades of HEADTAIL (I) • Since 2006 a number of modifications have been introduced into the HEADTAIL code, mainly in order to: • Broaden the range of problems that can be studied and understood using the code (see following slides) • Improve computation speed and accuracy of the results • Revisit some parts of the code to optimize calculations over some loops or minimize conditional statements • Introduce frozen models for electron cloud and wake fields (only applicable in some specific cases) • Make it more user-friendly and thus increase the number of potential users of the code inside and outside of CERN. “HEADTAIL upgrade“ D. Quatraro, G. Rumolo and B. Salvant(work in progress) “Practical User Guide for HEADTAIL“ G. Rumolo and F. Zimmermann, CERN-SL-Note-2002-036-AP Giovanni Rumolo

  13. Recent upgrades of HEADTAIL (II) • Features whichhavebeenadded to theHEADTAILcode Transverse plane: . • Theinitialdistribution of electronscanbeself-consistentlyloadedfrom a build-upcode (ECLOUD) run • Morewakefieldoptionshavebeenincluded: • Theinteractionwiththeresistive wall impedance has beenextended to includetheinductiveby-passeffect and near-walleffects • Thewakefieldcanbeloadedfrom an externaltable, calculated as Fouriertransform of a knownimpedance (e.g. kickerorresistive wall in lowenergy). Itaccepts an inputhavingtheZ-BASE outputformat. • Interaction of thebunchwithseveral different resonatorsplaced at locationswith different betafunctions (the list needs to beinput on a separatedfile) Giovanni Rumolo

  14. Recent upgrades of HEADTAIL (III) • Features whichhavebeenadded to theHEADTAILcode Transverse plane (cont‘d): • Thebeamtransportwith a simple rotation one-turnmatrixcanbeoptionallyreplacedbytransportusingthecorrectlattice of themachine • Sectormapsgeneratedby MAD-X betweenselectedpoints of the ring areloaded and usedforthetransportbetweenthesepoints (R. Tomás 2006) • Thebetafunctions, as readfrom a MAD-X Twissfile, areusedforbuildingthelinear transportmatricesbetween kick points (D. Quatraro2007, seenextslides) This has theadvantage of easierimplementation of chromaticitythroughadjustment of thephaseadvancebetween kick pointsbythefractionalpart of thechromaticshift • ThesignalfromseveralBPMscanbesaved and usedforfurtheranalysis Giovanni Rumolo

  15. Recent upgrades of HEADTAIL (IV) • Features which have been added to the HEADTAIL code Longitudinal plane: • A higher harmonic rf system has been introduced with adjustable relative phase to the main rf system (e.g., Bunch Shortening and Bunch Lengthening modes) and a voltage ramp. • Full motion inside an accelerating bucket has been implemented (GR & B. Salvant 2008) • Phenomena on the energy ramp can be simulated without approximations • Transition crossing can be modeled in detail • So far without gtr-jump scheme • With and without higher order terms of h Giovanni Rumolo

  16. Transverseplane (I) Transport matricesbuiltfrom a MAD-X Twissfile Giovanni Rumolo

  17. Transverseplane (II) Transport matricesbuiltfrom a MAD-X Twissfile • HEADTAILreadstune andchromaticityvaluesfromthestandardinputfile .cfg • MAD-Xisruninternally and thelatticeismatchedto thegiven tune and chromaticityvalues • Transport matricesarethenbuiltfromtheTwissfileoutputby MAD-X • Thelocalchromaticitiesxj+1,jare also contained in theTwissfile, and theyareused to giveparticlestheircorrectphaseadvances at each turn according to theirmomenta (evolvingaccordingthesynchrotronmotion) Giovanni Rumolo

  18. Transverseplane (III) Interaction/observationpoints Giovanni Rumolo

  19. Transverseplane (IV) Spacechargekicks Giovanni Rumolo

  20. Transverseplane (V) E-cloud/wakefield/observationpoints 200 interaction points with space charge randomly chosen Interaction with electron cloud in all the MBB dipoles MBB Observation points at all the BPMs Interaction with wake fields at all the kickers Giovanni Rumolo

  21. Transverseplane (VI) TMCI in the SPS fromthekickerimpedance (mode shifts) Mode shifting and coupling has been studied for an SPS bunch under the action of the wake fields from all the kickers. Kicks (20 per turn) were applied to the bunch particles exactly at the kickers’ locations. Giovanni Rumolo

  22. Transverseplane (VII) TMCI in the SPS fromthekickerimpedance (mode shifts) The red lines correspond to the one-kick approximation. The wake fields from the different kickers have been weighted by the beta’s in the kicker locations, added up and applied to the bunch once per turn. Giovanni Rumolo

  23. Transverseplane (VIII) TMCI in the SPS fromthekickerimpedance (growth rates) Giovanni Rumolo

  24. Longitudinal plane (I) Production of flatbunches: double rf-system in the SPS 0.7 MV 0 Idea from “Studies of beam behavior in a double RF system“, E. Shaposhnikova in APC Meeting 06.07.2007 Giovanni Rumolo

  25. Longitudinal plane (II) Production of flat bunches: double rf-system in the SPS • Importance of this option: • SPS: The 800 MHz cavity is used in BS mode in normal operation to keep the beam stable • LHC upgrade: Stability studies for a beam in a double rf-system in BL mode (flat bunch) Giovanni Rumolo

  26. Longitudinal plane (III) Production of flat bunches: longitudinal dipole kick • Importance of this option: • LHC upgrade: Simulation studies of stability of flat hollow bunches Giovanni Rumolo

  27. Longitudinal plane (IV) Bunch lengthening and microwave instability in the SPS Potential Well Bunch Lengthening regime Microwave Instability regime Broad-band, Z/n=10 W, fr=700 MHz Giovanni Rumolo

  28. Longitudinal plane (V) Bunch lengthening and microwave instability in the SPS Bunch shape evolution in the regime of bunch lengthening (1011 ppb, left movie) and just above the threshold for microwave instability (1.5 x 1011 ppb, right movie) Giovanni Rumolo

  29. Longitudinal plane (VI) Accelerating bucket and transition crossing • Phenomena on the energy ramp can be simulated without approximations • Transition crossing can be modeled in detail • So far without gtr-jump scheme • With and without higher order terms of h Giovanni Rumolo

  30. Longitudinal plane (VII) Transition crossing in the PS Giovanni Rumolo

  31. Longitudinal plane (VII) Transition crossing in the PS To have a better picture of the longitudinal phase space, only few particles at defined synchrotron amplitudes are plotted (10 subsequent turns for each particle) Giovanni Rumolo

  32. Longitudinal plane (VIII) Transition crossing in the PS Analytical solution by Elias anticipated exactly the same type of evolution of the phase space ellipse when crossing transition Giovanni Rumolo

  33. Longitudinal plane (IX) Transition crossing in the PS The agreement between the analytically calculated evolution and the one simulated with HEADTAIL is very good. Giovanni Rumolo

  34. Longitudinal + Transverse.... Transition crossing in the PS with a BB impedance  Relativistic gamma Unstable at  = 5.25 Linear scale <y> Vertical position of centroid [m] Log scale <y> Growth rate ~ 60 µs Giovanni Rumolo

  35. Conclusions & outlook • HEADTAIL is amulti-purposetoolthatcanbeused to do particletrackingwith a variety of collectiveinteractions (electroncloud, resonatorimpedances, resistive wall, spacecharge) • HEADTAIL has beenimproved • isinterfacedwith MAD-X and Z-BASE to track a singlebunch in a real latticewithlocalizedimpedancesources • cantrack a singlebunch in a double harmonicrfsystem and in an acceleratingbucket (also acrosstransition) • HEADTAILisconstantlyunderdevelopment • To makeitmoreperformant and user-friendly • To addfeaturesthatcanenlargeitsrange of applicability • Nearfutureupgradeplans: • A robust modelfor longitudinal spacecharge • Correctlyincludewakefields in thelowenergyrange • Extension to multi-bunchsimulations Giovanni Rumolo

  36. Transverseplane (VI) E-cloud/wakefield/observationpoints Giovanni Rumolo

More Related