de Prisco, Renato

Edgar, Sargsyan

Eshraqi, Mohammad

Heine Dølrath, Thomsen

Miyamoto, Ryoichi

Lund University Publications

LUND UNIVERSITYPO Box 117221 00 Lund+46 46-222 00 00Statistical error studies in the ESS linacEshraqi, Mohammad; de Prisco, Renato; Miyamoto, Ryoichi; Edgar, Sargsyan; Heine Dølrath,Thomsen2014Link to publicationCitation for published version (APA):Eshraqi, M., de Prisco, R., Miyamoto, R., Edgar, S., & Heine Dølrath, T. (2014). Statistical error studies in theESS linac. 3323-3325. Paper presented at 5th International Particle Accelerator Conference, IPAC 2014,Dresden, Germany.Total number of authors:5General rightsUnless other specific re-use rights are stated the following general rights apply:Copyright and moral rights for the publications made accessible in the public portal are retained by the authorsand/or other copyright owners and it is a condition of accessing publications that users recognise and abide by thelegal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private studyor research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portalRead more about Creative commons licenses: https://creativecommons.org/licenses/Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will removeaccess to the work immediately and investigate your claim.STATISTICAL ERROR STUDIES IN THE ESS LINACM. Eshraqi∗, R. Miyamoto, E. Sargsyan, ESS, Lund, SwedenR. De Prisco, ESS, Lund, Sweden and LNL-INFN, Legnaro, ItalyH. D. Thomsen, ISA, Aarhus, DenmarkAbstractFollowing the completion of the latest layout of the ESSlinac statistical error studies have been performed to definethe field vector quality and alignment tolerances. Based onthese tolerances and error study results a scheme for thecorrection system is proposed that assures low losses andpermits hands-on maintenance. This paper reports on thestrategy of simulating and performing the error studies aswell as setting the tolerances.INTRODUCTIONThe high power linac of the European Spallation Source,ESS, accelerates 62.5 mA of protons up to 2 GeV in a se-quence of normal conducting and superconducting accelerat-ing structures. These protons are to be used for the spallationprocess in which a high flux of pulsed neutrons will be gen-erated in a neutron rich target material.The high reliability and availability of the accelerator re-quires short repair times which sets a loss limit for hands-onmaintenance of the machine. Hands-on maintenance andmachine protection set limits of 1 W/m and 0.1 W/dm re-spectively, on beam losses. On top of being demandingon the nominal design, the tolerances have to be studied aswell to make sure that the accelerator, with realistic toler-ances is capable of delivering 5 MW of power with powerlosses in the order of 10−7. The 2013 baseline, code namedOptimusPlus is presented in [1].STRATEGY AND LIMITSAs the first step for starting the statistical error studies itis needed to define a strategy on how to proceed and whereto set the limits or how large errors to accept. This processcould be re-iterated as some of the resulted tolerances whichare not very demanding could be tightened in favor of thosewhich are more costly to achieve or maintain. For this firststep, we have set the limits on losses at 99% confidencelevel to be within the 1 W/m limit. There is a limit on theemittance growth due to errors too. On the one hand notinjecting into a ring ESS linac is not so restricted on theemittance of the final beam it delivers. On the other handa significantly higher emittance could lead to major losses.Considering both arguments, an emtitance twice that of thenominal case without errors was set as the limit for the finalemittance in the presence of errors.ESS linac consists of 5 accelerating structures, RFQ, DTL,Spoke, medium-β, and high-β, plus two transport lines,MEBT, and HEBT. These sections have different lengths,but it takes almost the same time for the beam to travel∗ mamad.eshraqi@esss.sethrough each section. Therefore, the additional emittancegrowth per section due to errors was decided to be limitedto 7√2 − 1, or 10% per section in each plane (for 99% of thecases), setting a second limit for defining tolerances.Having set a strategy in place to define the static tolerances,it is also important to set the limit on dynamic errors andjitters. While the former is static and could be corrected oraccounted for in the downstream structures or devices, thelatter would be left uncorrected. To make sure the dynamicerrors do not cause unwanted effects, the criteria to set themis to have an effect which is less than 1× rms spread of thebeam in the plane of study.To study the transverse errors a functional beam trajectorycorrection system should be in place. This has been done byoptimizing the positions of the steerers and their correspond-ing beam position monitors, BPMs, specially in the drifttube linac, DTL, where the number of choices is limited.The focus in the other parts of the linac has been on reducingthe number of active BPMs, without loosing the control overbeam trajectory. Enabling the correction system, with theright limit on the steerer strengths, the transverse toleranceshave been set. These processes have been performed sectionby section and the tolerances for each section are set. Tocheck the sensitivity to these errors, all the errors are appliedat 50%, 100% and 150% of the accepted value. Finally, toinvestigate where the possible hot spots are and create aloss-map, errors are applied to the linac lattice from RFQexit to the target.Another type of errors, which has not yet been fully in-vestigated is the systematic errors, such as floor settlementof the accelerator, phase reference line delays, or magneticimperfections and multipoles.ERRORS INVESTIGATEDThe errors investigated in this study, irrespective of theirtime dependency belong to one of the following types: ma-chining, welding, positioning, powering, and the input beamerrors. The errors are uniformly distributed between plusand minus of the defined tolerance. These could be differentfrom section to section.RFQThe beam is generated at the RFQ input, with a gaus-sian distribution truncated at 4 × σ with 100,000 macro-particles [2]. To set the tolerances for acceptable beams,position, angle, and Twiss parameters of the beam have beenvaried. The machining errors in the RFQ include errors inthe longitudinal and transverse profile of the vanes. Weldingerrors investigated are the vane welding errors that could beProceedings of IPAC2014, Dresden, Germany THPME04404 Hadron AcceleratorsA08 Linear AcceleratorsISBN 978-3-95450-132-83323 Copyright©2014CC-BY-3.0andbytherespectiveauthorsvertical/horizontal shift of the vertical vanes (called paral-lel/perpendicular) in this study and the corresponding errorson horizontal vanes. These errors could have a differentvalue, still within the limit, on two ends of the vane causinga tilt. The RFQ is being built in few sections, and the align-ment of these units with respect to each other (shifts and tilts)are also included. The last error that has been covered in theRFQ is the voltage jitter. Tolerances of the RFQ are listedin table 1. The parameters of the beam, their average, andextents are saved at the end of the RFQ. The result of errorson the final beam out of the RFQ is presented in table 2.Table 1: Tolerances of the ESS RFQ (Max Values)Error Value UnitInput beam alignment position 0.2 mmInput beam alignment angle 2 mradInput beam Twiss mismatch (α) 20 %Input beam Twiss mismatch (β) 10 %Longitudinal vane profile 0.02 mmTransverse vane curvature 0.02 mmParallel and perpendicular vane shift 0.03 mmParallel and perpendicular vane tilt 0.06 mradHorizontal and vertical segment shift 0.03 mmSegment tilt around X and Y axis 0.06 mradVane voltage jitter 0.5 %MEBT, SCL, and HEBTIn the medium and high energy beam transport, MEBTand HEBT, and the superconducting linac (Spoke, medium-β and high-β sections), the errors applied are the following:Quadrupoles: Alignment of the quadrupoles including theirtransverse position, rotations around the beam axis, andgradient errors. Rotation of quad perpendicular to the beamaxis was excluded from these studies since the effect, underthe same alignment condition, was negligible.Cavities: Alignment of the cavities including their transverseposition, rotations perpendicular to the beam axis, static anddynamic accelerating field amplitude and rf phase errors.Dipoles: Alignment of the dipoles including their transverseposition, rotations perpendicular to the beam axis, and fielderror.Input beam: The variations of the beam parameters at theend of the RFQ with errors are used as beam errors at theinput of the MEBT, including the position and angle errors,emittances, mismatch in Twiss parameters, energy jitter andcurrent variations. The nominal distribution out of the RFQis used as input distribution.Table 2: Beam Errors Included in the Error Studies at theMEBT Input (Max Values)dxy dφ dxy’ dE dε m dImm deg mrad keV % mABeam 0.3 0 1 36.2 5 5 0.625DTLThe DTL uses permanent magnet quadrupoles for trans-verse focusing [3]. Each tank is fed by one klystron andtherefore all the errors caused at that level are coupled. Syn-chronous phase and field amplitude errors in each cell aredetermined by the shape and position of drift tubes and areuncoupled. The applied errors here are:PMQs: The same types of errors as powered quadrupoles,with different amplitudes, are applied here.RF: Uncoupled field and phase errors are applied to rf cells.These errors are due to machining or installation errors andare static in time. Coupled field and phase errors are appliedto all cells of each tank. These errors are due to rf set pointsand are static and dynamic, with different amplitudes.Table 3: Tolerances for the ESS Linac (Max Values)∆xy φxy φz ∆G ∆φr f ∆r fmm deg deg % deg %mebtQuad 0.2 0.06 0.5Cav (S∗) 0.5 0.115 1 1Cav (D) 0.1 0.1dtlQuad 0.1 0.5 0.2 0.5Cell (S) 0.5 1Tank (S) 1 1Tank (D) 0.1 0.1sclQuad 0.2 0.06 0.5Cav (S) 1.5 0.129 1 1Cav (D) 0.1 0.1hebtQuad 0.2 0.06 0.5Dipole 0.2 0.06 0.05∗ S: Static, D: DynamicERROR STUDYThe error studies are performed using the codeTraceWin [4], using 100,000 macro particles. The 3D PIC-NIC space charge routine is used with a 10 × 10 × 10 mesh.The beam distribution at the beginning of RFQ is gaussiantruncated at 4×σ. The transported beam through the RFQ issaved and used for error studies. To define the dependencieson different parameters each parameter was studied individ-ually (excluding the symmetries, e.g. between vertical andhorizontal planes) in this stage. Each case is simulated using1000 linacs with gradually increasing errors such that theaforementioned limits are not passed. Finally all the errors(including symmetries) are applied to each section to checkif the combined effect of all errors is still within the limits.In the next stage the accelerator from RFQ exit to the targetwas used in the error studies. Tolerances of each componentin each section is listed in table 3.THPME044 Proceedings of IPAC2014, Dresden, GermanyISBN 978-3-95450-132-83324Copyright©2014CC-BY-3.0andbytherespectiveauthors04 Hadron AcceleratorsA08 Linear AcceleratorsIn the presence of these errors the beam behaves differ-ently than nominal. The positions of the tracked particlesare stored during error studies and post processing wouldshow how close the beam gets to the aperture, and howmuch beam power is confined within a certain radius in thepresence of errors. The power density levels which are indi-cators of these are shown in figure 1, and the average of thenormalized rms emittances are shown in figure 2.0 100 200 300 400 500 600−40−2002040L (m)x(mm)10−3 10−2 10−1 1 101102 103 104 105 1060 100 200 300 400 500 600−40−2002040L (m)y(mm)Figure 1: Power density levels from the RFQ exit to thetarget. The beam power outside of the outermost line is1 × 10−3 W. Red line shows the beam aperture.0 100 200 300 400 500 60000.20.40.60.81L (m)εrms(π.mm.mrad) xyzFigure 2: Average emittance evolution over 1000 linacs.The average losses, mainly due to losses in longitudinalplane, and the confidence level of these losses are shown infigures 3 and 4. The peaks observed in these figures are dueto the particles, which have not been captured inside the rfbucket after the frequency jump or have been in the tails ofthe beam out of the RFQ and are transported through thelinac. These particles that are the cause of the increased haloobserved in figure 1 are lost after the first vertical bend whereoff momentum particles are bent above the beam trajectory.SUMMARYThe end to end runs have been performed using a gaussianbeam truncated at 4 × σ, generated at the RFQ input. Thesebeam has been transported through the RFQ and the out-put beam is used as the input distribution for the following0 100 200 300 400 500 60000.1L (m)Averageloss(W)Figure 3: Average beam power loss.0 100 200 300 400 500 60004812L (m)Loss(W)99.9%99%90%Figure 4: Confidence level beam power loss.simulations and error studies. Individual error studies onstand-alone sections of the linac are performed to set thetolerances. To estimate the beam losses along the linac thesetolerances are applied to an integrated lattice which runsfrom MEBT input to the HEBT output. These end to enderror studies show that the average losses is in the order of0.1W, a number which is consistent with the losses observedat SNS with a proton beam. At 99% confidence level thebeam power loss is less than 1 W in each meter.REFERENCES[1] M. Eshraqi, et.al. "The ESS Linac", Proc. IPAC’14, Dresden,Germany, THPME043.[2] A. Ponton, "Note on the ESS RFQ Design Update", ESSTechnical Report, 2014.[3] R. D. Prisco, et.al., "ESS DTL Status: Redesign and opti-mizations", Proc IPAC’14, Dresden, Germany, THPME041.[4] R. Duperrier, N. Pichoff and D. Uriot, Proc. InternationalConf. on Computational Science, Amsterdam, The Nether-lands, 2002.Proceedings of IPAC2014, Dresden, Germany THPME04404 Hadron AcceleratorsA08 Linear AcceleratorsISBN 978-3-95450-132-83325 Copyright©2014CC-BY-3.0andbytherespectiveauthors

Statistical error studies in the ESS linac

Abstract

Similar works

Full text

Available Versions

Lund University Publications