In order to set up a powerful proton source for a future Neutrino Factory, increasing at the same time the flux of protons available for new and existing facilities, CERN is studying a 2.2 GeV superconducting H- linac for 4 MW beam power, called SPL. The superconducting part of this linac covers the energy range from 120 MeV to 2.2 GeV. Three sections made of 352 MHz cavities with nominal ß of 0.52, 0.7 and 0.8 bring the beam energy up to 1 GeV. From this energy, superconducting cavities from LEP, or ß =0.8 cavities, can be used to reach the final energy of 2.2 GeV. This paper covers the optimisation for the superconducting part, the beam dynamics design principles, the matching between sections, and the results of multiparticle simulations with up to 50 million particles. To demonstrate the stability of the design matched and mismatched input beams are used

Gerigk, F

Ryne, M

Vretenar, R D

In order to set up a powerful proton source for a future Neutrino Factory, increasing at  the same time the flux of protons available for new and existing facilities, CERN is studying a  2.2 GeV superconducting H- linac for 4 MW beam power, called SPL. The  superconducting part of this linac covers the energy range from 120 MeV to 2.2 GeV. Three sections  made of 352 MHz cavities with nominal beta of 0.52, 0.7 and 0.8 bring the beam energy up to 1 GeV.  From this energy, superconducting cavities from LEP or beta 0.8 cavities can be used up to the  final energy of 2.2 GeV. This paper covers the optimisation for the superconducting part, the beam  dynamics design principles, the matching between sections, and the results of multiparticle  simulations with up to 50 million particles. To demonstrate the stability of the design, matched  and mismatched input beams are used

Gerigk, F.

Vretenar, M.

Ryne, Robert D.

eScholarship - University of California

Design of the superconducting section of the SPL Linac at CERN

In order to set up a powerful proton source for a future Neutrino Factory, increasing at the same time the flux of protons available for new and existing facilities, CERN is studying a 2.2 GeV superconducting H- linac for 4 MW beam power, called SPL. The superconducting part of this linac covers the energy range from 120 MeV to 2.2 GeV. Three sections made of 352 MHz cavities with nominal beta of 0.52, 0.7 and 0.8 bring the beam energy up to 1 GeV. From this energy, superconducting cavities from LEP or beta 0.8 cavities can be used up to the final energy of 2.2 GeV. This paper covers the optimization for the superconducting part, the beam dynamics design principles, the matching between sections, and the results of multiparticle simulations with up to 50 million particles. To demonstrate the stability of the design, matched and mismatched input beams are used

UNT Digital Library

DESIGN OF THE SUPERCONDUCTING SECTION OF THE SPL LINACAT CERNF. Gerigk, M. Vretenar, CERN, Geneva, SwitzerlandR.D. Ryne, LBNL, Berkeley, USAAbstractIn order to set up a powerful proton source for a futureNeutrino Factory, increasing at the same time the flux ofprotons available for new and existing facilities, CERN isstudying a 2.2 GeV superconducting H− linac for 4 MWbeam power, called SPL. The superconducting part of thislinac covers the energy range from 120 MeV to 2.2 GeV.Three sections made of 352 MHz cavities with nominal βof 0.52, 0.7 and 0.8 bring the beam energy up to 1 GeV.From this energy, superconducting cavities from LEP, orβ = 0.8 cavities, can be used to reach the final energy of2.2 GeV. This paper covers the optimisation for the super-conducting part, the beam dynamics design principles, thematching between sections, and the results of multiparticlesimulations with up to 50 million particles. To demonstratethe stability of the design, matched and mismatched inputbeams are used.1 INTRODUCTIONThe SPL is a high intensity H− linac designed for anenergy of 2.2 GeV and a beam power of 4 MW [1]. It isproposed as a new injector for the CERN proton complex,with the aim to improve the beams delivered to the CERNusers, and to be the proton driver for a future radioactivebeam facility and for a high-intensity Neutrino Factory [2].The high energy part of this linac makes use of the super-conducting cavities recuperated from the decommissionedLEP collider. The RF frequency for the linac has been fixedat 352 MHz, in order to use the LEP klystrons and other RFcomponents. Table 1 summarises the main linac design pa-rameters.Table 1: Main linac design parametersParticles H−Output energy 2.2 GeVMean current during pulse 13 mAMax. bunch current 22 mADuty cycle 14 %Mean beam power 4 MWRepetition frequency 50 HzBeam pulse duration 2.8 msNo. of particles per pulse 2.27 ×1014 H−/pulseRF frequency 352.2 MHzεtransv.,r.m.s.,norm. 0.4 π mm mradεlong.,r.m.s.,norm. 0.3 πo MeV0.755 π mm mrad2 LAYOUT OF THESUPERCONDUCTING SECTIONStarting at 120 MeV, three or four families of super-conducting cavities are foreseen. A first section of 4-cellβ = 0.52 cavities made of bulk niobium brings the beamto 236 MeV, followed by a section of 4-cell cavities with anominal β of 0.7, which is the minimum β for which thestandard CERN technique of sputtering niobium on coppercan be applied [3]. At 380 MeV a section of 5-cell β = 0.8cavities starts. Their cryostats [4] and cut-off tubes with allthe ancillary equipment (input and HOM couplers) can berecuperated from LEP. Above 1.1 GeV two options havethen been considered to reach the final energy [5], either topass to LEP cavities, or to continue with the β = 0.8 cavi-ties, more efficient in terms of gradient and transit time fac-tor but more expensive to produce. These two options areindicated as (a) and (b) in Table 2, which summarises themain design parameters for the superconducting section.Table 2: Main layout parametersβ Wout E0T No. of No. of RF length[MeV] [MV/m] cavities sources [m]0.52 236 3.5 42 42 tetrodes 1010.7 383 5 32 32 tetrodes 800.8 1111 9 52 13 klystrons 1661.0 (a) 2204 7.5 104 18 klystrons 3240.8 (b) 2235 9 76 19 klystrons 237To reduce the effect of cavity vibrations on the beam, themore sensitive low-β cavities are fed by individual tetrodeamplifiers, while in the high-energy sections four β = 0.8or six β = 1 cavities are fed by one LEP klystron.The use of modern surface processing techniques allowsa higher gradient for the β = 0.8 cavities: 9 MV/m in-stead of the 7.5 MV/m achieved in LEP operation. To-gether with the considerably higher transit time factor ofthe β = 0.8 cavities between 1.1 and 2.2 GeV, version (b)becomes 87 m shorter than version (a). Due to the higherpeak power per cavity the number of cavities per klystroncan be reduced from six in version (a) to four in version(b), simplifying the vector sum compensation of cavity er-rors. Furthermore a new cavity design permits moving themechanical resonances away from the linac repetition fre-quency. Since the estimated difference in cost between thetwo options is negligible (2% of the overall linac cost) [5],the β = 0.8 version has now been assumed as the referencelayout, and the following considerations will refer to it.3 BEAM DYNAMICSQuadrupole doublets with an aperture of 120 mm pro-vide the transverse focusing throughout the linac. The max-imum number of βλ per focusing period varies between 17in the β = 0.52 section (⇒ three 4-cell cavities) and 33in the β = 0.8 section. Due to the low longitudinal phaseadvance in the high energy part, the length of the focusingperiods was doubled from 16.5 βλ below 1.1 GeV to 33 βλabove 1.1 GeV, thus providing space for two cryostats withaltogether eight 5-cell cavities.All multiparticle simulations were carried out at 40 mA,twice the nominal current, using the parallel 3D PIC codeIMPACT [6]. For matching and designing the linac a mod-ified version of the r.m.s. envelope code FIX3D [7] wasemployed. Since IMPACT offers the capability to simulatea beam with up to 108 particles (25% of the actual numberof particles in an SPL bunch!), several runs were made todetermine the number of particles which is actually neces-sary for meaningful results. Figure 1 shows the results forruns with a mismatched input beam (30% quadrupolar mis-match. The variation in transverse emittance with respectto a run with 50 million particles is plotted. While the im-0.99811.0021.0041.0061.0081.011.0121.0141.016105 106 107 108number of particlesr.m.s.99 %99.9 %99.99 %Figure 1: Relative variation of transverse emittance as afunction of the number of particles in a compu-tation with 30% quadrupolar mismatchprovement from 105 to 106 particles is clearly visible, aneven higher number of particles does not seem to improvethe accuracy of the results. A similar study was made to de-termine the size of an appropriate space charge grid. Runswith 106 particles and grids between 323 and 2563 showedless than 0.7 % variation of the 99.99% emittance betweenthe 1283 and the 2563 grid. Finally we fixed the simulationparameters to 106 particles on a 1283 space charge grid.3.1 MATCHING AND PHASE SLIPMulti cell cavities which are built for a given particlevelocity and operated over a range of velocities, provide asingle cell “synchronous phase” for the beam that deviatesfrom the “average phase” of the cavity (Fig.2). This phaseslippage reduces the transit time factors, the longitudinalfocusing forces, and the energy acceptance of the machine.The reduction of the energy acceptance (the height of theRF bucket) is determined by the reduced transit time fac-tor times an additional “slip factor”, which accounts for thenonlinear dependence of the focusing forces on the slip an-gle [8]. When simulating multi cell structures with largeslip angles (±55o in our case), the “slip factor” is oftenignored, which yields wrong phase advance values, incor-rect magnet settings and cavity phasing, and thus increasedmismatch at every transition between sections. Therefore,special care was taken to ensure that the matching code andthe multiparticle code used the same RF gap model and thesame method of dealing with phase slippage. In our caseboth codes make use of the on-axis field maps as calculatedby SUPERFISH [9] and apply the correct single cell phasesthat are seen by the beam (see Fig. 2).-80-60-40-2002040600 100 200 300 400 500 600phase [deg]length [m]Figure 2: Mean bunch phase at cell centres along the linacThe matching between sections is achieved by varyingexisting beam line elements before and after the transition.3.2 DESIGN PRINCIPLESThe design is based on a systematic evaluation of differ-ent settings for the matched phase advance values of eachfocusing period. By testing several optics for their stabilityto a mismatched input beam, we found that the tune ratiosand their location in the “Hofmann Charts” [10] provide animportant guideline for the beam dynamics layout. In thefinal design we avoid the unstable regions of the chart byadjusting the tune ratios appropriately. The transitions be-tween sections are designed to keep the phase advance permeter as smooth as possible (Fig.3). Due to the changinglength of the focusing periods at transitions this results in0246810120 100 200 300 400 500 600[deg]transverselongitudinal20304050607080900 100 200 300 400 500 600[deg]length [m]transverselongitudinalFigure 3: Zero current phase advance per meter (upper)and per period (lower)substantial but innocuous jumps of the phase advance perperiod. Despite these jumps, the zero current phase ad-vance is always kept below 90o (Fig.3). The ratio betweenlongitudinal and transverse “beam temperature” varies be-tween 1.6 in the beginning and 0.8 towards the end of thelinac.3.3 SIMULATION RESULTSIn the matched case there is practically no emittancegrowth, even the 99.99% emittance stays fairly constant(Fig. 4). The ratio between the minimum beam pipe ra-00.511.522.533.540 100 200 300 400 500 600emittance [pi mm mrad]0123456780 100 200 300 400 500 600emittance [pi mm mrad]length [m]Figure 4: Transverse (upper) and longitudinal (lower) emit-tances for the matched case in ascending order:r.m.s., 99%, 99.9%, and 99.99%dius and the r.m.s. beam size varies between 16 and 24,providing enough safety margin against machine activationby lost particles.The stability of the design was tested with mismatchedinput beams, following the approach given in [11]. Forbunched beams, every mismatch can be decomposed intothree eigenmodes: the Quadrupolar mode, the High-frequency, and the Low-frequency mode. By changing theinput Twiss parameters α and β by the same amount onecan excite the three modes separately with a maximum am-plitude at the beginning of the linac. This excitation is inde-pendent of the position where the mismatch is induced andprovides a reasonable criterion for comparing mismatchedbeams in different designs. The three eigenmodes are ex-cited with the largest oscillation showing a 30% mismatch.In case of the Quadrupolar and the High-frequency modethe dominant mismatch amplitudes are found in the trans-verse planes, the planes where the highest emittance growthrates are observed (Table 3). In spite of the strong mis-match, the transverse r.m.s. emittance growth never ex-ceeds 20%. The highest longitudinal emittance growth (7%r.m.s.) is found for Low-frequency mode excitation, wherethe dominant mismatch oscillation occurs in the longitu-dinal plane. The 99.99% emittances in Table 3 indicatethe formation of beam halo for strong mismatch. However,even in the worst case (High-frequency mode excitation)the 100% transverse beam radius remains below 16 mm,providing sufficient safety margin with respect to the mini-mum beam pipe radius at the quadrupoles of 60 mm.Table 3: Maximum emittance growth rates for matchedand mismatched input beamsmatched Quad. High Lowεr.m.s.,x/y 1.03/1.01 1.18/1.19 1.08/1.04 1.04/1.02εr.m.s.,z 1.00 1.00 1.01 1.07ε99%,x/y 1.06/1.07 2.19/2.48 1.23/1.14 1.06/1.05ε99%,z 1.04 1.04 1.13 1.75ε99.99%,x/y 1.21/1.20 4.68/5.20 9.90/2.15 1.21/1.23ε99.99%,z 1.24 1.21 1.41 5.144 CONCLUSIONSThe code IMPACT with 1 million particles and an ap-propriate space charge grid of 1283 provides a powerfultool for studying the stability of the beam dynamics designand the possible halo formation due to mismatched inputbeams. In the case of the SPL superconducting section, acareful design that follows some basic rules and that avoidsspace charge resonances by a proper selection of the work-ing point in the “Stability Charts” developed by Hofmann[10], shows minimum emittance growth in the presence ofmismatch. The energy spread in the presence of mismatchis appropriate for loss free ring injection.5 ACKNOWLEDGEMENTSThis research used resources of the National Energy Re-search Scientific Computing Center.6 REFERENCES[1] Ed. M. Vretenar. Conceptual Design of the SPL, a High-Power Superconducting H− Linac at CERN,CERN 2000-012.[2] R. Garoby. Current Activities for a Neutrino Factory atCERN, CERN/PS-RF 2001-007. In Proc. HEACC, 2001.[3] R. Losito. CERN SL-Note-2000-047-CT. Geneva.[4] C. Benvenuti et al. Production and Test of 352 MHzNiobium-Sputtered Reduced-β Cavities. In Proc. 8’thWorksh. on RF Superconductivity, Abano Terme, Italy, page1038, 1997.[5] F. Gerigk. CERN-OPEN-2001-024. Geneva.[6] J. Qiang; R.D. Ryne; S. Habib; V. Decyk. An Object-Oriented Parallel Particle-In-Cell Code for Beam Dynam-ics Simulation in Linear Accelerators. Journal of Computa-tional Physics, 163(2):434–451, 9/2000.[7] R.D. Ryne. LA-UR-95-391. LANL, Los Alamos, 1995.[8] F. Gerigk. CERN-NUFACT-NOTE 2001-072. Geneva.[9] J.H. Billen; L.M. Young. LA-UR-96-1834. LANL.[10] F. Gerigk; I. Hofmann. this conference.[11] A. Letchford; K. Bongardt; M. Pabst. Halo Formation ofBunched Beams in Periodic Focusing Systems. In Proc. ofPAC 1999, page 1767. PAC, 1999.

Ryne, RD

Vretenar, M

CERN Document Server

Design of the superconducting section of the SPL LINAC at CERN

DESIGN OF THE SUPERCONDUCTING SECTION OF THE SPL LINACAT CERNF. Gerigk, M. Vretenar, CERN, Geneva, SwitzerlandR.D. Ryne, LBNL, Berkeley, USAAbstractIn order to set up a powerful proton source for a futureNeutrino Factory, increasing at the same time the flux ofprotons available for new and existing facilities, CERN isstudying a 2.2 GeV superconducting H− linac for 4 MWbeam power, called SPL. The superconducting part of thislinac covers the energy range from 120 MeV to 2.2 GeV.Three sections made of 352 MHz cavities with nominal βof 0.52, 0.7 and 0.8 bring the beam energy up to 1 GeV.From this energy, superconducting cavities from LEP, orβ = 0.8 cavities, can be used to reach the final energy of2.2 GeV. This paper covers the optimisation for the super-conducting part, the beam dynamics design principles, thematching between sections, and the results of multiparticlesimulations with up to 50 million particles. To demonstratethe stability of the design, matched and mismatched inputbeams are used.1 INTRODUCTIONThe SPL is a high intensity H− linac designed for anenergy of 2.2 GeV and a beam power of 4 MW [1]. It isproposed as a new injector for the CERN proton complex,with the aim to improve the beams delivered to the CERNusers, and to be the proton driver for a future radioactivebeam facility and for a high-intensity Neutrino Factory [2].The high energy part of this linac makes use of the super-conducting cavities recuperated from the decommissionedLEP collider. The RF frequency for the linac has been fixedat 352 MHz, in order to use the LEP klystrons and other RFcomponents. Table 1 summarises the main linac design pa-rameters.Table 1: Main linac design parametersParticles H−Output energy 2.2 GeVMean current during pulse 13 mAMax. bunch current 22 mADuty cycle 14 %Mean beam power 4 MWRepetition frequency 50 HzBeam pulse duration 2.8 msNo. of particles per pulse 2.27 ×1014 H−/pulseRF frequency 352.2 MHzεtransv.,r.m.s.,norm. 0.4 π mm mradεlong.,r.m.s.,norm. 0.3 πo MeV0.755 π mm mrad2 LAYOUT OF THESUPERCONDUCTING SECTIONStarting at 120 MeV, three or four families of super-conducting cavities are foreseen. A first section of 4-cellβ = 0.52 cavities made of bulk niobium brings the beamto 236 MeV, followed by a section of 4-cell cavities with anominal β of 0.7, which is the minimum β for which thestandard CERN technique of sputtering niobium on coppercan be applied [3]. At 380 MeV a section of 5-cell β = 0.8cavities starts. Their cryostats [4] and cut-off tubes with allthe ancillary equipment (input and HOM couplers) can berecuperated from LEP. Above 1.1 GeV two options havethen been considered to reach the final energy [5], either topass to LEP cavities, or to continue with the β = 0.8 cavi-ties, more efficient in terms of gradient and transit time fac-tor but more expensive to produce. These two options areindicated as (a) and (b) in Table 2, which summarises themain design parameters for the superconducting section.Table 2: Main layout parametersβ Wout E0T No. of No. of RF length[MeV] [MV/m] cavities sources [m]0.52 236 3.5 42 42 tetrodes 1010.7 383 5 32 32 tetrodes 800.8 1111 9 52 13 klystrons 1661.0 (a) 2204 7.5 104 18 klystrons 3240.8 (b) 2235 9 76 19 klystrons 237To reduce the effect of cavity vibrations on the beam, themore sensitive low-β cavities are fed by individual tetrodeamplifiers, while in the high-energy sections four β = 0.8or six β = 1 cavities are fed by one LEP klystron.The use of modern surface processing techniques allowsa higher gradient for the β = 0.8 cavities: 9 MV/m in-stead of the 7.5 MV/m achieved in LEP operation. To-gether with the considerably higher transit time factor ofthe β = 0.8 cavities between 1.1 and 2.2 GeV, version (b)becomes 87 m shorter than version (a). Due to the higherpeak power per cavity the number of cavities per klystroncan be reduced from six in version (a) to four in version(b), simplifying the vector sum compensation of cavity er-rors. Furthermore a new cavity design permits moving themechanical resonances away from the linac repetition fre-quency. Since the estimated difference in cost between thetwo options is negligible (2% of the overall linac cost) [5],the β = 0.8 version has now been assumed as the referencelayout, and the following considerations will refer to it.0-7803-7191-7/01/$10.00 ©2001 IEEE. 3909Proceedings of the 2001 Particle Accelerator Conference, Chicago3 BEAM DYNAMICSQuadrupole doublets with an aperture of 120 mm pro-vide the transverse focusing throughout the linac. The max-imum number of βλ per focusing period varies between 17in the β = 0.52 section (⇒ three 4-cell cavities) and 33in the β = 0.8 section. Due to the low longitudinal phaseadvance in the high energy part, the length of the focusingperiods was doubled from 16.5 βλ below 1.1 GeV to 33 βλabove 1.1 GeV, thus providing space for two cryostats withaltogether eight 5-cell cavities.All multiparticle simulations were carried out at 40 mA,twice the nominal current, using the parallel 3D PIC codeIMPACT [6]. For matching and designing the linac a mod-ified version of the r.m.s. envelope code FIX3D [7] wasemployed. Since IMPACT offers the capability to simulatea beam with up to 108 particles (25% of the actual numberof particles in an SPL bunch!), several runs were made todetermine the number of particles which is actually neces-sary for meaningful results. Figure 1 shows the results forruns with a mismatched input beam (30% quadrupolar mis-match. The variation in transverse emittance with respectto a run with 50 million particles is plotted. While the im-0.99811.0021.0041.0061.0081.011.0121.0141.016105 106 107 108number of particlesr.m.s.99 %99.9 %99.99 %Figure 1: Relative variation of transverse emittance as afunction of the number of particles in a compu-tation with 30% quadrupolar mismatchprovement from 105 to 106 particles is clearly visible, aneven higher number of particles does not seem to improvethe accuracy of the results. A similar study was made to de-termine the size of an appropriate space charge grid. Runswith 106 particles and grids between 323 and 2563 showedless than 0.7 % variation of the 99.99% emittance betweenthe 1283 and the 2563 grid. Finally we fixed the simulationparameters to 106 particles on a 1283 space charge grid.3.1 MATCHING AND PHASE SLIPMulti cell cavities which are built for a given particlevelocity and operated over a range of velocities, provide asingle cell “synchronous phase” for the beam that deviatesfrom the “average phase” of the cavity (Fig.2). This phaseslippage reduces the transit time factors, the longitudinalfocusing forces, and the energy acceptance of the machine.The reduction of the energy acceptance (the height of theRF bucket) is determined by the reduced transit time fac-tor times an additional “slip factor”, which accounts for thenonlinear dependence of the focusing forces on the slip an-gle [8]. When simulating multi cell structures with largeslip angles (±55o in our case), the “slip factor” is oftenignored, which yields wrong phase advance values, incor-rect magnet settings and cavity phasing, and thus increasedmismatch at every transition between sections. Therefore,special care was taken to ensure that the matching code andthe multiparticle code used the same RF gap model and thesame method of dealing with phase slippage. In our caseboth codes make use of the on-axis field maps as calculatedby SUPERFISH [9] and apply the correct single cell phasesthat are seen by the beam (see Fig. 2).-80-60-40-2002040600 100 200 300 400 500 600phase [deg]length [m]Figure 2: Mean bunch phase at cell centres along the linacThe matching between sections is achieved by varyingexisting beam line elements before and after the transition.3.2 DESIGN PRINCIPLESThe design is based on a systematic evaluation of differ-ent settings for the matched phase advance values of eachfocusing period. By testing several optics for their stabilityto a mismatched input beam, we found that the tune ratiosand their location in the “Hofmann Charts” [10] provide animportant guideline for the beam dynamics layout. In thefinal design we avoid the unstable regions of the chart byadjusting the tune ratios appropriately. The transitions be-tween sections are designed to keep the phase advance permeter as smooth as possible (Fig.3). Due to the changinglength of the focusing periods at transitions this results in0246810120 100 200 300 400 500 600[deg]transverselongitudinal20304050607080900 100 200 300 400 500 600[deg]length [m]transverselongitudinalFigure 3: Zero current phase advance per meter (upper)and per period (lower)3910Proceedings of the 2001 Particle Accelerator Conference, Chicagosubstantial but innocuous jumps of the phase advance perperiod. Despite these jumps, the zero current phase ad-vance is always kept below 90o (Fig.3). The ratio betweenlongitudinal and transverse “beam temperature” varies be-tween 1.6 in the beginning and 0.8 towards the end of thelinac.3.3 SIMULATION RESULTSIn the matched case there is practically no emittancegrowth, even the 99.99% emittance stays fairly constant(Fig. 4). The ratio between the minimum beam pipe ra-00.511.522.533.540 100 200 300 400 500 600emittance [pi mm mrad]0123456780 100 200 300 400 500 600emittance [pi mm mrad]length [m]Figure 4: Transverse (upper) and longitudinal (lower) emit-tances for the matched case in ascending order:r.m.s., 99%, 99.9%, and 99.99%dius and the r.m.s. beam size varies between 16 and 24,providing enough safety margin against machine activationby lost particles.The stability of the design was tested with mismatchedinput beams, following the approach given in [11]. Forbunched beams, every mismatch can be decomposed intothree eigenmodes: the Quadrupolar mode, the High-frequency, and the Low-frequency mode. By changing theinput Twiss parameters α and β by the same amount onecan excite the three modes separately with a maximum am-plitude at the beginning of the linac. This excitation is inde-pendent of the position where the mismatch is induced andprovides a reasonable criterion for comparing mismatchedbeams in different designs. The three eigenmodes are ex-cited with the largest oscillation showing a 30% mismatch.In case of the Quadrupolar and the High-frequency modethe dominant mismatch amplitudes are found in the trans-verse planes, the planes where the highest emittance growthrates are observed (Table 3). In spite of the strong mis-match, the transverse r.m.s. emittance growth never ex-ceeds 20%. The highest longitudinal emittance growth (7%r.m.s.) is found for Low-frequency mode excitation, wherethe dominant mismatch oscillation occurs in the longitu-dinal plane. The 99.99% emittances in Table 3 indicatethe formation of beam halo for strong mismatch. However,even in the worst case (High-frequency mode excitation)the 100% transverse beam radius remains below 16 mm,providing sufficient safety margin with respect to the mini-mum beam pipe radius at the quadrupoles of 60 mm.Table 3: Maximum emittance growth rates for matchedand mismatched input beamsmatched Quad. High Lowεr.m.s.,x/y 1.03/1.01 1.18/1.19 1.08/1.04 1.04/1.02εr.m.s.,z 1.00 1.00 1.01 1.07ε99%,x/y 1.06/1.07 2.19/2.48 1.23/1.14 1.06/1.05ε99%,z 1.04 1.04 1.13 1.75ε99.99%,x/y 1.21/1.20 4.68/5.20 9.90/2.15 1.21/1.23ε99.99%,z 1.24 1.21 1.41 5.144 CONCLUSIONSThe code IMPACT with 1 million particles and an ap-propriate space charge grid of 1283 provides a powerfultool for studying the stability of the beam dynamics designand the possible halo formation due to mismatched inputbeams. In the case of the SPL superconducting section, acareful design that follows some basic rules and that avoidsspace charge resonances by a proper selection of the work-ing point in the “Stability Charts” developed by Hofmann[10], shows minimum emittance growth in the presence ofmismatch. The energy spread in the presence of mismatchis appropriate for loss free ring injection.5 ACKNOWLEDGEMENTSThis research used resources of the National Energy Re-search Scientific Computing Center.6 REFERENCES[1] Ed. M. Vretenar. Conceptual Design of the SPL, a High-Power Superconducting H− Linac at CERN,CERN 2000-012.[2] R. Garoby. Current Activities for a Neutrino Factory atCERN, CERN/PS-RF 2001-007. In Proc. HEACC, 2001.[3] R. Losito. CERN SL-Note-2000-047-CT. Geneva.[4] C. Benvenuti et al. Production and Test of 352 MHzNiobium-Sputtered Reduced-β Cavities. In Proc. 8’thWorksh. on RF Superconductivity, Abano Terme, Italy, page1038, 1997.[5] F. Gerigk. CERN-OPEN-2001-024. Geneva.[6] J. Qiang; R.D. Ryne; S. Habib; V. Decyk. An Object-Oriented Parallel Particle-In-Cell Code for Beam Dynam-ics Simulation in Linear Accelerators. Journal of Computa-tional Physics, 163(2):434–451, 9/2000.[7] R.D. Ryne. LA-UR-95-391. LANL, Los Alamos, 1995.[8] F. Gerigk. CERN-NUFACT-NOTE 2001-072. Geneva.[9] J.H. Billen; L.M. Young. LA-UR-96-1834. LANL.[10] F. Gerigk; I. Hofmann. this conference.[11] A. Letchford; K. Bongardt; M. Pabst. Halo Formation ofBunched Beams in Periodic Focusing Systems. In Proc. ofPAC 1999, page 1767. PAC, 1999.3911Proceedings of the 2001 Particle Accelerator Conference, Chicago

Design of the Superconducting Section of the SPL LINAC at CERN

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Design of the Superconducting Section of the SPL LINAC at CERN

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