For the REX-ISOLDE upgrade a superconducting linac
based on 101.28MHz Quarter Wave Resonators (QWRs) is
foreseen downstream of the normal conducting (NC) linac.
Currently the REX-ISOLDE linac can accelerate ions with
a mass to charge ratio in the range of 3 < A/q < 4.5 up to
an energy of 2.8 MeV/u. The upgrade aims to reach a minimum
final beam energy of 10 MeV/u for A/q=4.5 in two main stages. The first stage consists of installing two  cryomodules loaded with 10 cavities able to reach 5.5 MeV/u
at the end of the present linac and the second consists of
replacing part of the existing NC linac and adding further
cryomodules. We report here on a beam dynamics study of
the accelerator for the two installation stages.status: publishe

Fraser Matthew A

Jones Roger M

Pasini M

Voulot D

English

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BEAM DYNAMICS STUDIES FOR THE SCREX-ISOLDE LINAC AT CERNM. Pasini∗, D. Voulot, CERN, Geneva, SwitzerlandM. A. Fraser, R. M. Jones, Cockcroft Institute, UK and University of Manchester, Manchester, UKAbstractFor the REX-ISOLDE upgrade a superconducting linacbased on 101.28 MHz Quarter Wave Resonators (QWRs) isforeseen downstream of the normal conducting (NC) linac.Currently the REX-ISOLDE linac can accelerate ions witha mass to charge ratio in the range of 3 < A/q < 4.5 up toan energy of 2.8 MeV/u. The upgrade aims to reach a finalbeam minimum energy of 10 MeV/u for A/q=4.5 in twomain stages. The first stage consists of installing two cry-omodules loaded with 10 cavities able to reach 5.5 MeV/uat the end of the present linac and the second consists ofreplacing part of the existing NC linac and adding furthercryomodules. We report here on a beam dynamics study ofthe accelerator for the two installation stages.INTRODUCTIONThe REX-ISOLDE linac for the ISOLDE RadioactiveIon Beam facility at CERN [1] consists of a normal con-ducting linac where the RIB gets accelerated in differentstages: a 101.28 MHz 4-rod Radio Frequency Quadrupole(RFQ) takes the beam from 5 to 300 keV/u, a 101.28 MHzinterdigital drift tube (IH) structure boosts the beam en-ergy up to 1.2 MeV/u, three 101.28 MHz split ring cavi-ties accelerate to reach 2.2 MeV/u and a final 202.28 MHzIH structure is used to vary the energy between 2.2 and 3MeV/u. The HIE-ISOLDE project [2] looks at the overallupgrade of the facility, i.e. an increase of the final energyof the radioactive ion beam, an improvement of the beamquality and flexibility and an increase of the beam inten-sity. The linac upgrade will consist of a superconductingmachine [3] providing 39.6 MV of effective acceleratingvoltage with an average synchronous phase φs of -20 deg.utilising 32 101.28 MHz QWRs split into two families: lowand high β cavities. The first stage of the upgrade plan con-sists of installing 10 high β cavities grouped in two cry-omodules downstream of the present NC linac (stage 1).The second stage will be installed in two parts. Firstly, twomore high β cryomodules will be added (stage 2a) down-stream from those in stage 1 and secondly the split ring cav-ities and the 202.56 MHz IH cavity will be replaced with 12low β cavities grouped in 2 cryomodules (stage 2b). Fig-ure 1 shows a schematic of the different installation stages.The final energy for stage 1 and stage 2 is respectively 5.5MeV/u and 10 MeV/u for A/q=4.5.The focusing scheme foresees the employment of 200mm long SC solenoids, which allow a high mismatch fac-tor tolerance with respect to a standard triplet or doublet∗matteo.pasini@cern.chFigure 1: A Schematic of the HIE-ISOLDE linac stages.Stage 1 is shown at the top, while stage 2 can be split intotwo sub-stages depending on the physics priorities: the lowenergy cryomodules will allow the delivery of a beam withbetter emittance; the high energy cryomodule will enablethe maximum energy to be reachedfocusing scheme [4]. This brings a significant advantagefor the tuning and operation of the machine. In fact, RIBsaccelerators in general make use of a high intensity stablebeam as a pilot beam with an A/q ratio that is as close aspossible to the A/q of the wanted RIB. This is in fact neces-sary, since the very low RIB’s intensity is practically invis-ible to conventional beam instrumentation. Once the pilotbeam is established, a scaling action is performed and a fo-cusing lattice with high mismatch tolerance guarantees bet-ter beam transport in the machine after scaling, where pos-sible beam mismatch can occur. In addition, because SCsolenoids allow the intermodule distance to be minimized,the longitudinal acceptance of the linac is not reduced andmulti-charge state acceleration can be performed [5]. Aschematic of the two cryomodules is shown in Figure 2.With this configuration the beam diagnostics instrumentsare ideally positioned at the beam waist location in theinter-cryomodule region where a pair of steering magnetswill also be installed.BEAM DYNAMICS SIMULATIONSFor the simulations of the complete HIE-LINAC (stage2b) a 1 m long matching section with 4 quadrupoles be-tween the first IH-structure and the first cryomodule istaken into account. It is important to keep this sectionas short as possible in order to minimize the longitudinalbeam debunching. The input beam parameters for the sim-ulations are constrained by the IH-cavity output beam andwere calculated using TRACE3D [6]. The resonators wereset to operate at a synchronous phase of -20 deg., and to in-crease the longitudinal phase spread capture at injection,the first resonator was phased at -40 deg. The last res-onator in the first cryomodule was also re-phased, at -30Figure 2: Schematic of the cryomodules design. On thetop the low β cryomodule and on the bottom the high βcryomoduledeg., in order to further decrease the longitudinal phasespread of the beam after the first cryomodule. The simu-lations were implemented to first-order in LANA [7] usinga “square field’ distribution for the cavities and solenoidsand the results confirmed with Path Manager [8], whichuses a thin-lens approximation for lattice elements. Twothousand particles were simulated and space-charge forcesneglected because of the low beam intensity.The solenoidal magnetic fields were adjusted to achievematched beams along the HIE-LINAC. The three solenoidsin the second and third cryomodules were used to matchthe beam across the transition region between the low andhigh-energy sections. Matched solutions were found fordifferent values of the phase advance per cryomodule µ inthe low-energy section and the resulting transverse emit-tance growth along the HIE-LINAC investigated. Thesource of transverse emittance growth comes essentiallyfrom the beam phase spread inside the RF gap, as can beseen from the expression for the RF defocusing impulse,∆p, acting on a single particle, and the growth can be con-trolled by choosing an appropriate phase advance:∆p ∝sin(φ)βγr (1)where r is the particles radial displacement, φ is its aver-age longitudinal phase and βγ are the relativistic factorsassociated with its motion. From (1), a monotonic de-crease in transverse emittance growth would be expectedas the phase advance increases and the extent of the beamin the transverse plane shrinks, provided the spread in anyof the other variables does not dominate. The results of thispreliminary survey are shown in Figure 3, which shows adecrease of emittance growth with phase advance per cry-omodule above 80 deg, as expected, but anomalous be-haviour below 80 deg.40 60 80 100 120 140 160Phase Advance per Cryomodule in Low-Energy Section (deg.)01020304050RMS Emittance Growth (%)0100200300400500100% Emittance Growth (%)RMS100%Figure 3: Final emittance growths in the HIE-LINAC withphase advance per cryomodule in the low-energy section.The variables in Equation 1 are well controlled in thesimulations and, in particular, the spread of the longitu-dinal phase of the beam does not vary enough to accountfor this anomalous behaviour at low phase advance. Thisanomalous behaviour was investigated by isolating the lowand high-energy sections of the HIE-LINAC and simulat-ing the behaviour of the transverse emittance growth, withphase advance, separately. The input beam parameters forthe low-energy section were identical to the previous sim-ulations but the input parameters for the high-energy sec-tion were calculated at point B in Figure 1, (i.e. 1664 mmdownstream from the 9-gap). The RMS emittance behavesas expected, as shown in Figures 4 and 5, and the trans-verse emittance growth reduces as the transverse beam sizeshrinks.40 60 80 100 120 140 160Phase Advance per Cryomodule in Low-Energy Section (deg.)05101520RMS Emittance Growth (%)050100150200100% Emittance Growth (%)RMS100%Figure 4: Emittance growth with phase advance in low-energy section.We conclude that the anomalous behaviour in Figure 3results from the matching region between the two sections40 60 80 100 120Phase Advance per Cryomodule in High-Energy Section(deg.)051015202530RMS Emittance Growth (%)050100150200250300100% Emittance Growth (%)RMS100%Figure 5: Emittance growth with phase advance in high-energy section.of the HIE-LINAC. In order to confine the beam at higherphase advance, larger magnetic fields must be used in thefocusing elements. We proceed with the beam dynamicsstudy by selecting the matched solution which providesminimal emittance growth without demanding excessivelyhigh solenoidal magnetic fields.CONCLUSIONDue to the development of the cryomodule design, theinter-cryomodule distance, i.e. the distance from the lastcavity in one cryomodule to the first cavity in the followingone, was increased to 800 mm; a modification which wouldhave little impact on the findings of our preliminary survey.Both stage 1 and stage 2 scenarios were simulated and theresults of the full linac installation are shown in Fig. 6. Thechosen matched solution requires 130 deg. phase advancein the first section, and 90 deg. in the second. Both theRMS transverse and longitudinal emittance grow no morethan 4% throughout the HIE-LINAC, and, even with the re-phasing of the first and sixth resonators, the target energyof 10 MeV/u is reached, with A/q = 4.5.The input and output beam parameters are listed in Ta-ble 1 for the two installation stages. The average solenoidalmagnetic field in the low-energy section is 5.1 T and 7.4 Tin the high-energy section.Future study will aim to better understand the anomalousbehaviour observed above. Additional simulations study-ing the effect of the intrinsic dipole component [9] of theQWRs and higher order effects of the focussing lattice areanticipated. These simulations will focus on field mappingsfor both the cavity and the solenoids.REFERENCES[1] http://isolde.web.cern.ch/ISOLDE/[2] M. Lindroos, et al., HIE-ISOLDE : the technical options,CERN-2007-008∈T,RMS G’th (%)012345∈T,100% G’th (%)01020304050∈L,RMS G’th (%)02468∈L,100% G’th (%)020406080E (MeV/u)0 2 4 6 8 10 12 14 16 18Distance (m)0246810Envelope RMSRMSRMS100%100%Beam Env. (mm)012345Figure 6: Beam dynamic for a simulation with phase ad-vance of 130 and 90 deg. in the low and high-energy sec-tions, respectively. From top to bottom: max and rms en-velope, 100% and rms transverse emittance growth, 100%and rms longitudinal emittance growth, beam energy as afunction of the linac lengthTable 1: Beam ParametersParameter Input OutputStage 1αT -0.150 -0.165βT (cm/mrad) 0.100 0.132ǫT,100%,norm (π cm mrad) 0.030 0.037αL 1.425 -0.355βL (deg/keV) 0.027 0.038ǫL,100%,norm (π ns keV/u) 2.000 2.517Stage 2αT -0.200 -0.209βT (cm/mrad) 0.100 0.138ǫT,100%,norm (π cm mrad) 0.030 0.036αL 1.281 1.013βL (deg/keV) 0.035 0.044ǫL,100%,norm (π ns keV/u) 2.000 2.746[3] M. Pasini, et al., A SC upgrade for the REX-ISOLDE accel-erator at CERN, these proc.[4] R. Laxdal, et al., Progress in the Conceptual Design of theISAC-II Linac at TRIUMF, PAC2001, Chicago, US[5] M. Pasini, et al., Beam Dynamics Studies on the ISAC-IIPost-Accelerator at TRIUMF, EPAC2002, Paris, France[6] K.R. Crandall et al., Trace 3-D Documentation, LA-UR-97-886[7] D. V. Gorelov, P. N. Ostrumov, Application of LANA Codefor Design of Ion Linac, Proc. of Linac Conference 1996[8] A. Perrin and J.F. Amand, Travel v4.06, user manual, CERN(2003).[9] P. N. Ostroumov and K. W. Shepard, Physical Review STAB,4, 110101 (2001)

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