In this note a muon front-end without cooling is presented. The muons are captured, ro-tated and accelerated to the energy needed for injection into the first muon recirculator. The cavity parameters are consistent with those used for the CERN reference scenario [1]. The number of muons obtained per year is roughly one order of magnitude less than the one obtained with the cooling channel. Therefore such a scheme could be a first step to a neutrino factory keeping the option of later upgrade

Hanke, K

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN-Nufact-Note-059Muon Front-End without CoolingK. HankeAbstractIn this note a muon front-end without cooling is presented. The muons are captured, ro-tated and accelerated to the energy needed for injection into the first muon recirculator.The cavity parameters are consistent with those used for the CERN reference scenario [1].The number of muons obtained per year is roughly one order of magnitude less than theone obtained with the cooling channel. Therefore such a scheme could be a first step to aneutrino factory keeping the option of later upgrade.Geneva, SwitzerlandDecember 21, 20001 IntroductionIn the design of a muon front-end for a future neutrino factory cooling is one of the mostchallenging issues. Theoretical and experimental studies are underway to examine the feasibilityof ionization cooling in such an application. In this note we present a muon front-end withoutcooling. It is based on the same cavity parameters as the CERN cooling channel describedelsewhere [1]. Therefore the two schemes are compatible and a scheme without cooling couldbe a first step towards a neutrino factory. The scheme proposed here is not to be confused withthe one described in [2], for which it has been shown that it does not give any reasonable muonyield.As it has been shown that cooling reduces the transverse emittance by a factor of 4 in eachplane, taking out the cooling will reduce the muon yield by approximately a factor of 16. Carefulmodeling of the longitudinal optics can partially compensate for this and in the end lead to areasonable number of muons per year.In a first section the subject of the recirculator acceptance will be addressed. Then the varioussections of the front-end will be described in detail: decay channel, capture and rotation inlongitudinal phase space and subsequent acceleration of the muons up to 2 GeV kinetic energy.The simulations presented here have been performed with the code PATH [3]. Transverse andlongitudinal constraints have been included to make the simulation as complete as possible.All simulations have been done under exactly the same conditions (target data, rf and solenoidmodeling) as those done for the CERN cooling channel.2 Recirculator AcceptanceThe figure of merit for any front-end design is the muon yield within the acceptance ofthe first muon recirculator at injection. For the CERN reference scenario the transverse phasespace acceptance is given by 1.5 π cm rad (normalized) [4].In the longitudinal plane the bunch area A in the decay ring has to be matched. As A is aninvariant upon transfer from the first muon recirculator to the second and to the decay ring(longitudinal matching during the transfer is not possible), this is hence the parameter to bematched at injection into the first recirculator. Depending on what convention is used the valueof A is given byA = πσeσzE/cwhere its value is 0.0185 eVs [5], or byA = π2σe2σzE/cin which case its value is 0.074 eVs [4, 6]. Here, σe is the relative rms energy spread and σz isthe rms bunch length. The second definition is the one which is generally used. We will howevergive the muon yield for both values.It is useful to assume a value for the recirculator acceptance in order to estimate the muon yieldper year and to optimize the front-end optics. However, the real acceptance of the muon recir-culators and hence the final muon yield can only be found by tracking the particle distributionat the exit of the front-end through these machines. This will be subject of future work.3 Target DataThe target data have been generated with FLUKA for a 2.2 GeV proton beam instan-taneously impinging on a 26 mm Hg target in a 20 T solenoid field [7]. As the real target issupposed to be 260 mm long, a linear extrapolation is done when calculating the muon yield inSection 6. It should be stressed that the target data file used for these simulations is the samethat has been used for the simulation of the cooling channel [1].14 Lay-out of the Front-EndThe muon front-end consists of five main sections: decay channel, phase rotation, ac-celeration at f=44 MHz, acceleration at f=88 MHz and acceleration at f=176 MHz. Figure 1shows schematically the lay-out of the front-end. In the following sections we summarize themain parameters of the various sections.176 MHz section88 MHz section44 MHz sectionphase rotationtarget andcapture 200 MeV200 MeV300 MeV1 GeV2 GeVpion decayFigure 1: Schematic lay-out of the muon front-end without cooling.4.1 Decay ChannelThe decay channel allows practically all pions to decay into muons. The lay-out of thedecay channel is exactly the same as for the CERN reference scenario [1]. Table 1 gives themain parameters of this section. The particle distribution in longitudinal phase space at the exitof the decay channel is shown in Fig. 2. As can be seen, the total muon distribution covers atotal length [m] 30solenoid field [kG] 18aperture [cm] 60Table 1: Lay-out of the decay channel.01002003004005006007008009001000-4 -3 -2 -1 0 1 2 3 4phase at 44 MHz [rad]kinetic energy [MeV]Figure 2: Longitudinal phase space distribution of muons at the exit of the decay channel.2large energy range and by no means one can inject the whole set of particles into any subsequentaccelerator. Therefore, a cut in kinetic energy is performed and only particles between Ekin =100 MeV and Ekin = 300 MeV are considered in the following simulations.4.2 Phase RotationThe phase rotation section reduces the energy spread of the selected subset of muons.This is performed by a series of cavities at f=44 MHz and appropriate setting of the phase. Thelay-out of this section is identical with the one used for the CERN cooling channel (see Tab. 2).The particle distribution in longitudinal phase space at the exit of the phase rotation section isshown in Fig. 3.total length [m] 38solenoid field [kG] 18aperture [cm] 60frequency [MHz] 44cavity length [m] 1.0gradient [MV/m] 2.0synchronous phase [deg] variablekinetic energy [MeV] 200Table 2: Lay-out of the phase rotation section.050100150200250300-4 -2 0 2 4 6phase at 44 MHz [rad]kinetic energy [MeV]Figure 3: Longitudinal phase space distribution of muons at the exit of the phase rotation sec-tion.34.3 Acceleration at 44 MHzIn a first acceleration section at f=44 MHz muons are accelerated on crest to about300 MeV kinetic energy. The parameters of the section are given in Tab. 3. The particle dis-total length [m] 44solenoid field [kG] 22.7aperture [cm] 60frequency [MHz] 44cavity length [m] 1.0gradient [MV/m] 2.0synchronous phase [deg] 0kinetic energy [MeV] 200 - 300Table 3: Lay-out of the 44 MHz acceleration section.tribution in longitudinal phase space at the exit of this section is shown in Fig. 4.050100150200250300350400-0.5 0 0.5 1 1.5 2 2.5phase at 44 MHz [rad]kinetic energy [MeV]Figure 4: Longitudinal phase space distribution of muons at the exit of the 44 MHz section.4.4 Acceleration at 88 MHzThe second acceleration section is at f=88 MHz and accelerates the beam to a kineticenergy of about 1 GeV.The change of frequency from 44 MHz to 88 MHz implies a change of the aperture from 60 cmdiameter to 30 cm diameter. In order to match the beam envelope to the smaller aperture, amatching section is included which consists of a 0.5 m long solenoid at 40 kG and a drift spaceof 0.22 m.The phase of the cavities in this section alternates between +45o and −45o to ensure that theparticle distribution does not rotate in the longitudinal phase space but stays flat thus avoiding anexcessive increase in energy spread. The parameters are given in Tab. 4. The particle distributionin longitudinal phase space for different steps of the acceleration is shown in Fig. 5.4total length [m] 280solenoid field [kG] 50.0aperture [cm] 30frequency [MHz] 88cavity length [m] 0.5gradient [MV/m] 4.0synchronous phase [deg] ± 45kinetic energy [MeV] 300 - 1000Table 4: Lay-out of the 88 MHz acceleration section.0200400600800100012000 1 2 3 4 5phase at 88 MHz [rad]kinetic energy [MeV]Figure 5: Longitudinal phase space distribution of muons during acceleration to 1 GeV. Notethat phase cuts are performed for the sake of setting the synchronous phase correctly in thesimulation.There is presently no dedicated matching section between the section at f=88 MHz and thefollowing one at f=176 MHz.4.5 Acceleration at 176 MHzThe final acceleration section is at f=176 MHz and brings the beam to the injectionenergy of 2 GeV. The synchronous phase in this section is set to 0o which yields optimumacceleration efficiency. The parameters of the final acceleration section are given in Tab. 5. Theparticle distribution in longitudinal phase space for different steps of the acceleration is shownin Fig. 6.5 Transverse OpticsAppropriate solenoid settings ensure maximum transmission of the muons through thechannel. The maximum achievable field is for the given geometry around 50 kG which stillleaves some safety margin [8]. There are however losses, in particular at the transitions betweensections with different apertures. The individual solenoid settings for the various sections are5total length [m] 112solenoid field [kG] 60.0aperture [cm] 20frequency [MHz] 176cavity length [m] 0.5gradient [MV/m] 10.0synchronous phase [deg] 0kinetic energy [MeV] 1000 - 2000Table 5: Lay-out of the 176 MHz acceleration section.050010001500200025000 0.5 1 1.5 2phase at 176 MHz [rad]kinetic energy [MeV]Figure 6: Longitudinal phase space distribution of muons during acceleration to 2 GeV. Again,phase cuts ensure correct setting of the synchronous phase.found in the corresponding parameter tables.At present, the PATH model uses a hard-edge approximation with fringe fields for the solenoidfields. The cavity model is a zero-length element with a field computed according to the boreradius. In order to represent better the real configuration , i. e. cavities with solenoids around thebores, at least a preliminary cavity and solenoid design is required. The field maps have then tobe computed and included in the PATH model. This will be subject of further studies.A formalism for matching in the transverse phase space between different sections of a solenoidchannel is being developed and will be integrated in PATH [9].6 Muon YieldThe muon yield within the acceptance limits given in Section 2 has been computed atthe exit of the various stages of the simulation. The muons within the acceptance limits havebeen converted into muons/year, assuming a number of 1023 protons per year on the target.The results are given in Tab. 6. These values are to be compared to the corresponding valuesobtained for the CERN reference scenario, i.e. 2× 1020 µ/year for an acceptance of 0.0185 eVsand 1.5 π cm rad and 5.5× 1020 µ/year for an acceptance of 0.074 eVs and 1.5 π cm rad.60.0185 eVs 0.074 eVs1.5 π cm rad 1.5 π cm radrotation 4.6 ×1019 1.3 ×102044 MHz 4.4 ×1019 9.1 ×101988 MHz 4.0 ×1019 8.8 ×1019176 MHz 3.8 ×1019 5.9 ×1019Table 6: Muons per year within recirculator acceptance at different stages of the front-end.7 Conclusions and Future WorkIt has been shown that an optimized muon front-end without cooling can provide roughlyone order of magnitude less muons than the CERN reference scenario with cooling.The numbers given in Section 6 represent the present status of this work. Further work willinclude different modeling of the solenoid fields as well as optimized transverse matching.Furthermore, future simulations should be run at higher statistics, since the numbers quoted inTab. 6 have been extrapolated from small numbers of muons found at the end of the channeland are hence subject to fluctuations.8 AcknowledgementsI would like to thank G. Franchetti, E. Keil, A. Lombardi and S. Russenschuck for helpfuldiscussions.References[1] A. Lombardi, A 40-80 MHz System for Phase Rotation and Cooling, CERN Neutrino Fac-tory Note 34 (2000).[2] K. Hanke, Muon Capture and Acceleration without Phase Rotation and Cooling, CERNNeutrino Factory Note 39, (2000).[3] Simulation Code PATH, CERN version.[4] E. Keil, private communication.[5] E. Keil, Muon Recirculating Linear Accelerator Design, transparencies shown in theNFWG meeting of April 19, 2000, p. 9.http://nfwg.home.cern.ch/nfwg/nufactwg/23/min19apr00.htm[6] E. Keil, A 50 GeV Muon Storage Ring Design, CERN SL-2000-013 (AP) and CERN Neu-trino Factory Note 26, p.15, (2000).[7] N. Vassilopoulos, private communication.[8] S. Russenschuck, private communication.[9] G. Franchetti, private communication.7

Muon Front-End without Cooling

Abstract

Similar works

Full text

Available Versions

CERN Document Server