We discuss a GEANT4 simulation of the phase rotation system for a neutrino factory. The comparison with the beam transport code PATH shows a good agreement. Preliminary results for the energy disposition in the cryostat of the superconducting 1.8 T solenoid are briefly presented

Giani, S

Gilardoni, S S

Grichine, V M

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHNuFact Note 102November 12, 2001Geant4 Simulation of Phase Rotationfor Neutrino FactoryS. Giania, S. Gilardoni a,b1,V.M. Grichineaa Cern, CH-1211 Geneve 23, Switzerlandb De´partement de Physique, Universite´ de Gene`ve, SwitzerlandAbstractWe discuss a Geant4 simulation of the phase rotation system fora neutrino factory. The comparison with the beam transport codePATH shows a good agreement. Preliminary result for the energydeposition in the cryostat of the superconducting 1.8 T solenoid isbriefly presented.1Contacting author. Supported by the CERN Doctoral Student Program.CERN-OPEN-2002-04412/11/2001timeWSlow particles arrivelate: AcceleratedFast particles arrive early: Decelarated timeWFigure 1: This sketch shows the principle of how the phase rotation works.Since muons in the energy window considered are not ultra-relativistic, anenergy spread corresponds to a velocity spread. More energetic muons arriveearly at the RF section and they are decelerated while low energetic muonsarrive late at the RF and they are accelerated.1 Brief description of simulation programThe phase rotation is the section of the neutrino factory whose aim is toreduce the muon energy spread by a factor of two. Muons coming from piondecay are spreaded in a kinetic energy interval between 1 GeV down to fewMeV, while the interesting muons are the one around 200 MeV. One desiresto capture particles in a energy acceptance of 200 ± 100 MeV and reducethe energy spread to ±50 MeV. This is possible using a set of 21 RF (RadioFrequency) cavities that slows down high energy particles and accelerate lowenergy particles. This process is shown in ﬁgure 1.1.1 Geometry and materialsA Geant4 world physical volume of cylindrical shape (G4Tube) with thelength of 29.4 m and the radius of 1.3 m consists of 21 RF. One 44 MHzRF cavity at 2 MV/m is 1.4 m long and the geometry is taken from [2](seeﬁgure 2). The ﬁeldmap of the solenoid surrounding one RF was generatedby POISSON [5]. The ﬁeld was normalised to have the same focusing poweras for an hard edge solenoid of 2 Tesla and 1 meter long (see ﬁgure 3 for theun-normalised ﬁeld distribution).The world volume was ﬁlled with air of the following contents (here andbelow we use weight concentrations) 0.7537N + 0.2315O + 0.0128Ar at apressure of 10−8 atm. The pressure roughly corresponds to technical vac-uum that can be provided for big hermetical volumes. Each sections consistsof stainless steel cover (0.73Fe + 0.16Cr + 0.09Ni) surrounding a cryostatﬁlled with liquid helium. Inside the liquid helium a superconducting niobiumsolenoid generates the ﬁeld of ﬁgure 3. For providing better program perfor-mance all section parts were described by cylinders (G4Tube). A small gapof 1 micron was provided for touching surfaces.1SC solenoid SC solenoidBeamaxis60 cm106 cm226 cm140 cm unit lengthE field lines in the44 MHz RF cavityE field lines in the44 MHz RF cavity96 cm21 cm21 cm 9 cm2 mm thick stainless steelNiobium in LHevacuum106 cm60 cmNiobium in LHeSUPERCONDUCTINGSOLENOIDASSEMBLYTWO 44 MHZ CAVITIES MODULESFigure 2: Cavity design from [2]. This geometry is described “as it is” in theGeant4 simulation.1.51.7522.252.52.7533.25-20 0 20 40 60 80 100 120 140 160z(cm)B(T)Figure 3: Un-normalised longitudinal magnetic field component for along thebeam axis of one RF cavity.21.2 Interactions of particles with materialsThe geometry was irradiated by a ﬂux of positive muons selected in a kineticenergy interval between 100 and 300 MeV. The incoming particle spectrawere calculated by a MARS [4] simulation that includes pion production,pion focusing and decay. The muons interact with matter by ionizationenergy loss, bremsstrahlung and pair creation. In addition they experiencemultiple scattering.Secondary electrons experience ionization energy loss, bremsstrahlungand multiple scattering. Secondary X-ray and gamma quanta experiencephotoabsorption, Compton scattering and conversion.100125150175200225250275300120 125 130 135 140 145 150 155 160t(nsec)Ek(MeV)140160180200220240260220 222 224 226 228 230 232 234 236 238 240Time(nsec)Ek(MeV)Figure 4: Longitudinal phase space for muons produced by pion decay chan-nel (right) at the beginning of the phase rotation. The left figure shows theGeant4 simulation (full dots, blue), and PATH (open dots, red) after thephase rotation.2 Results of simulationThe Geant4 simulation was compared to a PATH [7] simulation of thephase rotation reference scheme [6] to validate the RF implementation inGeant4 . Table 1 shows the nice agreement between the two simulations fortransmission coeﬃcients, while a small diﬀerence, discussed in the following,could be noticed in the longitudinal plane (ﬁgure 4).3Input Transmission In cutPATH 15222 100% 77%Geant4 10436 94% 79%Table 1: Particles “In cut” are calculated as the percent of the input muonsselected in a window defined by 140 MeV< Ekinetic <260 MeV and in oneRF period of 44 MHz.The two distributions of ﬁgure 4 diﬀer for the tail due to the following reasons:• in the Geant4 simulation the phase of the reference particle is chosenby injecting a 200 MeV muon in the center of the beam line. The arrivaltime of this particle at the diﬀerent RF ﬁxes the synchronous phase.This procedure is good enough only in ﬁrst approximation, while codeslike PATH calculate the average particle before each RF. The averageparticle takes into account the evolution of the whole bunch in thechannel, which is ignored by a single particle approach. To improve theGeant4 RF implementation, one could imagine to use the Geant4stack facility. All the muons could be tracked just before one RF wherethe particles are stored into the stack. Once all the particles reach theRF, the average muon is evaluated and then the tracking restarts untilthe next RF, where this process is repeated2.• the particles used for the two simulation are not the same, but theaverage quantities like spot size, time and energy distribution are thesame.• the RF length was 1 m for the PATH simulation (as in the CERNreference scenario), while in the Geant4 simulation the cavity is 1.4m long, according to the very last design from [2]. The average gradientper meter was kept constant.3 Energy deposition in the superconductingsolenoidsThe energy deposition in the cryostat was calculated by the Geant4 simula-tion using the full geometry shown in ﬁgure 2. All positive muons producedby pion decay (see ﬁgure 5) and accepted by the previous channel are trackedin the phase rotation, where part of them are lost due to mismatch. The phaserotation channel was optimise to transport with the higher possible eﬃciencythe muons described in table 1. Only 6% of them are lost in the channel formismatch or decay, while if one considers the whole muon distribution, thenthe transmission decreases from 94% to 69%. The energy deposited in the2The implementation of this procedure is under development4020040060080010001200100 150 200 250 300 350 400 450 500 550t(nsec)Ek(MeV)-200020040060080010001200200 250 300 350 400 450 500 550t(nsec)Ek(MeV)Figure 5: All muon spectra at the beginning of the phase rotation(left) andat the end of the channel(right)1031041050 50 100 150 200 250 300 350R(mm)Ed(MeV)-5000500100015002000250030003500-5000 0 5000 10000 15000 20000 25000 30000z(mm)Ed(MeV)Figure 6: Integrated energy deposited versus radius (left) and versus positionin the channel(right)cryostat+solenoid is calculated by Geant4 . In ﬁgure 6 on left one couldsee the energy deposited versus the radius and integrated versus the z co-ordinate. The spikes correspond to the energy deposited in the 2 mm thicksteel surfaces of the cryostat, which are visible also in right histogram wherethe energy deposited is integrated versus the radius and plotted versus theposition along the beam axis. From this ﬁgure one could see that most ofthe power losses are due to the mismatch of the beam in the ﬁrst four cells,5after which it decreases and stays constant along the channel.The energy deposition integrated versus the radius and z, normalised to onecell, gives 30.8 W/m, which is twice the recommended limit for a traditionalcryogenic system. As solution, the beam losses could be diluted in the decaychannel, of which a careful redesign could be envisaged.4 Discussion and conclusionsA simulation of the CERN reference scheme for the phase rotation usingGeant4 was presented in this note. The RF implementation in Geant4is validated by the nice agreement with the simulation of the same channelusing the PATH code. The energy deposition in the cryostat+solenoid ofthe RF system calculated by Geant4 is 30.8 W/m.5 AcknowledgementsThe authors are thankful to Alessandra Lombardi for useful discussions, andfor reading the manuscript and giving many constructive comments. Thiswork was supported by the IT, EP and PS Divisions of CERN and in theframework of the HARP–Geant4 collaboration project.A Introduction to Geant4Geant4 is an object-oriented toolkit for simulation in High Energy Physics,Space, and Medical applications [1].The Geant4 software has been developed by a world-wide collaborationof about 100 scientists from over 40 institutions and laboratories participat-ing in more than 10 experiments in Europe, Russia, Japan, Canada and theUnited States. Geant4 has exploited advanced software engineering tech-niques and Object Oriented technology to improve the validation of physicsresults and in the same time to make possible the distributed software designand development in the world-wide collaboration. The ﬁrst Geant4 pro-duction version was released by the end of 1998, as it was scheduled in theDRDC P58 project proposal at the end of 1994. Since then, regular bian-nual releases have been performed, maintained and supported for the users.Geant4 has a multi-disciplinary nature, providing functionality in a set ofdiﬀerent scientiﬁc ﬁelds. The Geant4 Object-Oriented design allows theuser to understand, extend, or customise the toolkit in all the domains. Atthe same time, the modularity of the Geant4 software allows the user toload and use only the components he needs. The main functionality of thediﬀerent domains is outlined here.The Geant4 physics processes exploit Object-Oriented Technology tomake transparent how physics results are produced. The way cross sections6are calculated (via formulas, data ﬁles, etc. and eventually using diﬀerentdata-sets with restricted applicability by particle, energy, material) is clearlyexposed via Object-Oriented design and it is separated from the way theyare accessed and used in the algorithms. The user can overload both thesefeatures. The way the ﬁnal state is computed is again separated from thetracking and is split into alternative or complementary models, accordingto, for example, the energy range, the particle type, the material. Multipleimplementations of physics processes and models are possible and have beenmade available. No numbers should be hard-coded in formulas and algo-rithms, but only variables and constants should be used. An extensive setof units is deﬁned in Geant4 and all the numerical quantities are expressedthrough units explicitly, thus making the Geant4 physics independent fromthe units chosen by the user.The Electromagnetic physics manages lepton physics, gamma, x-ray andoptical photon physics, and muon physics. It includes various implementationof ionization and Bremsstrahlung (both with diﬀerential treatment for energyloss and with integration of cross-sections in function of energy), the latterwith LPM eﬀect, as well as multiple scattering (with lateral displacementand without any path length restriction), and annihilation. It includes aswell multiple implementations of the photoelectric (also with ﬂuorescence)and Compton (also with polarisation) eﬀects, pair conversion, synchrotronand transition radiation, scintillation, refraction, reﬂection, absorption andRayleigh eﬀect. Low energy extensions, down to 1 KeV and below, areimplemented and will continue to be produced in the framework of a jointproject with the European Space Agency. The validity range of all the muonprocesses (based on theoretical models) scales up to the PeV region, allowingthe simulation of ultra-high energy and cosmic physics.The Hadronic physics oﬀers both a data parameterisation-driven set ofmodels, and a variety of theory- driven models for physics beyond test-beamsenergies, as well as treatment of low energy neutron transport. Parameterisation-driven models include high energy inelastic scattering, as well as low energyinelastic and elastic scattering, ﬁssion, capture and dedicated processes forstopping kaons and pions physics. The theory-driven models provide twostring parton models in the high energy regime (with the possibility to in-terface to Pythia7 for the hard-scattering), as well as intra-nuclear trans-port models and pre-equilibrium, and a variety of de-excitation models, in-cluding evaporation, photo-evaporation, ﬁssion, Fermi break-up and multi-fragmentation. The low energy neutron transport is based on best selectionsof evaluated data (such as ENDF-B VI, JENDL, CENDL, ENSDF, JEF,BROND, IRDF, exploiting the ﬁle system to maximise a granular and trans-parent access to the data sets for the user) and it oﬀers event biasing options,allowing radiation background studies. Lepton-hadron interactions, such asmuon-nuclear interactions, photo-ﬁssion and general gamma-meson conver-sion are also implemented. Object-Oriented technology allows to plug-and-play models, for example a theory-driven evaporation model is also used by7a parameterised stopping-pion model.The Geometry provides an ISO STEP compliant solid modeller, allowingexchange of models from CAD systems, and provides the equation of motionsolvers in diﬀerent ﬁelds and geometrical boundaries conditions for the prop-agation of particles. Multiple solid representations, such as ConstructiveSolid Geometry, Boundary Represented Solids (including NonUniformRa-tionalBSplines), Swept Solids, Boolean Operations, are supported accordingto the ISO STEP standard. Thus Geant4 can perform physics simulationin CAD detector models. Diﬀerent navigation algorithms in the geometri-cal data bases allow an high degree of automation in the optimisation ofﬂat or hierarchical volumes structures. Diﬀerent integrators, beyond clas-sical Runge-Kutta, and including multi-turn perturbative methods, allow acorrect treatment for various ﬁelds of variable non-uniformity and diﬀeren-tiability. A proper integration is also performed to update the particles timeof ﬂight during transportation.The Tracking manages the evolution of the track’s status determined bythe physics interaction occurring at a given time, at a given location, ordistributed in space-time. The tracking system manages any of these kindsof interactions, or any combination of them, leading to a closed generalisationof the traditional classiﬁcation in discrete and continuous physics processes(which is found back as a special case). In order to fully exploit the validityranges of the physics models, Geant4 does not apply any tracking cuts,but relies only on production thresholds, thus all particles are tracked downto zero range. In addition, Geant4 can ensure a consistent and material-independent accuracy of the simulation because the production cuts are setin range, rather than in energy (and the tracking allows automatic correcttreatment of near-boundary regions via the capability of processes to producesecondaries below threshold). Of course, the user can optionally deﬁne cutsin energy, path length, time-of-ﬂight, for special treatment of selected areasin the experimental set-up.The Run, Event and Track management allows the simulation of theevent kinematics, together with primary and secondary tracks, and it pro-vides the functionality to perform studies of anything from pile-up to trig-ger and loopers via a triple stacking mechanism. A fast parameterisationframework (which can be triggered on particle type, volume, etc.) is inte-grated with the full simulation, allowing independent and simpliﬁed detectordescriptions and at the same time a correct treatment near cracks. Fast pa-rameterisations allow the direct production of hits corresponding to a fullshower development for several detector types. Finally the Hits and Digidomains provide the functionality to reproduce the read-out structure of thedetector and its electronic response, independently from the geometry usedfor the tracking.Visualisation and User Interface make use of abstract Object-Orientedinterfaces to allow drivers of multiple standard and specialised graphics sys-tems, and interaction with sophisticated GUIs or command line and batch8systems. The implemented visualisation drivers allow the use of X11, PostScript,OpenGL, OpenInventor, VRML, and DAWN, which allows engineering qual-ity drawings and automatic detection of volumes overlaps. The implementeduser interfaces allow batch sessions (including the processing of macro ﬁles),interactive sessions based on command lines interfaces, as well as fully graph-ical user interface sessions such as with OPACS or MOMO, the latter includ-ing automatic code generation for detector description and materials deﬁni-tion. The VRML2 driver also allows interactive picking of physics objects,such as tracks and hits, visualising in real time the associated physics infor-mation.Particle Data Group compliant particle deﬁnitions, including hundreds ofbaryonic and mesonic resonances and ions) and decay processes and modes,have been implemented and are available. Extensive possibilities of interac-tion with the Geant4 system are oﬀered to the user via a kit of dedicateduser-action classes. A wide set of utilities, including a complete set of ran-dom number generators, physics units and constants, as well as isotopes,elements, compounds deﬁnitions, and interface to event generators and toODBMS, complete the toolkit.References[1] Geant4 Collaboration, CERN/LHCC 98-44, Geant4 : AnObject-Oriented Toolkit for Simulation in HEP; see also the web site:http://wwwinfo.cern.ch/asd/geant4/geant4.html[2] F. Gerigk, Private Communication[3] GEANT3 , CERN Program Library Long Write-up, W5013 (1993).[4] N.V. Mokhov, “The MARS Code System User’s Guide”, Fermilab-FN-628(199 5)N.V. Mokhov, “MARS Code Development, Benchmarking and Applica-tions” Fermilab-Conf-00-066(2000)O.E. Krivosheev and N.V. Mokhov, “A New MARS and its Applications”,Fe rmilab-Conf-98/43 (1998)N.V. Mokhov, S.I. Striganov, A. Van Ginneken, S.G. Mashnik, A.J.Sierk and J. R anft, “MARS Code Developments”, Fermilab-Conf-98/379(1998)[5] J. H. Billen et. al., “Poisson Superﬁsh”, LA-UR-96-1834[6] L. Lombardi, “A 40-80 MHz System for Phase Rotation and Cooling”,CERN Neutrino Factory Note 37 (2000)[7] A. Perrin, “PATH Manual”9

GEANT4 simulation of phase rotation for neutrino factory

Abstract

Similar works

Full text

Available Versions

CERN Document Server