Geant4 Systematic Study of the FRACAS Apparatus for Hadrontherapy Cross Section Measurements
PPrepared for submission to JINST
Geant4 Systematic Study of the FRACAS Apparatus forHadrontherapy Cross Section Measurements
E. Barlerin, S. Salvador , M. Labalme
Laboratoire de Physique Corpusculaire de Caen, Normandie Univ, ENSICAEN, UNICAEN, CNRS/IN2P3,14000 Caen, France
E-mail: [email protected]
Abstract: In this work, we report on systematic Monte Carlo (MC) studies for the FRACASapparatus, a large acceptance mass spectrometer that will be used to measure the fragmentationcross sections of C ions for hadrontherapy. The apparatus will be made of a beam monitor,trackers surrounding a magnet and a Time-Of-Flight (TOF) wall. Using Geant4 simulations of thewhole system and in-house developed reconstruction algorithms we studied the influence of thetracker positions and spatial resolutions on the charge and mass reconstruction efficiencies. Anoptimal configuration was found where the upstream tracker positions should be located 6 cm awayfrom the target and spaced by 4 cm and their spatial resolution should be 100 µm. The downstreamtrackers positions will have to be changed according to the beam energy mostly to preserve thegeometrical efficiency of the system. Their spatial resolutions, even though of a lesser importancecompared to the upstream trackers, should be around 1 mm or better. In this optimal configuration,we were able to obtain an overall fragment identification efficiency above 90% for beam energiesranging from 100 to 400 MeV/nucleon.Keywords: Instrumentation for hadron therapy, Simulation methods and programs, Mass spec-trometers, Particle identification methods Corresponding author. a r X i v : . [ phy s i c s . i n s - d e t ] S e p ontents During a hadrontherapy treatment, nuclear interactions between the beam ions and the humantissues can occur. These interactions lead to a reduction of the primary beam intensity and to thecreation of lighter and faster fragments resulting in a mixed radiation field. An accurate knowledgeof those nuclear interaction processes through their double differential cross sections is then crucialto precisely control the dose deposited in the tumor and the surrounding healthy tissues [1–3].Although different experiments have already been performed to obtain those cross sections for a C beam below 100 MeV/nucleon on different targets [4–6], double differential cross sections arestill scarce for beam energies between 100 and 400 MeV/nucleon.The FRAgmentation of CArbon and cross Sections (FRACAS) large acceptance mass spec-trometer under construction, will be used to measure those double differential cross sections on– 1 –arget of medical interest such as C, H, O, N and Ca. Among the different measurements neededto extract the cross sections such as the fragment angle of emissions and energies, the identifica-tion of the fragment remains crucial. In a mass spectrometer, the particle identification is usuallytwo fold: first the charge of the fragment is extracted and then its mass. In our case, the chargeidentification will be done by means of a ∆ E—TOF method [7]. A set of tracking detectors (alsoreferred as trackers) will be associated to a deflecting magnet in order to reconstruct the mass of theparticles using its magnetic rigidity. The use of these methods in the case of a mass spectrometerhas been proven to be the most accurate identification method for ions with kinetic energies in therange from 150 MeV/nucleon to 400 MeV/nucleon [6, 8] because of the high probability of particlefragmentation in thick calorimeter-like detectors.During the detector design phase, a large part of the process consisted in studying the wholeapparatus using Geant4 MC simulations along with in-house developed reconstruction algorithms.This allowed to optimize the properties of the detectors in particular the trackers, in terms of positionand spatial resolutions.In this paper, the setup of FRACAS will be detailed and the MC simulations performed willbe described along with the reconstruction algorithms developed to analyse the data. Finally theresults of the influence of the tracker positions and spatial resolutions on the fragment identificationefficiency will be presented and discussed.
Figure 1 shows a schematic view of the FRACAS experimental setup. It will be composed of aBeam Monitor (BM) located in front of the target, trackers surrounding a magnet and a scintillatingdetector wall for TOF and partial energy measurements ( ∆ E).The BM will consist of a multi-stage Parallel Plate Avalanche Counter (PPAC) operated at lowisobutane (iC H ) pressure. One stage with a thin gap will be used for timing purposes to give the start for the TOF measurement while two other stages with thicker gaps and stripped anodes will beused to extract the beam position and shape with a spatial resolution expected to be below 100 µmin both directions.The TOF-wall, which will provide the stop for the TOF measurements and the partial energyreleased by the fragments, will be a modular system involving 384 scintillating detectors that can bearranged in different configurations. Each module will be composed of a YAP:Ce crystal coupledto a PhotoMultipier Tube (PMT). A detailed description of the TOF system along with first timingperformances can be found in [9].The magnet will be a large acceptance dipole with a magnetic field of 0.7 T in the center ofits gap (detailed in section 2.2) providing sufficient mass separation of the fragments of the samecharge.The trackers will measure the fragment interaction positions in order to obtain their trajectoriesbefore and after the magnet, referred to as up- and downstream trackers, respectively. The upstreamtrackers should have small active areas due to their proximity with the target and be made of solid-state detectors. On the contrary, the downstream trackers would need to have a large active area of– 2 –t least 50 ×
50 cm in order to detect as many fragments as possible considering the acceptance ofthe magnet. The most common detectors to achieve large active areas and low material budget areusually gaseous detectors such as MultiWire Proportional Chambers (MWPCs), or Time ProjectionChambers (TPCs). The downstream trackers were then considered as gaseous detectors in our study. MonitorBeamTargetTrackers Magnet Trackers ToF-wall(two configurations)
Figure 1 . Sketch of the FRACAS mass spectrometer showing all the detection elements. The TOF-wall isshown in two different configurations depending on the incident beam energy.
The simulations were made using Geant4.10.5.1 with the
FTFP_BERT_HP physics list for nucleus-nucleus interactions and electromagnetic_option3 for electromagnetic processes. In the simulations,only the active parts of the detectors were modelled. The two tracking stages of the beam monitorwere both modelled as 10 ×
10 cm active surface and 7 mm gap volumes of iC H at 25 mbar.The timing stage of the beam monitor was modelled with the same active surface and gas pressurebut with a gap of 1.6 mm.The target was modelled as a 5 mm long PMMA (C H O ) cylinder with a diameter of 5 mm.The two upstream trackers were both described as 25 ×
25 mm and 200 µm thick volumes ofsilicon. The two downstream trackers were modelled as 50 ×
50 cm and 8 mm thick volumes ofargon at 1 bar.Each of the 384 pixels of the TOF wall, arranged in 16 rows of 24 modules, was composedof 25.4 × and 1.5 mm thick YAP:Ce crystals coupled to a PMT with optical grease. Inthis study, we included in post-analysis the coincidence resolving time of the TOF system (BM andTOF-wall) as a normal distribution with a Full-Width-at-Half-Maximum (FWHM) of 300 ps, andthe energy resolution of the scintillating detectors R L following eq. (2.1) obtained from experimentalmeasurements using γ sources. R L = (cid:18) √ E + . (cid:19) × L , (2.1)– 3 –ith L is the scintillation light in equivalent number of photoelectrons and E the deposited energyin keV.Quenching behaviours of the scintillating material were included in the function L usingeq. (2.2) extracted from [10] that converts the deposited energy into equivalent scintillation photo-electrons. L = a (cid:20) E (cid:20) − a AZ E ln (cid:18) + E a AZ (cid:19) (cid:21) + a a AZ ln (cid:18) E + a AZ a A + a AZ (cid:19) (cid:21) (2.2)with a the conversion factor from energy to collected number of photoelectrons, a , a and a thequenching factors whose values are given in table 1, A, the mass and Z, the atomic number of theinteracting fragment. Table 1 . Values of the a i parameters used in eq. (2.2). a (a.u.) a (a.u.) a (Mev/nucleon) a × ×
110 cm . A measured magnetic field map of the ALADIN magnet installed atGSI [7] was integrated in the simulation.The whole system was placed in air at atmospheric pressure.In this study, the goal is to correctly identify the fragments produced in the target by the beamparticles. Therefore, only the C ions that fragmented in the target are considered and the fragmentsproduced elsewhere in the apparatus, for instance in the magnet iron frame, are not included in thedata analysis.Figure 2 shows a schematic view of the simulation detailing the several position referencesused in this paper. The systematic study consisted in varying the positions and spatial resolutions ofthe trackers. The beam monitor, the target and the magnet were kept at the exact same positions forall the simulations. The TOF-wall had different positions for each beam energy, chosen to have thesame geometrical efficiency and roughly the same TOF value for the beam ions. Its position waschanged at distance D to the magnet and an angle φ with respect to the beam trajectory so that a C ion from the beam going through the magnetic field impinged in the central TOF-wall module.The positions of the upstream trackers were defined by the distance of the target to the firstupstream tracker (
T aT ) and the distance between the two upstream trackers ( TT up ). Concerningthe downstream trackers, their positions were defined by the distance to the exit of magnet gap andthe first downstream tracker ( MT ) and the distance between the two downstream tracker ( TT down ).The trackers were not located closer than 10 cm to the magnet due to the leakage fields.The simulations were made for four different beam energies: 100, 200, 300 and 400 MeV/nucleon.For each beam energy, multiple simulations with 10 primary C ions were made by varying theup- and downstream tracker positions fixing the upstream tracker spatial resolutions to 100 µm andthe downstream tracker spatial resolutions to 1000 µm in both directions. Table 2 summarizes thevalues and ranges of the elements positions used in the simulations for each beam energy.– 4 – able 2 . Values and ranges of the FRACAS element positions evaluated in the Geant4 simulations for thedifferent beam energies.
Beamenergy(MeV/nucleon) φ (°) D (cm) T aT (cm) TT up (cm) MT (cm) TT down (cm)100 12.5 55 ≥ ≤ ≥ ≤ ≥ ≤ ≥ ≤ ≥ ≤ ≥ ≤ ≥ ≤ ≥ ≤ x and y directions were varied independently as the magnetic field deviates the fragments only in the x direction.A last set of simulations was made with the optimal configuration of the tracker positionsand spatial resolutions for each beam energy in order to obtain the overall fragment identificationefficiencies of the apparatus. Figure 2 . Simple sketch of the Geant4 simulation of FRACAS showing the different references of theelement positions. – 5 – .3 Fragment identification
The identification of a fragment can be decomposed in two parts: the charge reconstruction and themass reconstruction. However, in order to reconstruct the mass of the fragments, their trajectoriesmust be reconstructed beforehand. The following sections will detail the different processes usedin the fragment identification.
The charge identification is done using the ∆ E—TOF method by plotting the partial released energyof a charged particle in a material against its time of flight. The different particle charges are thendistributed along lines that can be fitted using a simplified version of the Bethe-Bloch formulawithout radiative corrections: ∆ E = a · Z β · (cid:20) ln (cid:18) β b − β (cid:19) − β (cid:21) (2.3)with a a parameter describing the conversion of the partial released energy into scintillationphotons and b a parameter describing the properties of the YAP crystal given by eq. (2.4) and thesemi-empirical formula in eq. (2.5) from [11]. b = m e c I YAP = I YAP = eV (2.4)given by I YAP Z eff = . + . × Z − . and Z eff =
26 (2.5)Figure 3 shows examples of the partial energy released ∆ E of the fragments in the TOF-walldetectors converted in scintillation photoelectrons, versus the TOF expressed as the reduced velocity β for a C beam at (a) 100 MeV/nucleon and (b) 400 MeV/nucleon. The red curves represent theBethe-Bloch function with varying Z from 1 to 6 whose parameter a are fitted to the different eventpopulations. The charge of the fragment is then obtained by minimizing the event distance to theclosest Bethe-Bloch line using a simple dichotomy algorithm. A more detailed description of thismethod can be found in [7]. Fragments with the same number of charge are separated in a magnetic field according to theirmagnetic rigidity: B ρ = . · AZ · βγ sin ( θ ) (2.6)with θ the angle between the magnetic field and the trajectory of the fragment, B the intensityof the magnetic field, A and Z the number of mass and charge of the fragment, β and γ the Lorentzfactors and 3.10716 the conversion factor between mq and AZ .The number of charge Z is already extracted with the ∆ E—TOF method and β and γ are givenby the TOF measure. The radius ρ must be obtained through the reconstruction of the trajectories.The algorithm used to reconstruct the trajectories of the fragments works as a Kalman filter [12].It tests all the possible combinations between the position of each tracker and selects the ones that– 6 – Time of Flight (ns) · E ( nb o f pho t on s ) D N u m be r o f f r ag m en t s
400 MeV/n
10 15 20 25 30
Time of Flight (ns) · E ( nb o f pho t on s ) D N u m be r o f f r ag m en t s
100 MeV/n
Z=1Z=2Z=3Z=4Z=5Z=6 Z=1Z=2Z=3Z=4Z=5Z=6 (a) (b)
Figure 3 . Partial energy released ∆ E of the fragments in the TOF-wall detectors converted in scintillationphotoelectrons, versus the TOF expressed as the reduced velocity β for a C beam at (a) 100 MeV/nucleonand (b) 400 MeV/nucleon. The red curves represent the Bethe-Bloch function with varying Z from 1 to 6. are most likely to be a trajectory of a fragment. Figure 4 shows an example of how these stepsare computed for the trajectory reconstruction between the TOF-wall and the downstream trackers.It starts from the TOF-wall by taking as a starting point of a trajectory the center of a pixel thathas scintillated, ( x a , y a ) n . It then constructs tracks using this position and the measured positions( x b , y b ) n on the second downstream tracker, and extrapolates those to the first downstream tracker,leading to the ( x d , y d ) n points. It was considered that the fragments moved in straight lines inair without scattering. For each measured position ( x c , y c ) n on the first downstream tracker, theprobability of being part of a trajectory is calculated based on their distance to the extrapolatedpoints ( x d , y d ) n .The steps are repeated to extrapolate to the second and to the first upstream trackers assumingthat only the x direction of the fragments are deflected by the magnetic field and that the y coordinatesare not affected. The final step is to extrapolate the trajectories to the target, where it is consideredthat all the trajectories came from its center. The probability for a combination of measured pointsto be part of a fragment trajectory is the product of the probability computed at each extrapolationstep. A threshold is then applied to keep only the most probable combinations. In the case wheretwo reconstructed trajectories shared the same detector position, the one with the highest probabilityis kept. The threshold value was set to 10 − , giving a trajectory reconstruction efficiency above90% in optimal conditions.The radius ρ of the trajectory in the magnetic field is then extracted using the upstream anddownstream trajectories and basic trigonometry. The mass identification is achieved by plotting the parameters ρ Z sin ( θ ) previously obtained againstthe reduced velocity β of the fragment. The fragments would then distribute along lines given byeq. (2.7) adapted from eq. (2.6) according to their number of mass A . f ( A ) = . A βγ B (2.7)– 7 – igure 4 . The first steps of the trajectory reconstruction algorithm between the TOF-wall and the downstreamtrackers. The same can be applied for the reconstruction to the upstream trackers. A simple dichotomy algorithm is then used to minimize the distance between a given fragmentand each line to associate the fragment with its mass.Figure 5 shows an example of ρ Z sin ( θ ) versus β for a beam energy of 100 MeV/nucleon. Thered curves represent the eq. (2.7) with A varying from 1 to 12. b Reduced velocity q Z s i n r N u m be r o f f r ag m en t s
100 MeV/n
A=1A=2A=3A=4A=5A=6A=7A=8A=9A=10A=11A=12
Figure 5 . Example of a mass identification map showing ρ Z sin ( θ ) as a function of the reduced velocity β for a C beam at 100 MeV/nucleon. The red lines represent eq. (2.7) for masses from 1 to 12. – 8 –
Results
The charge identification efficiency is evaluated as the ratio between the number of fragments thathad their charge correctly identified and the number of fragments that hit the TOF-wall. It mostlyrelates on the TOF system through the energy resolution on the partial released energy and thecoincidence resolving time of the TOF. The trackers might affect it when the fragments encounterscattering in their material but their positions and spatial resolutions do not affect those results.Table 3 shows the charge identification efficiency for each beam energy. The charge identifica-tion is achieved with an efficiency above 97% for a beam energy of 100 MeV/nucleon and almostreached 99% for the highest beam energy.
Table 3 . Charge reconstruction efficiency of the fragments for each beam energy
Beam energy (MeV/nucleon) Charge identification efficiency100 (97.6 ± ± ± ± Considering the way the algorithm works, the two main parameters that affects the trajectoryreconstruction efficiency are the position of the detectors and their spatial resolutions.The trajectory reconstruction efficiency is defined here as the ratio between the number offragments that have their trajectory reconstructed and the number of fragments having a trajectorythat went through all the detectors.
Figure 6 shows the trajectory reconstruction efficiency as a function of the upstream tracker positionsfor the different beam energies.For all the beam energies, the trajectory reconstruction efficiency is better than 91% if thedistance
T aT is greater than 4 cm and the distance between the two trackers TT up is larger than4 cm. Placing the first upstream tracker in a shorter distance to the target and the two trackersfar from each is critical as the trajectory reconstruction efficiency drops significantly with smallervalues of T aT , especially at 100 and 200 MeV/nucleon. Overall, the highest efficiencies are achievedwhen 4 ≤ T aT ≤ ≤ TT up ≤ MT and TT down to achieve a good trajectoryreconstruction efficiency. In fact, to keep the efficiency above 92% when increasing the beam energy,– 9 – a) (b)(c) (d) Figure 6 . Trajectory reconstruction efficiency as a function of the upstream tracker positions at(a) 100 MeV/nucleon, (b) 200 MeV/nucleon, (c) 300 MeV/nucleon, (d) 400 MeV/nucleon. the lowest value of MT should go from 10 cm at 100 MeV/nucleon to 40 cm at 400 MeV/nucleon.In the mean time, the highest values of TT down went from 12 cm to almost 70 cm.Table 4 summarizes the positions of the up- and downstream trackers that give the best trajectoryreconstruction efficiencies at the different beam energies. Table 4 . Optimal configurations of the downstream tracker positions for the different beam energies
Energy(MeV/nucleon) MT (cm) TT down (cm)100 10—20 ≤ ≤ ≤ a) (b)(c) (d) Figure 7 . Trajectory reconstruction efficiency as a function of the downstream tracker positions at(a) 100 MeV/nucleon, (b) 200 MeV/nucleon, (c) 300 MeV/nucleon, (d) 400 MeV/nucleon.
In this part only the results at 400 MeV/nucleon are shown as the influence of the tracker spatialresolutions for the other beam energies were comparable.The spatial resolution of the downstream trackers in the x direction (i.e. the deflecting direction)have no clear influence on the trajectory reconstruction efficiency. In fact, it is stable at 92% fora spatial resolution going from 100 µm to 2500 µm. This is mostly due to the fact that thespatial resolution of the downstream trackers in the x direction is only used for the first step ofthe trajectory reconstruction, from the TOF-wall and the second downstream tracker to the firstdownstream tracker.Figure 8 shows the trajectory reconstruction efficiency as a function of the upstream trackerspatial resolutions and the downstream tracker spatial resolutions in the y direction. Degradingthe upstream spatial resolution from 100 µm to 1500 µm induces a loss of 35% of efficiency. Theoptimal spatial resolution for the upstream trackers seems to be 100 µm. For the downstreamtrackers, the loss of efficiency induced by degrading the spatial resolution in the y direction from500 µm to 3000 µm is less than 5%. Setting it around 1500 µm must be sufficient as lowering it– 11 –ould not give a better efficiency. Figure 8 . Trajectory reconstruction efficiency as a function of the upstream tracker spatial resolution and thedownstream trackers spatial resolution in the y direction at 400 MeV/nucleon. As for the trajectory reconstruction, the two parameters that influence the mass identificationefficiency are also the tracker positions and spatial resolutions. To evaluate the efficiency of themass identification only, the algorithm is used on correctly reconstructed trajectories.
Here only the results at 100 MeV/nucleon are shown as they gave results that are more constrainingthan the other beam energies, especially for the downstream tracker positions. Figure 9 shows themass identification efficiency as a function of the upstream and the downstream tracker positions at100 MeV/nucleon.The upstream tracker positions show no large influences on the mass identification efficiency.It is always kept above 97% and the highest efficiencies are obtained when the second upstreamtracker is the closest to the entry of the magnet.The downstream tracker position is however a more critical parameter as the mass identificationefficiency could fall down to 88% in the worst case where the trackers are closer than 17 cm toeach other. The mass identification efficiency is above 96% when the distance between the exit ofthe magnet and the first downstream tracker MT is kept below 17 cm and the distance between thetrackers is lower than 20 cm. – 12 – a) (b) Figure 9 . Mass identification efficiency as a function of the position of (a) the upstream trackers, (b) thedownstream trackers at 100 MeV/nucleon.
Figure 10 shows the mass identification efficiency as a function of the downstream trackers spatialresolutions in the x direction for different upstream tracker spatial resolutions at the different beamenergies.The mass identification efficiency shows a strong dependency on the upstream tracker spatialresolutions. For example at 100 MeV/nucleon and a downstream tracker x spatial resolution of1 mm, degrading the spatial resolution of the upstream trackers from 100 µm to 1 mm reduces theefficiency from 96% to less than 90%. The effect is even more emphasised when increasing thebeam energy with an efficiency around 74% at 400 MeV/nucleon.The downstream tracker spatial resolution has however a smaller effect on the mass identifi-cation than the upstream one. Degrading the x spatial resolution from 1 mm to 3 mm results in aroughly 10% loss of efficiency for the lowest beam energy to only few percents when increasingthe energy. An optimal value of 1 mm for the spatial resolution of the downstream trackers in the x direction was chosen as a better one would not improve drastically the mass identification efficiency. Figure 11 and 12 show the fragment identification matrices obtained with an optimal configurationof the apparatus given in table 5, at the different beam energies. These are made by comparing thenumber of identified fragments including all the reconstruction and identification algorithms to thenumber of fragments produced reaching the TOF-wall. Globally, the combined performances ofthe three reconstruction algorithms is satisfactory as most of the fragments are correctly identifiedwith an overall efficiency better than (90 ± Be was identified for 5% as Li and for 3% as Li which drops its fragmentidentification efficiency down to 91%. Yet most of those low fragment identification efficienciesconcern fragments with a low production rate, while, on the opposite, the most produced fragments– 13 – a) (b)(c) (d)
Figure 10 . Mass identification efficiency as a function of the downstream tracker spatial resolutions in the x direction for different upstream tracker spatial resolutions at (a) 100 MeV/nucleon, (b) 200 MeV/nucleon,(c) 300 MeV/nucleon, (d) 400 MeV/nucleon. are globally well identified. For example, at each 4 energies, the α -particles which represent roughly50% of the produced fragments have an identification efficiency above 89%. The proportion of thelost fragments which correspond to bad trajectory reconstructions leading to an unknown fragment,decreases with the energy. The highest proportion of losts is for protons which goes from almost14% at 100 MeV/nucleon to 10% at 400 MeV/nucleon. The lowest masses are the most affecteddue to their smaller transverse momenta. For the other fragments, the proportion of losts is alwaysunder 10%. The results given by the analysis of the Geant4 simulations of the FRACAS apparatus allow us todraw some conclusions concerning the characteristics needed for the up- and downstream trackers.– 14 – able 5 . Optimal configurations of the tracker positions for the different beam energies
Energy(MeV/nucleon)
T aT (cm) TT up (cm) MT (cm) TT down (cm)100 4—8 4—7 10—20 ≤ ≤ ≤ The results showed that at each beam energy the configuration giving the best trajectory reconstruc-tion efficiency is by placing the first upstream tracker at 6 cm to the target and the second upstreamtracker at 4 cm of the first. Given the fact that the mass reconstruction efficiency was not clearlyaffected by the position of the upstream trackers, we conclude that this is an optimal configurationof the upstream tracker positions for all beam energies. Placing the upstream trackers further awayfrom the target or from each other will not lower the trajectory reconstruction efficiency but it willlower the geometric efficiency of the apparatus, unless the size of their active area was increased.The trajectory reconstruction efficiency and the mass reconstruction efficiency both seemed tostrongly rely on the upstream tracker spatial resolutions. Thus, it will be crucial that the technologychosen for them provides a spatial resolution better than 100 µm, while keeping the material budgetas low as possible. As a solution, pixelated or stripped silicon detectors have shown to have aspatial resolution that can reach up to 2 µm [13, 14] Another solution could be diamond detectorswith stripped metallized anodes as they can provide a spatial resolution of around 26 µm [15] andsustain a higher integrated flux without being damaged. However, both solutions being based onsolid state detectors, they may increase the material budget above the requirements. Moreover, dueto their proximity with the target, the upstream trackers will have to work under high particle rates.In the case of stripped detectors a large amount of hit position ambiguities may arise. This was nottaken into account in the Geant4 simulations done for this work as the position of the fragmentswere considered to be correctly measured.
Unlike the upstream trackers, the results concerning the downstream trackers showed that theirposition must be changed for each beam energy. The trajectory reconstruction efficiency andthe mass reconstruction efficiency were both mainly affected by the downstream tracker spatialresolutions in the x direction. The spatial resolution in the y direction also influenced the massreconstruction efficiency but at a lower level. As the downstream trackers need to cover a large area,being after the mass separation by the magnet, the simplest technology to use would be gaseousdetectors. This solution also allows to keep the material budget as low as possible. MWPCs canreach a spatial resolution of around 60 µm in the direction along the wires and 200 µm in thedirection perpendicular to the wires [16]. Some studies are ongoing on a prototype of an MWPC– 15 – H H H He He He Li Li Li Be Be Be B B C C C C Produced fragment H H H He He He Li Li Li Be Be Be B B C C C C losts R e c on s t r u c t ed f r ag m en t I den t i f i c a t i on e ff i c i en cy ( % )
200 MeV/n Global efficiency : 91.0% : 2.96% s H H H He He He Li Li Li Be Be Be B B C C C C Produced fragment H H H He He He Li Li Li Be Be Be B B C C C C losts R e c on s t r u c t ed f r ag m en t I den t i f i c a t i on e ff i c i en cy ( % )
100 MeV/n Global efficiency : 92.0% : 3.27% s (b)(a) Figure 11 . Fragment identification matrices for an optimal configuration of the apparatus at(a) 100 MeV/nucleon, (b) 200 MeV/nucleon. to determine the spatial resolution reachable in both directions. We also plan to study the use ofµ-RWELL [17] for the downstream trackers as they can reach a spatial resolution of around 50 µm.– 16 – H H H He He He Li Li Li Be Be Be B B C C C C Produced fragment H H H He He He Li Li Li Be Be Be B B C C C C losts R e c on s t r u c t ed f r ag m en t I den t i f i c a t i on e ff i c i en cy ( % )
400 MeV/n Global efficiency : 91.9% : 2.61% s H H H He He He Li Li Li Be Be Be B B C C C C Produced fragment H H H He He He Li Li Li Be Be Be B B C C C C losts R e c on s t r u c t ed f r ag m en t I den t i f i c a t i on e ff i c i en cy ( % )
300 MeV/n Global efficiency : 91.5% : 2.74% s (b)(a) Figure 12 . Fragment identification matrices for an optimal configuration of the apparatus at(a) 300 MeV/nucleon, (b) 400 MeV/nucleon.
Further studies will be done on the up- and downstream trackers to determine the amount ofghost hits generated in them, depending mainly on the geometry of the strips.– 17 –
Conclusion
Geant4 simulations and in-house developed reconstruction algorithms permitted a systematic studyof the influence of the detector positions and the spatial resolutions on the trajectory and themass identification efficiency of the FRACAS mass spectrometer. With an optimal configurationof the tracker positions and spatial resolutions it was possible to achieve a particle identificationefficiency above 90% with simulation data for beam energies ranging from 100 to 400 MeV/nucleon.Results showed that the position of the up and downstream trackers mostly affects the trajectoryreconstruction efficiency and that an optimal configuration can be determined at each beam energy.The upstream tracker spatial resolution is a crucial parameter that strongly influences bothtrajectory reconstruction and mass identification and should be kept around 100 µm to ensure ac-ceptable fragment identification performances. Silicon or diamond pixelated or stripped detectorsseem to be viable solutions for the development of the upstream trackers. Concerning the down-stream trackers, the spatial resolution in the x direction seem to be a lot more crucial than the spatialresolution in the y direction. An optimal value of the spatial resolution could be 1 mm in the x direction and 1.5 mm in the y direction. MWPC or µ-RWELL detectors using stripped read-outcan be viable technologies. References [1] T. T. Böhlen, F. Cerutti, M. Dosanjh, A. Ferrari, I. Gudowska, A. Mairani, and J. M. Quesada.Benchmarking nuclear models of FLUKA and GEANT4 for carbon ion therapy.
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