Study of an Alternative Pion Collector Scheme for the ESS Neutrino Super Beam Project

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UPTEC F 19004

Examensarbete 30 hp Februari 2019

Study of an Alternative Pion Collector Scheme for the ESS Neutrino Super Beam Project

Patrik Simion

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Teknisk- naturvetenskaplig fakultet UTH-enheten

Besöksadress:

Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

Postadress:

Box 536 751 21 Uppsala

Telefon:

018 – 471 30 03

Telefax:

018 – 471 30 00

Hemsida:

http://www.teknat.uu.se/student

Abstract

Study of an Alternative Pion Collector Scheme for the ESS Neutrino Super Beam Project

Patrik Simion

The ESSnuSB will produce a high intensity neutrino super beam based on the 3 ms long proton pulses at 14 Hz from the ESS linac. With the use of a conventional normal-conducting van der Meer horn, to collect pions from the neutrino target, these 3 ms pulses will have to be compressed to of the order of 1 microsecond in order to avoid overheating of the magnet current conductors. Since this pulse compression requires costly extensions to the accelerator complex a prototype design of an alternative normal-conducting hadron collector scheme that could be operated in DC mode has been studied. The magnet has been implemented in the simulation software FLUKA and extensive research has been made to analyse and maximise the flux of charged pions inside and downsteam of the magnet. Further simulations have been made to asses the flux of on-target neutrinos from the

alternative collector scheme in comparison to the corresponding flux of a van der Meer horn. Simulation results from the comparison show that the alternative magnet greatly improved the neutrino flux of a bare source but not to the extent necessary to replace the magnetic horn. A conclusion is presented on the future possibilities of an optimized design that can improve the neutrino flux.

Ämnesgranskare: Roger Ruber Handledare: Maja Olvegård

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Populärvetenskaplig sammanfattning

Fysiker världen över står idag inför en utmaning med att försöka förklara den överväldigande dominansen av materia över antimateria i vårt universum. För att hitta en förklaring söker vi oss till en av universums allra minsta beståndsdelar, neutriner, bland samlingen av fundamentala partiklar. Dessa tillhör en särskilt skygg kategori och är otroligt svåra att upptäcka eftersom att de näst intill aldrig interagerar med annan materia. Inte nog med att de är svåra att upptäcka, det har även visat sig att de kan oscillera mellan tre olika slag under deras resa.

Tanken med ESSnuSB är att generera neutriner av ett slag genom att avleda protoner, från den linjära accelerator som byggs vid European Spallation Source (ESS) i Lund, till ett strålmål.

När dessa protoner träar strålmålet så genereras det en mängd olika partiklar men främst pio- ner som sedan sönderfaller och skickar iväg neutriner. Men för att lyckas skapa en neutrinostråle så ställs det stora krav på den magnet som används för att fokusera och sortera bort oönskade partiklar när strålen genereras. Ett magnetiskt horn används konventionellt men det skulle kräva många kostsamma utbyggnader av acceleratorkomplexet i vårat fall. Vi har därför undersökt hur en alternativ magnetdesign kan användas, ett alternativ som skulle vara kompatibelt med den bentliga anläggningen.

Vi började med att skapa en prototypdesign och implementerade därefter en första orders approximation av dess magnetfält. Med hjälp av simuleringar kunde vi sedan följa pionernas bana och mäta hur eektivt den alternativa magneten hanterade dem. Vi var framförallt intresser- ade av att se hur hög intensitet av neutriner vi kunde lyckas få att träa den detektor som ska benna sig cirka 50 mil bort. Trots att prototypen här inte visade sig prestera lika bra som det konventionella magnetiska hornet så ser vi en stor potential för dess framtid. Genom att optimera prototypens design kan vi göra den mindre påträngande för partiklarnas bana och således göra det möjligt att släppa igenom en större andel av dem för att höja intensiteten. Vi ser även möjligheter i att pulsera den elektriska strömmen genom magneten för att temporärt skapa starkare magnetfält. Vi hoppas att vidare forskning kring vår prototyp leder till en ny fokuseringskomponent för neutrinoexperiment världen över.

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1 Introduction

The European Spallation Source (ESS) in Lund, Sweden, will provide the world's most powerful neutron source by the year 2023 [1]. A superconducting linear accelerator will produce a 61.5 mA 2.0 GeV proton beam in 2.86 ms long pulses at a rate of 14 Hz, oering a unique average power of 5 MW [2]. The incident proton bunches from the linac will be sent to a rotating tungsten target to produce slow neutrons for further use in at least 22 dierent neutron scattering and spectroscopy experiments [1]. With the ESS linac arises also an excellent opportunity for the generation of new neutrino experiments. By utilizing the ESS linac and its unparallelled power as a proton driver, another project called the ESS neutrino Super Beam (ESSnuSB) could generate a neutrino beam with tremendous intensity without the need for a dedicated proton driver [2].

The neutrino Super Beam would be generated without disrupting the ESS spallation neutron generation by increasing the pulse repetition rate, and a subsequent increase to 10 MW in average beam power, which would be shared evenly between the ESS neutron target and the ESSnuSB neutrino generation.

Figure 1: The European Spallation Source (ESS) with accumulator ring and dedicated target area.

The ESSnuSB project seeks to discover Charge Conjugation Parity violation (CP violation) in the leptonic sector through observation of neutrino oscillations [2]. When the measurement of the leptonic mixing angle θ13 in 2012 was found to be larger than anticipated, the sensitivity to leptonic CP violation proved to be signicantly higher at the second neutrino oscillation maximum compared to the rst maximum [3]. Another implication is that the ability to establish the neutrino mass hierarchy is enhanced [4]. According to the standard model (SM), neutrinos do not mix and are massless [5]. It has been shown experimentally, however, that neutrinos in reality possess non-zero masses and mixing does indeed exist [3]. A standing challenge in cosmology is to explain the baryon number asymmetry of the Universe (BAU) [6]. CP violation plays a crucial role in describing the abundance of matter over antimatter, however the SM has yet been unable to account for the observed larger abundance of matter. The discovery of leptonic CP violation

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could have great signicance in increasing our understanding of the Universe, and perhaps to understand the underlaying process needed to reach a level of BAU matching observation [7].

The ESSnuSB project therefore intends to generate the neutrino beam in a dedicated target station within the ESS area and to detect the neutrinos at the second oscillation maximum using a large volume water Cherenkow detector.

Impinging protons from the linac will generate charged pions in the target. These need to be eciently collected before they decay and form the neutrino Super Beam. The conventional method to achieve this task is to employ a van der Meer magnetic horn [8] to cover the target.

A horn is of a toroidal structure with the magnetic eld enclosed in the toroid. To generate the magnetic eld, a current of the order of 350 kA needs to ow through the walls of the structure. This high current can only be sustained for a very short time period due to the resulting heating of the structure. The nominal pulse from the linac is too long and will therefore have to be compressed from 2.86 ms to a few microseconds using an accumulator ring where protons are collected during multiple turns and extracted in a single turn [2]. However, in order to reach a satisfying injection eciency, charge-exchange injection, where an H⁻ ion is injected and immediately stripped, will have to be employed in the ring. The linac must then be able to accelerate H⁻ bunches in between the proton bunches for neutron production [9].

These required extensions to the ESS facility could be omitted if an alternative pion collector, that can handle the nominal proton pulse length, was to be used instead of a magnetic horn.

Such alternative collector could consist of a superconductive solenoid, investigated in [9] [10], or a superconductive magnetic horn, both of which are capable of operating at DC. However, making the horn superconducting is dicult due to the energy deposition from charged particles passing through the structure walls. A third alternative collector has been considered for a previous experiment at the Los Alamos National Laboratory [11]. An adapted version of this DC operated collector is a potential alternative to the magnetic horn. This report describes a study of the potential performance of such a collector in the case of the ESSnuSB.

2 The Experiment and its Requirements

Figure 2: Pion propagation from target to the far detector.

Protons from the linac will interact with the neutrino target and produce charged particles that are emitted with a wide spread in momentum and angle. Among these particles there will be charged pions which rapidly decay into muons and muon neutrinos as shown in Figure 3. It is desired to absorb as many muons as possible before they decay to minimize contamination in the

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experiment. The muon neutrinos will propagate through the ground to the far detector and, at some probability, be detected. During the ight, some of the muon neutrinos will oscillate and change avour in which case they will be registered as electron neutrinos in the far detector. If the muon neutrino ux is known at another detector, near the source, it is possible to determine the fraction of oscillated neutrinos. Separate measurements of the oscillation fraction will be made for neutrinos originating from positive pions and from negative pions. A comparison between the ratio is equivalent to comparing neutrino and anti-neutrino oscillations. If it is shown that the two fractions are not equal, it will be the rst discovery of leptonic CP violation. This discovery can contribute to the understanding of the imbalance between matter and antimatter in the universe.

Figure 3: Pion and muon decay.

2.1 Far Detector

The far detector proposed for the ESSnuSB project will register events in its half a Megaton of clear water through the emittance of Cherenkov radiation which forms when an electron/positron or a muon/anti-muon is emitted following a neutrino/anti-neutrino interaction. The photomulti- pliers inside the detector, around the water volume, captures the Cherenkov radiation in the form of light. It is possible to determine the avour of the emitted particle from analysing the distinct light patterns created. However, it is not possible to discern the charge of the emitted particle since the light pattern is the same for both signs, thus it can not determine if the interaction originated from a neutrino or an anti-neutrino. For the detector to determine the charge, and therefore distinguish antiparticle from particle, a magnetic eld would need to be present [9].

However, magnetizing a detector of this volume is unpractical if not impossible.

2.2 Collector

Since the far detector registers neutrino and anti-neutrino interactions with identical signals, two important sources of contamination arise. The rst source derives from the collector's eciency in charge separating the pion source. While focusing pions of one charge, the collector is simul- taneously challenged to defocus pions of the other and unwanted charge. When the defocused pions are not suciently deected from the beam axis, their decay produce a muon neutrino of the wrong sign that could register in the far detector. However, even if the collector could charge separate the pion source entirely, a second source of contamination would not be eliminated.

This second source of contamination is caused by the decay of muons which were generated in the pion decay and is further discussed under section 2.3.

2.3 Pion and Muon Propagation

Pions and muons are unstable particles that will eventually decay. The rest mass and life time at rest of these particles are presented in Table 1.

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Table 1: Pion and muon rest mass and life time.

Particle rest mass [MeV/c²] life time [s]

π^± 139.57 26 · 10⁻⁹

µ^± 105.66 2200 · 10⁻⁹

As the charged pions decay, they form a muon and a muon neutrino pair as presented in Figure 3 [12]. The muon neutrinos from the pion decays will be emitted at an angle θ relative to the pion trajectory, given by the probability function [9]

ρ(θ) =1

2sin θ 1 − β²

(1 − β cos θ)² (1)

with β = ^v_c, the particle speed normalized to the speed of light, c. The probability distribution from Eq. (1) is illustrated in Figure 4 for four dierent pion energies. Muon neutrinos from low energy pion decays will have a wide probability distribution which allows for large angles relative to the pion trajectory. The muon neutrinos from high energy pions will instead see a high probability to be emitted at smaller relative angles and are therefore more likely to arrive at the far detector, assuming that the pions were accurately focused before they decayed. Note that the emission angle shown in Figure 4 also determines how accurately the pions need to be focused depending on their momentum.

Figure 4: Probability distribution of neutrino emission angle for four dierent pion energies.

Further along the decay chain, the eventual muon decay will become an important factor which aects the contamination of the experiment. The three-body muon decay, shown in Figure 3, results in two additional neutrinos. These additional neutrinos could then aect the oscillation ratio measured in the experiment if they were registered in the far detector. By adapting the length of the decay tunnel we are able to minimize this contamination since the muons, as opposed to the neutrinos, will be absorbed when they encounter matter. The dierence in life time between the pions and muons means that the particles will travel dierent mean distances for a given momentum. We can thus calculate the length of the tunnel where it allows for a maximum of pion decays, but minimizes the number of muon decays. It has been shown that a tunnel length of around 25 metres is optimal in the horn case [9] [13].

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3 Target Station and Pion Distribution

3.1 Van der Meer Magnetic Horn

The high current, pulsed magnetic horn was rst proposed by Simon van der Meer in 1961 [8].

A magnetic eld is generated between two co-axial conic shaped sheets of conducting material where a high current ows, see Figure 5. Particles from a source placed inside the central cone, a

eld free region, will traverse the inner conducting sheet, reaching the magnetic eld region where the particles are focused or defocused relative to the beam axis depending on their respective charge. The conic shape of the horn has since then been developed into more complex geometries to allow focusing of particles with wider spreads in momenta and polar angle.

Figure 5: Left: Original van der Meer magnetic horn design [8]. Right: ESSnuSB adapted design with target cylinder.

For the ESSnuSB, the horn design has been adapted from the design in the EUROnu project [14], see Figure 5. A set of four target stations in parallel, each equipped with such a horn, have been proposed in order to reduce the destructive eects caused by the high power beam on a single target and horn system [2].

3.2 The Target and the Pion Source

The target design chosen for the ESSnuSB consists of a cylinder cannister packed with titanium spheres. The cylinder is 78 cm long, with a 1.5 cm radius, which corresponds to two nuclear interaction lengths of titanium in the packed-bed conguration [13]. This target is located in the

eld free region inside the magnetic horn, see Figure 5, and is cooled by cold helium gas owing among the spheres [14] [2].

A FLUKA simulation has been made using a 2 GeV proton beam and a target placed inside the eld free region of a magnetic horn. From this simulation the secondary particle momentum and position coordinates have been registered upon leaving the target cylinder. The secondary particles of interest are generated at a rate according to the fractions given in Table 2, given per proton on target (p.o.t). Note that a large part of the protons hitting the target does not interact to produce secondary particles. Also, Table 2 only shows a selection, but still a majority, of secondary particles produced in the target.

Table 2: Fractions of secondary particles produced in the FLUKA simulation.

Particle π⁺ π⁻ µ⁺ µ⁻

#/p.o.t. 0.29 0.17 3 · 10⁻⁴ 7 · 10⁻⁷

The pion distribution has a big spread in both momentum and polar angle as shown in Figure 6.

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Figure 6: The momentum and angular distribution of positive and negative pions when leaving the target.

From this distribution we acknowledge the need for a large acceptance collector. The pion distribution shown in Figure 6 is used as the particle source for the simulations presented in this project. Not only do we face a challenge in focusing pions at large angles, but also pions of a great range in momenta. However, by eliminating the pions moving opposite to the beam direction upon leaving the target, it is seen how a large amount of low momenta pions can be disregarded.

These backwards moving pions correspond to the grey area in Figure 7-8. Furthermore, given both the wide spread in neutrino emission angle and the small neutrino detection cross section at low energy [15], the low momenta pions are less likely to eventually be registered in the far detector. A splitting of the forward moving pions into arbitrary low and high momenta around 300 MeV/c, can be seen in Figure 7.

Figure 7: The momentum distribution of pions when leaving the target.

When analysing the angular distribution in Figure 8 it is seen how the corresponding pions from

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Figure 7 are organised. A narrower distribution which is centred around 0.5 radians becomes apparent by only selecting the pions with a momentum above 300 MeV/c.

Figure 8: The angular distribution of pions when leaving the target.

4 Alternative Collector

This section will cover the history and functionality of the alternative collector followed by an assessment of the magnetic eld produced in a collector adapted for the ESSnuSB. The collector is tasked to focus the higly divergent source of pions, while at the same time charge separating and defocusing pions of the unwanted sign, to form the neutrino beam. While focusing the beam, it also needs to provide a strong magnetic eld and minimal obstruction of the particle trajectory to ensure a high pion ux.

4.1 History

The alternative collector studied here was rst invented at the Los Alamos National Laboratory, USA, to be used as a direct-current focusing device for pions at low energy accelerators [11]. It was recognised that an alternative direct-current collector, which was cylindrically symmetrical and provided charge separation, was necessary. These two attributes were not found in the two previously proposed direct-current devices, the superconducting solenoid [16] and the "double dipole magnet" [11]. At Los Alamos, a 30 cm carbon target would produce pions, with a wide distribution in kinetic energy and polar angle, using the 800 MeV proton accelerator at the Los Alamos Meson Physics Facility (LAMPF). The pions would then be focused and charge separated by the focusing device to increase the resulting neutrino ux and decrease contamination at a detector further downstream, similarly to the ESSnuSB. A prototype of the alternative collector was constructed for optimal focusing at the LAMPF. The magnetic eld of the prototype was measured to verify the corresponding computer model for the collector, later used in simulations.

It was predicted through simulations that the neutrino intensity could be increased by a factor of four relative to an unfocused pion source [11].

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Figure 9: Alternative collector invented at Los Alamos, cross section in the xy-plane [11].

The device consists of a shell and eight evenly distributed ns, making it cylindrically symmetric, see Figure 9. The shell and the ns contain hollow bore copper conductors, with water cooling inside the centre bore, running along the beam axis i.e. perpendicular to the cross section of the collector in Figure 9. Notice that the width of these ns directly aect the acceptance of the collector since they obstruct a large part of the focusing region.

A focusing device of this sort is capable of producing a quasi-toroidal magnetic eld, with a given eld strength, using a lower direct current (DC) than the van der Meer horn. The DC operation therefore allows the alternative device to be operated continuously with a constant

eld, eliminating the need for compression of the proton pulses. In addition, the toroidal shape of the magnetic eld provides charge selection of the pions, a function which is missing in for example a superconducting solenoid [10].

4.2 Magnetic Field Map

Figure 10: Original picture showing rst quadrant of the discrete solenoid.

The adaptation from the collector tested at Los Alamos to one suited for the ESSnuSB project was made by Davide Tommasini at CERN. To account for the higher beam momentum, the number of conductors were increased which led to a widening of the ns. A two dimensional model of

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the adapted collector was then implemented in the Poisson Supersh program to generate the magnetic eld map shown in Figure 10.

The conductors carry the current along the beam axis. By passing the current in one direction inside the ns, and the opposite direction in the shell, a quasi-toroidal magnetic eld is generated which can be seen from the magnetic eld lines of Figure 10. The eld is directed counter-clockwise in Figure 10. Since the eld map was generated from a two dimensional model, variations in the eld along the beam axis is not described. This also means that there is no information available about potential fringe elds. For a complete description of the magnetic eld it would be necessary to construct the collector in a three dimensional magnetostatics simulation software.

The eld map is a discrete representation of the magnetic eld in the structure. Important values of the magnetic eld map was only given from discrete measuring points along the measurement line shown in Figure 10, along which the Bx and Bycomponents were provided. From these the direction and magnitude of the eld could be calculated. Shown in Figure 11 are the two magnetic eld components, Bx and By, together with the magnitude |B| = q

B_x²+ B²_y along the measurement points shown in Figure 10. Notice that the eld is approximately zero up to ve centimetres from the centre and reaches its maximum strength at a point around 60 centimetres where the ns end.

Figure 11: Field components and magnitude along the measured line.

5 Implementation in FLUKA

In order to study the performance of the alternative collector, we constructed a model of the dedicated ESSnuSB target station. The target area was arranged, see Figure 12, in the Monte Carlo simulation code FLUKA [17] [18] which is a wide range physics simulation program for particle transport and interaction. The collector and decay tunnel were constructed using the FLUKA Advanced Interface (Flair) [19] where the decay tunnel was constructed as a 25 m long 2x2 m rectangle. The beginning of the collector and decay tunnel was made to coincide. The

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magnetic eld map and the pion source distribution were imported through programming of the user dened routines.

Figure 12: Geometry in FLUKA showing the decay tunnel and collector.

5.1 Collector Geometry

The geometry of the collector was constructed according to the outlines of the magnet in Figure 10. For simplicity a completely absorbing material was chosen for the ns and shell, denoted

"black hole" in FLUKA. This means that a particle is immediately absorbed when it comes in contact with a surface and no further interaction between particle and material occurs. The open areas inside the collector was set to vacuum, thus no particle interactions took place there. A n was constructed by adding together two triangles and cutting away the sharp tip near the centre region. The remaining ns were then copied and rotated in steps of 45 degrees using the built-in functions of the simulations program. The octagonal shell was constructed by combining two squares of equal size, where one was rotated by 45 degrees, to form the inner boundary. This was then repeated using larger squares for the outer boundary and the shell region was then designated as the area between the two boundaries. The result is the cylindrically symmetrical collector presented in Figure 13 and its corresponding FLUKA implementation can be seen in Appendix A.

Figure 13: Geometry of the collector in FLUKA showing a cross section in xy-plane.

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5.2 Magnetic Field Implementation

The magnetic eld map was imported through programming of the user dened routine magd.f as has been described in [10] and is presented in Appendix C. A rst order approximation of the magnetic eld, visualised in Figure 14, was formed from a combination of the measured eld components of the eld map, Figure 11, and the shape of the eld lines in Figure 10. Such approximation was necessary since the measurement points of the eld map does not cover the entire cross section of the collector. Inside the collector are ten focusing regions containing the magnetic eld, eight sections between the ns, one inside the ns and one outside the ns but inside the octagonal shell. In the outer region of the collector, the magnetic eld was modelled as an ideal toroidal eld, i.e. the magnetic eld lines are circular, comparable to the shape of the eld outside of the ns seen in Figure 10. The same shape of the eld was set for the centre region of the collector though, with a very low magnitude. The magnetic eld between two ns were approximated as straight lines between the centre lines of two adjacent ns. This means that the curvature of the eld lines near the edges of the ns are ignored. Note that the lines grow denser further away from the centre in Figure 14, thus providing a eld gradient in the radial direction.

Figure 14: Visualisation of the approximated magnetic eld.

5.3 Scoring

In order to evaluate the particle propagation throughout the simulation, we made use of the boundary crossing (BXDRAW) user routine which serves to score particle properties as they passed through a surface or boundary. In the simulation, inside the collector, a particle was scored as it hit one of the eight ns or the shell, and as it exited the back or front of the collector.

Particles that exited the front of the collector would then propagate inside the decay tunnel were they would be scored as they hit a wall or the end. The user routine is presented in Appendix D. The registered boundary crossings were then analysed and post-processed in MATLAB through an automated process based on MATLAB scripts specically developed for this analysis, an example is presented in Appendix E.

6 Collector Handling of the Pion Source

For the Los Alamos conductor to be considered a viable alternative it needs to perform compara- bly to the magnetic horn in terms of the nal neutrino intensity and purity at the position of the far detector. An understanding of the collector was provided from analysing how the focusing

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properties and pion intensity changes at dierent collector lengths, and how these were aecting the neutrino intensity further down the trajectory. The nal assessment was made by comparing the neutrino intensity of the alternative collector to a magnetic horn.

6.1 Optimizing the Collector Length

The length of the collector was not decided beforehand and to analyse this free parameter provided insight into the focusing eciency of the collector. It is reminded that the simulated eld is a hard edge model and there are therefore no fringe elds present. It was seen from the simulation of three dierent lengths L of the collector that a larger amount of focused positive pions emerged from the front end of the shortest collector, see Figure 15. The higher total pion acceptance of the shorter collector was thought to translate into a higher neutrino yield. This was shown to be false by analysing the neutrinos scored at the end of the decay tunnel which is presented in Table 3.

Figure 15: Momentum distribution of positive pions leaving the front of the collector for three dierent collector lengths L = 180, 200, 220 cm.

It was found that when the length of the collector was increased it became more suited to focus higher momenta pions from the source. Shown in Figure 16 is the distribution of the focused positive pion source upon leaving the collector into the decay tunnel. In this gure, it can be noticed a waist in the angular spread which shifts towards higher momenta for a longer collector.

Also, the overall angular spread is smaller for a longer collector, meaning that the pions are exiting the collector at smaller angles relative to the beam axis. The change in focusing eciency can be explained by the simultaneous increase in magnetic eld length and collector length. Thus, the integrated eld experienced by the pions inside the collector is increased. This allows higher momenta pions to be more eectively focused to a parallel trajectory.

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Figure 16: Distribution of positive pions when leaving the front end of the collector, shown for three dierent collector lengths.

In addition, the relation between pion momentum and the neutrino emission angle from Eq. (1) must be considered. Low energy pion decays result in a larger spread in emission angle which eectively cancels the focusing eciency to some extent. It is seen in Table 3 how the longest collector results in the highest muon neutrino yield at the end of the tunnel. This collector corresponds to a situation where the focusing has been optimized for a higher range of momenta, where the spread in neutrino emission angle is lower.

Table 3: Number of neutrinos for three dierent collector lengths at the end of the decay tunnel.

Collector Length L [cm] νµ ν¯µ νe ν¯e

220 8805 155 42 0

200 8101 221 50 2

180 6535 258 58 3

Another important aspect is how the contamination is aected by the length of the collector. It is shown that the number of contaminating neutrinos, ¯ν_µ, ν_e, ¯ν_e, decrease when the length of the collector is increased. The estimated contamination at the end of the decay tunnel amounts to around 2, 3, 5 % for the respective L = 220, 200, 180 cm collectors, although the statistics for these numbers are very low. This means that a longer collector not only provides higher neutrino intensity, it is also more ecient at defocusing the unwanted pion sign. Since the longer collector resulted in a higher neutrino yield, while indicating lower contamination, a collector length of 220 cm was found to be most benecial and was studied in more detail.

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6.2 Propagation of Pions and Muons

An investigation of the pion and muon propagation was made to describe how these travel from the source and further on in the simulation until eventually stopped by the dierent boundaries.

An overview is presented, describing what happens to the pions from the source. In Table 4, the fraction of the original distribution is listed for the several possible boundary interactions and the case when the pion decays inside the collector.

Table 4: Table of particle propagation for the 220 cm collector.

Particle

interaction Fraction of π⁺

source [%] Fraction of π⁻ source [%]

Fins 58 49

Shell 23 35

Decays inside 4 4

Exit front 9 3

Exit back 6 10

It was observed that a majority of the positive pions were stopped by the ns inside the collector, 58 %, and the shell, 23 %. We compare this to the calculated geometrical obstruction, 42 %, given by the opening angle of each n of around 19 degrees. The reason for the higher fraction of obstruction in the simulation is likely due to the pions being emitted from the source at a radial oset, corresponding to the target cylinder radius, and that their direction is not perfectly radial. Overall, the ns of the collector obstruct much of the path and should be narrowed to increase the overall intensity.

Further on, the pions which exit the front of the collector will continue into the decay tunnel.

In Table 5 it is, in columns two and three, shown what happens to the pions which went into the decay tunnel, i.e. the 9 % and 3 % of π⁺ and π⁻ respectively from Table 4. Along with the pions in the decay tunnel, there will be muons which were generated when the pions decayed inside the collector and inside the tunnel. The last two columns of Table 5 shows the fate of muons entering and generated in the tunnel.

Table 5: Table of particle propagation inside the decay tunnel.

Particle interaction

π⁺ [%] π⁻ [%] µ⁺ [%] µ⁻ [%]

Tunnel wall 59 94 70 97

Tunnel end 12 <1 29 3

Decays in tunnel 29 5 <1 <1

When analysing these fractions in terms of beam contamination, we notice the dierence in decay fractions. Comparing the fraction from the focused π⁺ to the defocused π⁻, almost one third decay in-ight compared to the 5 %. Having a high fraction of focused pions decay is desired since it will provide the neutrino beam. At the same time, having a low amount of the defocused pions decay is desired since it constitutes a source of background contamination by generating unwanted neutrinos as shown in Figure 3. The second source of contamination stems from the muon decay which has a very low fraction in both instances. The majority of muons are blocked by the walls and the end of the decay tunnel. The very small portion of muons decaying inside the tunnel is desirable since a muon decay generates two neutrinos, see Figure 3, that contribute to the contamination of the experiment.

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6.3 Comparison

A nal comparison was made between the alternative collector and the magnetic horn presented in [13]. The comparison was also made to include an unfocused source that simulated the eect of having no collector at all present. In this case, the structure and magnetic eld of the collector was removed, leaving the bare source for the simulation run. A fourth comparison was added to represent a perfectly focused source. This meant that all positive pions were directed parallel to the beam axis upon exiting the source, the collector structure and magnetic eld was removed here as well.

In each of the four simulations, the nal neutrino distributions, incident on the 2x2 m surface, at the end of the tunnel were recorded. These distributions included all neutrinos regardless of their angle relative to the beam axis. To provide a more accurate representation of the possible neutrino ux at the far detector, a restriction in the neutrino angle was introduced. The reason for such a restriction derives from considering the 540 km distance to the far detector. Since the neutrinos were scored 25 m downstream from the source, only those that travel near parallel to the beam axis would potentially hit the far detector. It was decided to limit the distribution of muon neutrinos to include those with a transverse momentum less or equal to 0.03 GeV/c.

This limit could be lowered even further, however, to do this would require a larger amount of simulated pions from the source to account for the decreased statistics. Shown in Figure 17 is the momentum spread of the restricted distributions of muon neutrinos from the four dierent simulations.

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Figure 17: Muon neutrino momentum distribution at the end of the decay tunnel with transverse momentum ≤ 0.03 GeV/c.

It is evident that the alternative collector greatly increases the neutrino intensity relative to the bare source but not to the extent necessary to compete with the magnetic horn. As can be seen, the magnetic horn is better at providing a wide range of momenta and produces a higher neutrino ux.

7 Conclusion

The alternative collector has been assessed as a potential candidate in the ESSnuSB project for focusing and charge separating a pion source. A DC operated collector, like the one investigated here, would accept the nominal linac pulse which render the accumulator ring and the H⁻ upgrades to the linac redundant.

It was shown how the alternative collector was formed from the information provided in the magnetic eld map and the collector geometry, then constructed in a simulation of the target area.

The focusing of a highly divergent pion source was shown in Figure 16 for three dierent collector lengths and how the intensity of pions varied. By including the decay tunnel, the analysis was expanded to provide a more thorough explanation of the particle propagation through the target area and to show what could be expected at the far detector. A simulation of the magnetic horn was made and compared to the neutrino intensity of the alternative collector. The alternative collector was shown to produce a neutrino intensity about a factor 3 lower than the van der Meer

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Horn.

It is worth noting that the alternative collector investigated here is a very rst design which still has many parameters to be optimised. During this project, many potential improvements to the alternative collector were discussed. The small acceptance of the alternative collector, roughly 58 % of pions are absorbed by the ns, means that it is of interest to reduce the thickness of the ns and thereby increase the pion intensity. The present steady state design has a moderate current density which can be increased by pulsing the magnet. An estimate by Davide Tommasini, using the nominal ESS linac pulse, showed that the ns could be made thinner by a factor 3-4 for pulsed operation. The pulsed operation would however require more advanced cooling to counter the induced heat generation from the increased current density. In addition, the shape and gradient of the magnetic eld can be altered by shaping the ns and manipulating the conductor placement. In shaping the eld, eects such as particle deection away from the boundaries of the ns could potentially lower the amount absorbed. In addition, an inherent advantage of the magnetic horn comes from the shape of its structure, seen in Figure 5, which allows the magnetic eld to reach very close to the beam axis. This eectively makes sure that particles from the source with small opening angles are focused by the eld. A similar eect in the alternative collector could possibly be accomplished by shaping the structure longitudinally.

To investigate this, an extensive study of a three dimensional model in a magnet design program is needed, from where it would also be possible to investigate the eect of fringe elds. To design the collector in this way is beyond the scope of this project.

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References

[1] European Spallation Source, Activity Report 2015,

https://europeanspallationsource.se/news-press/publications, Accessed: 2016-02-21.

[2] E. Baussan et al., A very intense neutrino super beam experiment for leptonic cp violation discovery based on the european spallation source linac, Nuclear Physics B, vol. 885, no. Supplement C, pp. 127 149, 2014.

[3] M. C. Gonzalez-Garcia, M. Maltoni, and T. Schwetz, Updated t to three neutrino mixing:

status of leptonic CP violation, JHEP, vol. 11, p. 052, 2014.

[4] P. Coloma and E. Fernandez-Martinez, Optimization of neutrino oscillation facilities for large θ13, JHEP, vol. 04, p. 089, 2012.

[5] G. C. Branco, T. Morozumi, B. M. Nobre, and M. N. Rebelo, A Bridge between CP violation at low-energies and leptogenesis, Nucl. Phys., vol. B617, pp. 475492, 2001.

[6] G. C. Branco, Cosmology and CP violation, eConf, vol. C030603, p. VEN05, 2003.

[,403(2003)].

[7] F. R. Joaquim, Neutrinos, leptonic CP violation and the origin of matter, in CP Violation and the Flavour Puzzle: Symposium in Honour of Gustavo C. Branco. GustavoFest 2005, Lisbon, Portugal, July 2005, pp. 119134, 2005.

[8] S. van der Meer, A Directive Device for Charged Particles and Its use in an Enhanced Neutrino Beam, 1961.

[9] M. Olvegård, A pion collector based on superconducting solenoids : A feasibility study for the essnusb, Tech. Rep. 2016/06, Uppsala University, Department of Physics and Astron- omy, 2016.

[10] P. Simion, Implementation of a solenoidal magnetic eld map in FLUKA [http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-320791]. 2017.

[11] D. Koetke, R. Fisk, D. Koetke, and T. Dombeck, A direct-current pion focusing magnet for low energy in-ight muon-neutrino beams, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equip- ment, vol. 378, no. 1, pp. 27 34, 1996.

[12] K. A. Olive et al., Review of Particle Physics, Chin. Phys., vol. C38, p. 34, 2014.

[13] N. Vassilopoulos, The ESS neutrino super beam optimization design studies, NuFact work- shop, Beijing, China, 2013.

[14] E. Baussan, J. Bielski, C. Bobeth, E. Bouquerel, O. Caretta, P. Cupial, T. Davenne, C. Den- sham, M. Dracos, M. Fitton, G. Gaudiot, M. Kozien, L. Lacny, B. Lepers, A. Longhin, P. Loveridge, F. Osswald, P. Poussot, M. Rooney, B. Skoczen, B. Szybinski, A. Ustrzycka, N. Vassilopoulos, D. Wilcox, A. Wroblewski, J. Wurtz, V. Zeter, and M. Zito, Neutrino super beam based on a superconducting proton linac, Phys. Rev. ST Accel. Beams, vol. 17, p. 031001, Mar 2014.

[15] J. A. Formaggio and G. P. Zeller, From eV to EeV: Neutrino Cross Sections Across Energy Scales, Rev. Mod. Phys., vol. 84, pp. 13071341, 2012.

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[16] A. Batalov, M. Maslov, V. Rykov, P. Scherbakov, Z. Sharifullin, L. Shirshov, M. Grachev, and A. Samoilov, A focusing device for neutrino sources at meson factories, Nuclear Instru- ments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 251, no. 2, pp. 231 241, 1986.

[17] G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraroi, J. Ranft, S. Roesler, and P. R. Sala, The FLUKA code: Description and benchmarking, AIP Conf. Proc., vol. 896, no. SLAC-REPRINT-2007-184, pp. 3149. 19 p, 2007.

[18] A. Ferrari, P. R. Sala, A. Fasso, and J. Ranft, FLUKA: A multi-particle transport code (program version 2005). Geneva: CERN, 2005. CERN-2005-10; INFN/TC_05/11; SLAC- R-773.

[19] V. Vlachoudis, Flair: A powerful but user friendly graphical interface for FLUKA, in Proceedings of the Int. Conf. on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, New York, U.S.A. (2009), 2009.

[20] Fluka user routine source le. https://www.fluka.org/free_download/course/

demokritos2009/participants/ex08/source.f. [Online; Accessed 2016-03-26].

8 Appendix

8.1 Appendix A

Collector and target area conguration in FLUKA.

TITLE

L e n t i l l e Geometry

∗ Set the d e f a u l t s f o r precision s i m u l a t i o n s

DEFAULTS PRECISIO

∗ Define the beam c h a r a c t e r i s t i c s

BEAM 4 . 0 3140.0 1 . 0PION−

∗ Define the beam position

BEAMPOS 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0

SOURCE

GEOBEGIN COMBNAME

0 0

RPP binner1 −75.0 75.0 −75. 7 5 . 0 . 0 220.0

BOX binner2 −105.0 0 . 0 0 . 0 0 . 0 0 . 0 220.0 106.06601717798 −106.066017178 0 . 0 106.06601717798 106.06601717798 0 . 0

RPP bouter1 −100.0 100.0 −100. 100. 0 . 0 220.0

BOX bouter2 −142.0 0 . 0 0 . 0 0 . 0 0 . 0 220.0 141.42135623731 −141.4213562373 0 . 0 141.42135623731 141.42135623731 0 . 0

YZP bplane1 0 . 0 XZP bplane2 0 . 0

PLA bplane3 .70710678118655 .70710678118655 0 . 0 0 . 0 0 . 0 0 . 0 PLA bplane4 −.7071067811866 .70710678118655 0 . 0 0 . 0 0 . 0 0 . 0 WED bpin1 60.0 0 . 0 0 . 0 0 . 0 10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

WED bpin2 60.0 0 . 0 0 . 0 0 . 0 −10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

$start_transform −ROTPIN1

WED bpin3 60.0 0 . 0 0 . 0 0 . 0 10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.0 WED bpin4 60.0 0 . 0 0 . 0 0 . 0 −10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

$end_transform

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WED bpin5 60.0 0 . 0 0 . 0 0 . 0 10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

WED bpin6 60.0 0 . 0 0 . 0 0 . 0 −10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

$end_transform

WED bpin7 60.0 0 . 0 0 . 0 0 . 0 10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

WED bpin8 60.0 0 . 0 0 . 0 0 . 0 −10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

$end_transform

WED bpin9 60.0 0 . 0 0 . 0 0 . 0 10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

WED bpin10 60.0 0 . 0 0 . 0 0 . 0 −10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

$end_transform

WED bpin11 60.0 0 . 0 0 . 0 0 . 0 10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

WED bpin12 60.0 0 . 0 0 . 0 0 . 0 −10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

$end_transform

WED bpin13 60.0 0 . 0 0 . 0 0 . 0 10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

WED bpin14 60.0 0 . 0 0 . 0 0 . 0 −10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

$end_transform

WED bpin15 60.0 0 . 0 0 . 0 0 . 0 10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

WED bpin16 60.0 0 . 0 0 . 0 0 . 0 −10.0 0 . 0 −60.0 0 . 0 0 . 0 0 . 0 0 . 0 220.

$end_transform

ZCC b c e n t c i 1 0 . 0 0 . 0 5 . 1 ZCC b c e n t c i 2 0 . 0 0 . 0 6 0 . XYP body1 0 . 0

XYP body2 220.0

RPP body3 −190.0 190.0 −190. 190.0 −190.0 2500.

RPP body4 −220.0 220.0 −220.0 220.0 −220.0 2510.

RPP body5 −100.0 100.0 −100.0 100.0 202.0 2500.0 RPP body6 −101.0 101.0 −101.0 101.0 202.0 2500.0 END

∗ 1) Black Hole

BLKBODY 5 −body3 +body4

∗ 2) Void

VOID 5 +body3 −(bouter1 +bouter2 ) −body6

∗ 3) Octagon S h e l l o f L e n t i l l e

SHELL 5 +bouter1 +bouter2 −binner2

| +bouter1 +bouter2 −binner1

∗ 4) 1 s t Part o f L e n t i l l e F i e l d

RINM1 5 +bplane4 +b c e n t c i 2 +body2 −bplane2 −bpin1 −bpin4 −b c e n t c i 1 −body1

∗ 5) 2nd Part o f L e n t i l l e F i e l d

RINM2 5 +b c e n t c i 2 +body2 −bplane1 −bplane4 −bpin3 −bpin6 −b c e n t c i 1 −body1

∗ 6) 3 rd Part o f L e n t i l l e F i e l d

∗ 7) 4 th Part o f L e n t i l l e F i e l d

RINM6 5 +bplane1 +bplane4 +b c e n t c i 2 +body2 −bpin11 −bpin14 −b c e n t c i 1 −body1

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∗ 12) 1 s t Pin in L e n t i l l e RPIN1 5 +bpin1 −b c e n t c i 1

| +bpin2 −b c e n t c i 1

∗ 13) 2nd Pin in L e n t i l l e RPIN2 5 +bpin3 −b c e n t c i 1

∗ 14) 3 rd Pin in L e n t i l l e RPIN3 5 +bpin5 −b c e n t c i 1

∗ 15) 4 th Pin in L e n t i l l e RPIN4 5 +bpin7 −b c e n t c i 1

∗ 16) 5 th Pin in L e n t i l l e RPIN5 5 +bpin9 −b c e n t c i 1

∗ 17) 6 th Pin in L e n t i l l e

RPIN6 5 +bpin11 −b c e n t c i 1

∗ 20) Outer C y l i n d r i c a l F i e l d in L e n t i l l e

RINO 5 +binner1 +binner2 −bpin1 −bpin2 −bpin3 −bpin4 −bpin5 −bpin6

−bpin7 −bpin8 −bpin9 −bpin10 −bpin11

−bpin12 −bpin13 −bpin14 −bpin15 −bpin16 −b c e n t c i 2 +body2 −body1

∗ 21) Inner C y l i n d r i c a l F i e l d in L e n t i l l e RINC1 5 +b c e n t c i 1 +body2 −body1

∗ 22) Decay Tunnel RDECTUN 5 +body5

∗ 23)

RDECTBH 5 +body6 −body5 ENDGEOEND

∗ . . + . . . . 1 . . . . + . . . . 2 . . . . + . . . . 3 . . . . + . . . . 4 . . . . + . . . . 5 . . . . + . . . . 6 . . . . + . . . . 7 . . ASSIGNMA BLCKHOLE BLKBODY

ASSIGNMA VACUUM VOID

ASSIGNMA BLCKHOLE SHELL

ASSIGNMA VACUUM RINM1 1 .

ASSIGNMA BLCKHOLE RPIN1 ASSIGNMA BLCKHOLE RPIN2 ASSIGNMA BLCKHOLE RPIN3 ASSIGNMA BLCKHOLE RPIN4 ASSIGNMA BLCKHOLE RPIN5

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ASSIGNMA BLCKHOLE RPIN6 ASSIGNMA BLCKHOLE RPIN7 ASSIGNMA BLCKHOLE RPIN8

ASSIGNMA VACUUM RINO 1 .

ASSIGNMA VACUUM RINC1 1 .

ASSIGNMA VACUUM RDECTUN ASSIGNMA BLCKHOLE RDECTBH

MGNFIELD 3 0 . 1 0 . 0.05

ROT−DEFI 300. 4 5 . ROTPIN1

ROT−DEFI 300. 9 0 . ROTPIN2

ROT−DEFI 300. 135. ROTPIN3

ROT−DEFI 300. 180. ROTPIN4

ROT−DEFI 300. −135. ROTPIN5

USERDUMP 100. 3 6 . 0 . 0 1 . Dump

∗ Set the random number seed

RANDOMIZ 1 .

∗ Set the number o f primary h i s t o r i e s to be simulated in the run

START 2889504.

RADDECAY 1 . 99999

DISCARD −NEUTRIE −NEUTRIM −ANEUTRIE −ANEUTRIM STOP

8.2 Appendix B

Edit of the source.f subroutine found at [20] which handles the simulation of pions from the source distribution.

∗$ CREATE SOURCE.FOR

∗COPY SOURCE

∗

∗=== source ===========================================================∗

∗

SUBROUTINE SOURCE ( NOMORE ) INCLUDE ' (DBLPRC) '

INCLUDE ' (DIMPAR) ' INCLUDE ' (IOUNIT) '

∗

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ ∗

∗ New source f o r FLUKA9x−FLUKA20xy : ∗

∗ ∗

∗ Created on 07 january 1990 by Alfredo F e r r a r i & Paola Sala ∗

∗ Infn − Milan ∗

∗ ∗

∗ Last change on 08−feb −09 by Alfredo F e r r a r i ∗

∗ ∗

∗ This i s j u s t an example o f a p o s s i b l e user w r i t t e n source r o u t i n e . ∗

(27)

∗ note that the beam card s t i l l has some meaning − in the s c o r i n g the ∗

∗ maximum momentum used in d e c i d i n g the binning i s taken from the ∗

∗ beam momentum . Other beam card parameters are o b s o l e t e . ∗

∗ ∗

∗ Output v a r i a b l e s : ∗

∗ ∗

∗ Nomore = i f > 0 the run w i l l be terminated ∗

∗ ∗

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗

INCLUDE ' (BEAMCM) ' INCLUDE ' (FHEAVY) ' INCLUDE ' (FLKSTK) ' INCLUDE ' (IOIOCM) ' INCLUDE ' (LTCLCM) ' INCLUDE ' (PAPROP) ' INCLUDE ' (SOURCM) ' INCLUDE ' (SUMCOU) '

∗

LOGICAL LFIRST

REAL∗8 x , y , z , px , py , pz SAVE LFIRST

DATA LFIRST / .TRUE. /

∗======================================================================∗

∗ ∗

∗ BASIC VERSION ∗

∗ ∗

∗======================================================================∗

NOMORE = 0

∗ +−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ | F i r s t c a l l i n i t i a l i z a t i o n s : IF ( LFIRST ) THEN

∗ | ∗∗∗ The f o l l o w i n g 3 cards are mandatory ∗∗∗

TKESUM = ZERZER LFIRST = .FALSE.

LUSSRC = .TRUE.

∗ | ∗∗∗ User i n i t i a l i z a t i o n ∗∗∗

OPEN (21 , FILE = ' /home/ f l u p i x / Desktop / FlukaShared / SourceData / PiPl

&us . txt ' , STATUS = 'OLD' )

∗ OPEN (45 , FILE =' /home/ f l u p i x / Desktop / FlukaShared / SourceData /Out ' ) END IF

∗ |

∗ +−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

read (21 , ∗) x , y , z , px , py , pz

∗ Push one source p a r t i c l e to the stack . Note that you could as w e l l

∗ push many but t h i s way we r e s e r v e a maximum amount o f space in the

∗ stack f o r the s e c o n d a r i e s to be generated

∗ Npflka i s the stack counter : o f course any time source i s c a l l e d i t

∗ must be =0

NPFLKA = NPFLKA + 1

∗ Wt i s the weight o f the p a r t i c l e

(28)

WTFLK (NPFLKA) = ONEONE

WEIPRI = WEIPRI + WTFLK (NPFLKA)

∗ P a r t i c l e type (1= proton . . . ) . Ijbeam i s the type s e t by the BEAM

∗ card

∗ +−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ | ( Radioactive ) i s o t o p e :

IF ( IJBEAM .EQ. −2 .AND. LRDBEA ) THEN IARES = IPROA

IZRES = IPROZ IISRES = IPROM

CALL STISBM ( IARES , IZRES , IISRES ) IJHION = IPROZ ∗ 1000 + IPROA IJHION = IJHION ∗ 100 + KXHEAV IONID = IJHION

CALL DCDION ( IONID ) CALL SETION ( IONID )

∗ |

∗ +−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ | Heavy ion :

ELSE IF ( IJBEAM .EQ. −2 ) THEN IJHION = IPROZ ∗ 1000 + IPROA IJHION = IJHION ∗ 100 + KXHEAV IONID = IJHION

CALL DCDION ( IONID ) CALL SETION ( IONID )

ILOFLK (NPFLKA) = IJHION

∗ | Flag t h i s i s prompt r a d i a t i o n LRADDC (NPFLKA) = .FALSE.

∗ |

∗ +−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ | Normal hadron : ELSE

IONID = IJBEAM

ILOFLK (NPFLKA) = IJBEAM

∗ | Flag t h i s i s prompt r a d i a t i o n LRADDC (NPFLKA) = .FALSE.

END IF

∗ |

∗ +−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ P a r t i c l e g e n e r a t i o n (1 f o r p r i m a r i e s ) LOFLK (NPFLKA) = 1

∗ User dependent f l a g : LOUSE (NPFLKA) = 0

∗ User dependent spare v a r i a b l e s : DO 100 ISPR = 1 , MKBMX1

SPAREK (ISPR ,NPFLKA) = ZERZER 100 CONTINUE

∗ User dependent spare f l a g s : DO 200 ISPR = 1 , MKBMX2

ISPARK (ISPR ,NPFLKA) = 0 200 CONTINUE

∗ Save the track number o f the stack p a r t i c l e : ISPARK (MKBMX2,NPFLKA) = NPFLKA

NPARMA = NPARMA + 1

(29)

NUMPAR (NPFLKA) = NPARMA NEVENT (NPFLKA) = 0

DFNEAR (NPFLKA) = +ZERZER

∗ P a r t i c l e age ( s )

AGESTK (NPFLKA) = +ZERZER AKNSHR (NPFLKA) = −TWOTWO

∗ Group number f o r "low" energy neutrons , s e t to 0 anyway IGROUP (NPFLKA) = 0

∗ K i n e t i c energy o f the p a r t i c l e (GeV)

∗ TKEFLK (NPFLKA) = SQRT ( PBEAM∗∗2 + AM (IONID)∗∗2 ) − AM (IONID)

∗ do I need the parantheses around " energy "?

TKEFLK (NPFLKA) = SQRT( ( px∗∗2+py∗∗2+pz∗∗2)+AM(IONID)∗∗2) −AM(IONID)

∗ P a r t i c l e momentum

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

∗ PMOFLK (NPFLKA) = PBEAM

PMOFLK (NPFLKA) = SQRT( px∗∗2+py∗∗2+pz ∗∗2)

∗SQRT ( TKEFLK (NPFLKA) ∗ ( TKEFLK (NPFLKA)

∗ & + TWOTWO ∗ AM (IONID) ) )

∗ Cosines ( tx , ty , tz )

TXFLK (NPFLKA) = px/PMOFLK(NPFLKA) TYFLK (NPFLKA) = py/PMOFLK(NPFLKA)

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

∗ TZFLK (NPFLKA) = WBEAM TZFLK (NPFLKA) = pz/PMOFLK(NPFLKA)

∗SQRT ( ONEONE − TXFLK (NPFLKA)∗∗2

∗ & − TYFLK (NPFLKA)∗∗2 )

∗ P o l a r i z a t i o n c o s i n e s : TXPOL (NPFLKA) = −TWOTWO TYPOL (NPFLKA) = +ZERZER TZPOL (NPFLKA) = +ZERZER XFLK (NPFLKA) = x

YFLK (NPFLKA) = y ZFLK (NPFLKA) = z

∗ WRITE(45 , ∗) REAL( x ) , REAL( y ) , REAL( z ) , REAL( px ) , REAL( py ) ,

∗ &REAL( pz ) , REAL(TXFLK (NPFLKA) ) , REAL(TYFLK (NPFLKA) ) ,

∗ &REAL(TZFLK (NPFLKA) ) ,REAL(PMOFLK (NPFLKA) ) , REAL(TKEFLK (NPFLKA) )

∗ C a l c u l a t e the t o t a l k i n e t i c energy o f the p r i m a r i e s : don ' t change IF (ILOFLK(NPFLKA) .EQ. −2.OR. ILOFLK(NPFLKA) .GT.100 000 )

&THEN

TKESUM = TKESUM + TKEFLK(NPFLKA) ∗ WTFLK(NPFLKA) ELSE IF (ILOFLK(NPFLKA) .NE. 0 ) THEN

TKESUM = TKESUM + ( TKEFLK (NPFLKA) + AMDISC (ILOFLK(NPFLKA) ) )

& ∗ WTFLK (NPFLKA)

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TKESUM = TKESUM + TKEFLK (NPFLKA) ∗ WTFLK (NPFLKA)ELSE END IF

RADDLY (NPFLKA) = ZERZER

CALL GEOCRS ( TXFLK (NPFLKA) , TYFLK (NPFLKA) , TZFLK (NPFLKA) ) CALL GEOREG ( XFLK (NPFLKA) , YFLK (NPFLKA) , ZFLK (NPFLKA) ,

& NRGFLK(NPFLKA) , IDISC )

∗ Do not change t h e s e cards :

CALL GEOHSM ( NHSPNT (NPFLKA) , 1 , −11, MLATTC ) NLATTC (NPFLKA) = MLATTC

CMPATH (NPFLKA) = ZERZER CALL SOEVSV

RETURN

∗=== End o f subroutine Source =========================================∗

END

8.3 Appendix C

Magd.f subroutine governing the magnetic eld inside the collector.

∗

∗===magfld=============================================================∗

∗

SUBROUTINE MAGFLD ( X, Y, Z , BTX, BTY, BTZ, B, NREG, IDISC ) INCLUDE ' (DBLPRC) '

∗

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ ∗

∗ Created in 1988 by Alberto Fasso ` ∗

∗ ∗

∗ Last change on 06−Nov−10 by Alfredo F e r r a r i ∗

∗ ∗

∗ Input v a r i a b l e s : ∗

∗ x , y , z = c u r r e n t position ∗

∗ nreg = c u r r e n t r e g i o n ∗

∗ Output v a r i a b l e s : ∗

∗ btx , bty , btz = c o s i n e s o f the magn . f i e l d v e c t o r ∗

∗ B = magnetic f i e l d i n t e n s i t y ( Tesla ) ∗

∗ i d i s c = s e t to 1 i f the p a r t i c l e has to be d i s c a r d e d ∗

∗ ∗

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ Parameters ∗

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PARAMETER (NR = 101)

DOUBLE PRECISION BR(NR) ,BRX,BRY, DIR1 , DIR2 ,N, PI ,R, R2 , dr DIMENSION RB(NR)

PARAMETER ( PI = 3.14159265)

PARAMETER (DIR1 = −0.38268343236509) PARAMETER (DIR2 = 0.92387953251129) INTEGER i

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ LFIRST − Only runs once at f i r s t c a l l to r o u t i n e ∗

∗ Reads the magnetic f i e l d map and saves v a l u e s in r e s p e c t i v e v e c t o r s ∗

∗ RB( i ) − D i s c r e t e position v e c t o r in r a d i a l d i r e c t i o n ∗

∗ BR( i ) − Magnetic f i e l d magnitude in r a d i a l d i r e c t i o n ∗ LOGICAL LFIRST

SAVE LFIRST

DATA LFIRST / .TRUE. / IF (LFIRST) THEN

OPEN(UNIT = 20 , FILE = ' /home/ f l u p i x / Desktop / FlukaShared /LENTIL/

&FLUKAOUTPUTLENTIL. txt ' )

&RBDATA. txt ' )

&BRDATA. txt ' ) DO i = 1 , NR READ(40 , ∗) RB( i ) READ(41 , ∗) BR( i ) END DO

CLOSE(40 41) LFIRST = .FALSE.

ENDIF

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ Finds c l o s e s t r e p r e s e n t a t i o n o f simulated p a r t i c l e ∗

∗ in the position v e c t o r RB( i ) and r e t u r n s the index o f the ∗

∗ found position ∗ i = 1

dr = RB(NR) / (NR−1) R = SQRT(X∗∗2 + Y∗∗2) DO WHILE (R.GT.RB( i )+dr /2)

i = i +1 END DO

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ Resolves r a d i a l magnetic f i e l d i n t o x−y components ∗

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∗ and a s s i g n s the d i r e c t i o n c o s i n e s , BTX/BTY f o r each f i e l d ∗

∗ component in c a r t e s i a n c o o r d i n a t e s ∗ IDISC = 0

R2 = X∗∗2 + Y∗∗2 IF (NREG.EQ. 2 1 ) THEN GO TO 21

ELSE IF (NREG.EQ. 2 0 ) THEN GO TO 40

ELSE IF (NREG.EQ. 4 ) THEN GO TO 4

ENDIF

∗ INNER CYLINDER

21 CONTINUE

IF ( i .EQ. 1 ) THEN GO TO 30

GO TO 40ELSE ENDIF

∗ OUTER CYLINDER

20 CONTINUE

GO TO 40 RETURN

∗ RINM1

4 CONTINUE

BRX = DIR1∗BR( i ) BRY = DIR2∗BR( i ) GO TO 41

RETURN

∗ RINM2

5 CONTINUE

BRX = −DIR2∗BR( i ) BRY = −DIR1∗BR( i ) GO TO 41

RETURN

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∗ RINM3

6 CONTINUE

BRX = −DIR2∗BR( i ) BRY = DIR1∗BR( i ) GO TO 41

RETURN

∗ RINM4

7 CONTINUE

BRX = DIR1∗BR( i ) BRY = −DIR2∗BR( i ) GO TO 41

RETURN

∗ RINM5

8 CONTINUE

BRX = −DIR1∗BR( i ) BRY = −DIR2∗BR( i ) GO TO 41

RETURN

∗ RINM6

9 CONTINUE

BRX = DIR2∗BR( i ) BRY = DIR1∗BR( i ) GO TO 41

RETURN

∗ RINM7

10 CONTINUE

BRX = DIR2∗BR( i ) BRY = −DIR1∗BR( i ) GO TO 41

RETURN

∗ RINM8

11 CONTINUE

BRX = −DIR1∗BR( i ) BRY = DIR2∗BR( i ) GO TO 41

RETURN

∗ ZERO FIELD DEFINITION

30 CONTINUE

BTX = ZERZER BTY = ZERZER BTZ = ZERZER B = ZERZER RETURN

∗ CIRCULAR FIELD DEFINITION

40 CONTINUE

IF ( i .EQ. 1 ) THEN

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B = ZERZER BTX = ZERZER BTY = ZERZER ELSEBRX = −BR( i )∗Y/R2 BRY = BR( i )∗X/R2

B = SQRT(BRX∗∗2 + BRY∗∗2) BTX = BRX/B

BTY = BRY/B ENDIF

BTZ = ZERZER RETURN

41 CONTINUE

B = SQRT(BRX∗∗2 + BRY∗∗2) BTX = BRX/B

BTY = BRY/B BTZ = ZERZER RETURN

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗====================== End o f subroutine Magfld ======================∗

END

8.4 Appendix D

Subroutine mgdraw.f with the congured BXDRAW section which is responsible for scoring of all particles throughout the simulation.

∗$ CREATE MGDRAW.FOR

∗COPY MGDRAW

∗ ∗

∗=== mgdraw ===========================================================∗

∗ ∗

SUBROUTINE MGDRAW ( ICODE, MREG ) INCLUDE ' (DBLPRC) '

∗

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗ ∗

∗ MaGnetic f i e l d t r a j e c t o r y DRAWing: a c t u a l l y t h i s entry manages ∗

∗ a l l t r a j e c t o r y dumping f o r ∗

∗ drawing ∗

∗ ∗

∗ Created on 01 march 1990 by Alfredo F e r r a r i ∗

∗ INFN − Milan ∗

∗ Last change 05−may−06 by Alfredo F e r r a r i ∗

(35)

∗ INFN − Milan ∗

∗ ∗

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗

∗

INCLUDE ' (CASLIM) ' INCLUDE ' (COMPUT) ' INCLUDE ' (SOURCM) ' INCLUDE ' (FHEAVY) ' INCLUDE ' (FLKSTK) ' INCLUDE ' (GENSTK) ' INCLUDE ' (MGDDCM) ' INCLUDE ' (PAPROP) ' INCLUDE ' (QUEMGD) ' INCLUDE ' (SUMCOU) ' INCLUDE ' (TRACKR) '

∗

∗======================================================================∗

∗ ∗

∗ Boundary−(X) c r o s s i n g DRAWing: ∗

∗ ∗

∗ Icode = 1x : c a l l from Kaskad ∗

∗ 1 9 : boundary c r o s s i n g ∗

∗ Icode = 2x : c a l l from Emfsco ∗

∗ Icode = 3x : c a l l from Kasneu ∗

∗ Icode = 4x : c a l l from Kashea ∗

∗ Icode = 5x : c a l l from Kasoph ∗

∗ ∗

∗======================================================================∗

∗ ∗

ENTRY BXDRAW ( ICODE, MREG, NEWREG, XSCO, YSCO, ZSCO )

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

∗ CROSSINGS:

∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

100 FORMAT( F12 . 6 , 3X, F12 . 6 , 3X, F12 . 6 , 3X, F12 . 6 , 3X, F12 . 6 , 3X

& , F12 . 6 , 3X, F12 . 6 , 3X, F12 . 6 , 3X, F12 . 6 , 3X, F12 . 6

& , F12 . 6 , 3X, F12 . 6 , 3X, F12 . 6 , 3X, F12 . 6 )

OPEN (UNIT=35, f i l e= ' /home/ f l u p i x / Desktop / FlukaShared /LENTIL/D

&umpLentille88 . txt ' )

OPEN (UNIT=36, f i l e= ' /home/ f l u p i x / Desktop / FlukaShared /LENTIL/F

&a r D e t L e n t i l l e 8 8 . txt ' )

IF(MREG.EQ. 2 1 . and .NEWREG.EQ. 2 ) THEN

WRITE(35 , 100) REAL(XSCO) ,REAL(YSCO) ,REAL(ZSCO) ,

& REAL(CXTRCK) ,REAL(CYTRCK) ,REAL(CZTRCK) ,REAL(PTRACK) ,

& REAL(NEWREG) , REAL(JTRACK) , REAL(ZFLK(NPFLKA) ) ,

& REAL(TXFLK(NPFLKA) ) ,REAL(TYFLK(NPFLKA) ) ,

& REAL(TZFLK(NPFLKA) ) , REAL(PMOFLK(NPFLKA) ) END IF

Study of an Alternative Pion Collector Scheme for the ESS Neutrino Super Beam Project

Examensarbete 30 hp Februari 2019

Study of an Alternative Pion Collector Scheme for the ESS Neutrino Super Beam Project

Patrik Simion

Abstract

Study of an Alternative Pion Collector Scheme for the ESS Neutrino Super Beam Project

Patrik Simion

Populärvetenskaplig sammanfattning

Contents

1 Introduction

2 The Experiment and its Requirements

2.1 Far Detector

2.2 Collector

2.3 Pion and Muon Propagation

3 Target Station and Pion Distribution

3.1 Van der Meer Magnetic Horn

3.2 The Target and the Pion Source

4 Alternative Collector

4.1 History

4.2 Magnetic Field Map

5 Implementation in FLUKA

5.1 Collector Geometry

5.2 Magnetic Field Implementation

5.3 Scoring

6 Collector Handling of the Pion Source

6.1 Optimizing the Collector Length

6.2 Propagation of Pions and Muons

6.3 Comparison

7 Conclusion

References

8 Appendix

8.1 Appendix A

8.2 Appendix B

8.3 Appendix C

8.4 Appendix D