Cosmic Rays' study with a TRASGO detector

INTERNATIONAL DOCTORAL SCHOOL OF THE USC Damián García Castro PhD Thesis Cosmic Rays' study with a TRASGO detector Santiago de Compostela, 2022 Doctoral Programme in Nuclear and Particles Physics TESE DE DOUTORAMENTO COSMIC RAYS’ STUDY WITH A TRASGO DETECTOR Damián García Castro ESCOLA DE DOUTORAMENTO INTERNACIONAL DA UNIVERSIDADE DE SANTIAGO DE COMPOSTELA PROGRAMA DE DOUTORAMENTO EN FÍSICA NUCLEAR E DE PARTÍCULAS SANTIAGO DE COMPOSTELA 2022 DECLARACIÓN DE AUTOR DA TESE D. Damián García Castro Título da tese: Cosmic rays’ study with a TRASGO detector Presento a miña tese, seguindo o procedemento axeitado ao Regulamento, e declaro que: 1) A tese abarca os resultados da elaboración do meu traballo. 2) De selo caso, na tese faise referencia ás colaboracións que tivo este traballo. 3) A tese é a versión definitiva presentada para a súa defensa e coincide coa versión impresa presentada en formato electrónico. 4) Confirmo que a tese non incorre en ningún tipo de plaxio doutros autores nin de traballos presentados por min para a obtención doutros títulos. E comprométome a presentar o Compromiso Documental de Supervisión no caso de que o orixinal non estea na Escola. En Santiago de Compostela, 11 de Maio de 2022 Asdo. Damián García Castro AUTORIZACIÓN DO DIRECTOR DA TESE D. Juan Pablo Garzón Heydt En condición de: Director Título da tese: Cosmic rays’ study with a TRASGO detector INFORMA: Que a presente tese, correspóndese co traballo realizado por D. Damián García Castro, baixo a miña dirección, e autorizo a súa presentación, considerando que reúne os requisitos esixidos no Regulamento de Estudos de Doutoramento da USC, e que como director/titor non incorre nas causas de abstención establecidas na Lei 40/2015. En Santiago de Compostela, 11 de Maio de 2022 Asdo. Juan Pablo Garzón Heydt AUTORIZACIÓN DO TITOR DA TESE D. Héctor Álvarez Pol En condición de: Titor Título da tese: Cosmic rays’ study with a TRASGO detector INFORMA: Que a presente tese, correspóndese co traballo realizado por D. Damián García Castro, baixo a miña titorización, e autorizo a súa presentación, considerando que reúne os requisitos esixidos no Regulamento de Estudos de Doutoramento da USC, e que como titor non incorre nas causas de abstención establecidas na Lei 40/2015. En Santiago de Compostela, 11 de Maio de 2022 Asdo. Héctor Álvarez Pol TABLE OF CONTENTS TABLE OF CONTENTS .............................................................. 1 ABBREVIATIONS ........................................................................ i INTRODUCTION ......................................................................... 1 OBJECTIVES ............................................................................... 5 1 COSMIC RAYS ..................................................................... 9 1.1 DISCOVERING THE COSMIC RAYS ................................................... 9 1.2 PROPERTIES ................................................................................. 10 1.2.1 Energy spectrum ..................................................................................... 11 1.2.2 Composition ........................................................................................... 13 1.2.3 Sources and propagation ........................................................................ 14 1.3 INFLUENCE OF MAGNETIC FIELDS ................................................ 16 1.3.1 Intergalactic ............................................................................................ 17 1.3.2 Galactic .................................................................................................. 17 1.3.3 Heliospheric ........................................................................................... 17 1.3.4 Geomagnetic .......................................................................................... 18 1.3.4.1 South Atlantic Anomaly ................................................................. 19 1.3.4.2 Cutoff rigidity ................................................................................. 20 1.3.4.3 Latitudinal effect ............................................................................ 21 1.3.4.4 Atmospheric effect ......................................................................... 21 1.4 SOLAR MODULATION .................................................................... 22 1.5 INTERACTION WITH THE EARTH’S ATMOSPHERE ......................... 24 1.5.1 EAS ........................................................................................................ 24 1.5.1.1 Hadronic component ...................................................................... 25 1.5.1.2 Muonic component ......................................................................... 26 1.5.1.3 Eletromagnetic component ............................................................. 26 1.5.1.4 Time and density microestructure .................................................. 27 1.5.2 Atmospheric effects ................................................................................ 28 1.5.2.1 Pressure .......................................................................................... 28 1.5.2.2 Temperature ................................................................................... 29 1.6 DETECTION METHODS .................................................................. 32 1.6.1 Direct ..................................................................................................... 33 1.6.2 Indirect .................................................................................................. 33 2 GASEOUS IONIZATION DETECTORS ............................ 35 2.1 RADIATION-MATTER INTERACTION ............................................. 35 2.1.1 Interaction of charged particles with matter .......................................... 36 2.1.1.1 Heavy particles .............................................................................. 36 2.1.1.2 Electrons and positrons .................................................................. 40 2.1.2 Interaction of neutral particles with matter ............................................ 42 2.1.2.1 Photons .......................................................................................... 42 2.1.2.2 Neutrons ......................................................................................... 42 2.2 OPERATION PRINCIPLE OF GAS DETECTORS ................................ 43 2.2.1 Working regimes ................................................................................... 44 2.2.2 Avalanche multiplication ....................................................................... 45 2.3 RESISTIVE PLATE CHAMBERS ....................................................... 47 3 TRASGO DETECTORS ...................................................... 53 3.1 THE TRASGO PROJECT ................................................................. 53 3.2 DETECTORS ................................................................................. 54 3.2.1 TRAGALDABAS ................................................................................. 55 3.2.2 TRISTAN .............................................................................................. 58 3.2.3 muTT ..................................................................................................... 61 3.2.4 STRATOS ............................................................................................. 63 4 ELECTRONIC SYSTEMS .................................................. 67 4.1 INTRODUCTION TO THE COMPONENTS ......................................... 67 4.2 FRONT-END ELECTRONICS ........................................................... 68 4.2.1 DBO ...................................................................................................... 68 4.2.2 MBO ...................................................................................................... 69 4.3 DATA ACQUISITION SYSTEM ......................................................... 70 4.3.1 TRB ....................................................................................................... 70 4.3.1.1 TRB version 2 ................................................................................ 71 4.3.1.2 TRB version 3 ................................................................................ 71 4.3.2 Trigger system ....................................................................................... 71 4.4 ENVIRONMENTAL SENSORS .......................................................... 73 4.4.1 Presure .................................................................................................... 73 4.4.2 Relative humidity ................................................................................... 74 4.4.3 Temperature ........................................................................................... 74 4.5 POWER SUPPLY ............................................................................. 75 4.5.1 LV .......................................................................................................... 75 4.5.2 HV .......................................................................................................... 75 4.6 GAS SYSTEM ................................................................................. 77 4.6.1 Bubbler ................................................................................................... 77 4.7 TRISTAN-TRAGALDABAS EQUIPMENT .......................................... 78 4.7.1 TRISTAN ............................................................................................... 78 4.7.2 TRAGALDABAS .................................................................................. 83 5 SLOW CONTROL AND MONITORING ........................... 89 5.1 OVERVIEW .................................................................................... 89 5.2 PARAMETERS CONTROLLED BY THE SCMS ................................... 90 5.3 SENSOR READING ......................................................................... 91 5.3.1 Environment ........................................................................................... 91 5.3.2 Gas system ............................................................................................. 92 5.3.3 HV .......................................................................................................... 92 5.3.4 FEE ......................................................................................................... 92 5.3.5 DAQ ....................................................................................................... 93 5.4 ALARMS ....................................................................................... 94 5.5 VISUALIZATION ............................................................................ 96 5.5.1 TRISTAN ............................................................................................... 96 5.5.1.1 Daily reports ................................................................................... 96 5.5.1.2 Cell and multiplicity maps .............................................................. 98 5.5.2 TRAGALDABAS .................................................................................. 99 5.5.2.1 Grafana with PNP4Nagios .............................................................. 99 5.5.2.2 Cell and multiplicity maps ............................................................ 100 5.5.2.3 Charge report ................................................................................ 101 5.5.2.4 Cell Viewer ................................................................................... 102 6 CALIBRATION AND RECONSTRUCTION .................... 105 6.1 STRUCTURE OF UNPACKING AND CALIBRATION PROCESSES ...... 105 6.2 GEOMETRIC ACCEPTANCE ......................................................... 107 6.3 SIGNAL CALIBRATION ................................................................. 111 6.3.1 Charge ................................................................................................. 111 6.3.2 Time .................................................................................................... 114 6.3.3 Slewing correction ............................................................................... 119 6.4 RANDOM COINCIDENCES ............................................................. 120 6.5 ACTIVE AND DEAD TIMES ............................................................ 121 6.6 EFFICIENCY ................................................................................ 122 6.6.1 Tracking method .................................................................................. 123 6.6.2 Principal component analysis .............................................................. 124 6.6.3 Charge study ........................................................................................ 129 6.7 EVENT RECONSTRUCTION ........................................................... 131 6.8 PERFORMANCE ........................................................................... 136 6.8.1 Angular resolution ............................................................................... 137 6.8.2 Time resolution .................................................................................... 137 6.8.3 Position resolution ............................................................................... 138 7 RESULTS ........................................................................... 141 7.1 INTRODUCTION ........................................................................... 141 7.2 DATA-TAKING CAMPAIGNS ......................................................... 142 7.2.1 TRISTAN ............................................................................................ 142 7.2.1.1 Latitudinal survey 2018 ............................................................... 143 7.2.1.2 Latitudinal survey 2019-I ............................................................. 145 7.2.1.3 Latitudinal survey 2019-II ........................................................... 146 7.2.1.4 Santiago 2019 .............................................................................. 148 7.2.1.5 Antarctica 2020 ............................................................................ 149 7.2.2 TRAGALDABAS ............................................................................... 151 7.3 RAW DATA PROCESSING .............................................................. 151 7.3.1 Event reconstruction ............................................................................ 151 7.3.2 Calibration ........................................................................................... 153 7.3.3 Raw vs. calibrated data ........................................................................ 159 7.4 ATMOSPHERIC CORRECTIONS ..................................................... 162 7.4.1 Barometric effect ................................................................................. 163 7.4.2 Temperature effect ............................................................................... 165 7.4.3 Calibrated vs. corrected data ............................................................... 169 7.5 INFLUENCE OF GEOMAGNETIC FIELD AND SOLAR ACTIVITY ....... 171 7.5.1 Cutoff rigidity ...................................................................................... 171 7.5.2 Solar activity ........................................................................................ 178 7.5.3 SAA ...................................................................................................... 182 7.6 EXTENDED MULTIPLICITY STUDY ............................................... 183 7.6.1 Barometric effect .................................................................................. 184 7.6.2 Cutoff rigidity dependency ................................................................... 185 CONCLUSIONS ........................................................................ 189 RESUMO EN GALEGO ............................................................ 193 APPENDIX ................................................................................ 203 BIBLIOGRAPHY ...................................................................... 209 i ABBREVIATIONS AC Air Conditioning system ADC Analog-to-Digital Converter AEMET Agencia Estatal de Meteorología AGN Active Galactic Nuclei BAE-JCI Base Antártica Española-Juan Carlos I BIO Buque de Investigación Oceanográfica CDS Copernicus Climate Data Store CMB Cosmic Microwave Background CME Coronal Mass Ejection CR Cosmic Ray CSDA Continuous Slowing Down Approximation DABC Data Acquisition Backbone Core DACs Digital-to-Analog Converters DAQ Data Acquisition System DBO DaughterBOard DOY Day Of the Year DSA Diffusive Shock Acceleration Dst Disturbance short-time index DTC Differential Temperature Coefficient EAS Extensive Air Shower EBL Extragalactic Background Light ECMWF European Centre for Medium-Range Weather Forecast EGCR Extragalactic Cosmic Ray FD Forbush Decrease FEE Front-End Electronics FPGA Field-Programmable Gate Array FWHM Full Width at Half Maximum GCR Galactic Cosmic Ray ii GMDN Global Muon Detector Network GMF Galactic Magnetic Field GRBs Gamma Ray Bursts GSI Gesellschaft für SchwerIonenforschung GUI Graphical User Interface GWP Global Warming Power GZK Greisen-Zatsepin-Kuzmin HADES High Acceptance DiElectron Spectrometer HDD Hard Disk Drive HLD HADES List Data HMF Heliospheric Magnetic Field HPTDC High-Performance TDC HV High Voltage IGM Intergalactic Medium IGMFs Intergalactic Magnetic Fields IGRF International Geomagnetic Reference Field ISM Interstellar Medium Kp Planetary k-index LabCaF Laboratorio Carmen Fernández LAN Local Area Network LIP Laboratório de Instrumentação e física experimental de Partículas LSM Least-Squares-Method LV Low Voltage LVDS Low Voltage Differential Signaling MARTA Muon Array with RPCs for Tagging Air showers MBO MotherBOard MITO Muon Impact-Tracer Observer NEMO Neutron Monitor NH Northern Hemisphere NOAA National Oceanic Atmospheric Administration NTP Network Time Protocol ORCA Observatorio de Rayos Cósmicos Antártico PC Principal Component PCA Principal Component Analysis iii PCB Printed Circuit Board PoE Power over Ethernet PS Power Supply/ies Q2W Charge-to-Width RPC Resistive Plate Chamber RMS Root-Mean-Square RMSE Root-Mean-Square Error RRD Round Robin Database RTC Real Time Clock SAA South Atlantic Anomaly Saeta SmAllest sEt of daTa SBC Single-Board Computer SCMS Slow Control and Monitoring System SCR Solar Cosmic Ray SDI Serial Data Input SDO Serial Data Output SFP Small Form-Factor Pluggable SF Solar Flares SH Southern Hemisphere SNRs Supernova Remnants SPI Serial Peripheral Interface SS Solar System TDC Time-to-Digital Converter TimTrack Timing and Tracking TOF Time Of Flight ToT Time over Threshold TRAGALDABAS TRAsGo for the AnaLysis of the nuclear matter Decay, the Atmosphere, the earth Bfield And the Solar activity TRASGO TRAck reconStructinG bOx TRB TDC Read-out Board TRISTAN TRasgo para InveSTigaciones ANtarticas UDP User Datagram Protocol USC University of Santiago de Compostela UTM Marine Technology Unit WD WatchDog DAMIÁN GARCÍA CASTRO 6 6. Study the influence of the geomagnetic field and solar activity in the cosmic ray data registered by both detectors, together with the analysis of neutron monitor data taken by ORCA detectors during the first latitudinal survey. 7. Extend the analysis of TRISTAN data to high multiplicities to obtain the barometric and rigidity coefficients. TRASGO detectors are presented as an alternative to traditional technologies such as neutron monitors or muon detectors, which are bulkier and more expensive. The final impressions of the work developed in this thesis confirm the advantages of this technology compared to the aforementioned ones. The results will improve with the particle identification, muon-electron separation, and reconstruction of events with multiple particles, information only accessible with this kind of detectors. 1. Cosmic Rays 9 1 COSMIC RAYS In the early years of the 20th century, not long after Antoine Henri Becquerel and the Curies were awarded the Nobel Prize in Physics for the discovery and research of natural radioactivity, scientists came up against another mystery: the origin, nature and properties of a new form of energy detected coming from outer space, afterward coined with the charming term cosmic rays. 1.1 DISCOVERING THE COSMIC RAYS Up to the time that cosmic rays (CRs) were discovered, the source of natural radioactivity that cause the air, in a closed vessel, to be ionized was not known. Certainly, there was radiation coming from the Earth and the Sun, but the question was which of all sources was dominant and whether they were the only ones. The consensus in the scientific community was that the Earth’s soil was the primary source and so its effects could be shielded. Various experiments showed that shielding did not reduce the ionization rate, while others suffered the effects of numerous experimental errors [ 1 , 2 ]. It was in 1909–1910 when Theodor Wulf measured the ionization rate at different heights, on the ground and at the top of the Eiffel Tower, expecting an exponential decrease as the main assumption was that the Earth’s soil was the main source. No conclusive evidence was found due to the small change of the ionization rate for such an increase in the height [ 3 ]. The breakthrough in the investigation of this phenomenon came thanks to Domenico Pacini in 1910. Pacini performed a series of experiments measuring the ionization rate at different altitudes and underwater. The hypothesis that the origin of the penetrating radiation was only the soil couldn’t explain the obtained results [ 4 ]. DAMIÁN GARCÍA CASTRO 10 In 1912, Victor Hess during one of his flights aboard a hot air balloon reached 5 km height, improving previous results. In order to exclude the Sun as a source of incoming radiation, a flight was done during a near-total eclipse. Hess proved that ionization increased powerfully with height [ 5 ]. Therefore, he concluded that the origin of this penetrating radiation had to be extraterrestrial, which gained him the Nobel Prize in Physics in 1936. In the following years and decades, multiple experiments were carried out to investigate the nature of this radiation that Robert Millikan referred to as CRs in 1925 [ 6 ]. All of this research generates the following picture: most of the CRs are relativistic charged atomic nuclei, primarily protons (~ 86%) along with a-particles (~ 11%), and a contribution of heavier nuclei and electrons, which are originated in outer space. The Earth’s atmosphere is continuously bombarded by these highly energetic particles. The first interaction of CRs with an atmospheric target nuclei typically takes place between 10 and 30 km in height. The high-energy collisions produce lots of secondary particles like other protons, neutrons and pions, which can also interact again with the atmosphere forming an extensive air shower (EAS) (Section 1.5). An EAS consists of hadronic, muonic and electromagnetic components. They continue to grow as they go deeper into the Earth’s atmosphere until the energy of the secondary particles is insufficient to continue the process. Consequently, the size of the shower decreases and eventually dies out. Only a part of the shower reaches the surface, depending on the energy of the primary particle. The discovery of CRs sets the stage for the exciting field known as astroparticle physics. 1.2 PROPERTIES Since the identification of CRs, many scientists have examined the phenomenon and compiled a list of the properties of this new kind of radiation. Together with the energy spectrum, which gives us two physical puzzles that span a wide range of energy, we will discuss the composition, abundance, and propagation of CRs in this section. 1. Cosmic Rays 11 1.2.1 Energy spectrum The CR spectrum covers a wide range of energies that goes from around 10# eV up to 10$% eV, energies far above those reached in human-made particle accelerators with modern technology. The flux of observed CRs follows a remarkably smooth curve compatible with a power-law with minor deviations (Figure 1.1). Figure 1.1: Overview of the CR spectrum. Different colors indicate different experiments. Deviations from the power-law known as the knee and the ankle are indicated by arrows. (Used with permission of Annual Reviews, Inc. from [ 7 ]; permission conveyed through Copyright Clearance Center, Inc.) DAMIÁN GARCÍA CASTRO 12 The spectrum contains different structures that are worthwhile to be described. Starting with the low-energy range, the deviation from the general behavior is due to the effect of the Sun and solar modulation, which is described in Section 1.4. Moreover, at higher energies, the spectrum is split up into two regions defined by the “knee” and the “ankle” (Figure 1.2). The differential energy spectrum is parametrized by: dN dE=C+E,-+, (1.1) where C is a constant and / is the differential spectral index. This index remains almost constant at approximately 2.7 starting from 10# eV to about 10%0 eV. The so-called knee is the end of this region where the slope steepens from 2.7 to roughly 3.0. Beyond the knee there is a slight steeping around 10%1 eV, sometimes referred to as the “second knee”. The energy spectrum at 10%2 eV flattens back to an index of 2.7 at the so-called ankle. Finally, for energies above 4×10%# eV, there is a softening of the spectrum. The significance of this reduction is determined by comparing the observed flux to the number anticipated for an unabated spectrum that follows the same power law as seen for low energy [ 8 , 9]. Figure 1.2: The all-particle spectrum of primary CRs in the high-energy region. Different colors correspond to different experiments. (Reprinted with permission from [ 9 ]. Copyright by the American Physical Society.) 1. Cosmic Rays 13 Two models explain this flux suppression beyond 5×10%# eV. The Greisen-Zatsepin-Kuzmin (GZK) feature is caused by the interaction of energetic CRs with the cosmic microwave background (CMB) [ 10 ]. The second model explains the cut-off as the absolute maximum energy of the acceleration mechanism. Currently, the measurements are compatible with both models. 1.2.2 Composition The origin of CRs can be either galactic (GCRs), including those of solar origin, or extragalactic (EGCRs). It was already stated that most but not all of the CRs are protons. Their chemical abundances reveal information about where they come from and how they propagate. Figure 1.3 shows a comparison of the relative abundances found in GCRs and the solar system (SS). At first sight, the important differences are in those elements with atomic numbers directly under C and Fe. Figure 1.3: GCR and SS relative abundances normalized to 67 + 89 . (Used with permission from [ 11 ], Creative Commons CC-BY-NC-ND 4.0.) Significant proportions of the common heavier elements (such as carbon, oxygen, magnesium, silicon, and iron) travel the distance between their origins and the Earth without interacting significantly with the interstellar medium. This suggests that the elements are produced by nucleosynthesis like in the Sun. The enrichment in GCR DAMIÁN GARCÍA CASTRO 14 abundances, for the light elements (lithium, beryllium, and boron) and the sub-Fe group, are a result of spallation processes caused by carbon, oxygen, and iron near the Earth. Last but not least, the underabundance of hydrogen and helium is not really understood yet [ 12 ]. If the spallation cross-sections are known, it is then straightforward to deduce the quantity of matter traversed by CRs and their original composition. 1.2.3 Sources and propagation Even though CRs arrive evenly from all directions, the sources of CRs are not necessarily spread uniformly. There are four categories of CRs according to their energy (Table 1.1): Table 1.1: Energy ranges of CRs. Energy / eV CR type; origin and acceleration mechanism ~+101−10%< - SCRs; galactic origin and shock acceleration <3×10%0 - GCRs I; galactic origin and diffusive shock acceleration in supernova remnants (SNRs) ~+10%0−10%2 - GCRs II; galactic origin and second stage acceleration of GCRs I by shocks >10%2 - EGCRs; extragalactic origin and diffusive shock acceleration in extragalactic sources Diffusive shock acceleration (DSA), also known as first-order Fermi acceleration, is one of the most commonly accepted mechanisms for producing CRs. In Fermi’s mechanism, CRs accumulate energy by being scattered by turbulence up and downstream of the shock, crossing the shock multiple times [ 13 – 17 ]. CRs have a broad range of possible sources, covering from solar cosmic rays (SCRs) ejected in solar flares (SF) and coronal mass ejections (CMEs), GCRs produced in supernova explosions, SNRs and Wolf-Rayet stars, and finally to EGCRs which origin might be the intergalactic medium (IGM), gamma-ray bursts (GRBs), blazars and active galactic nuclei (AGNs). In order to accelerate to a certain energy, CRs must be confined in the acceleration region, so the acceleration 1. Cosmic Rays 15 physical site ( @A ) must be about the order of Lamor radius ( @B ) of a charged particle in a magnetic field: RD=E+ |q|+c+B≤RJ+, (1.2) with E and q as the energy and charge of the particle, B as the strength of the magnetic field of the source. This is the famous Hillas Criterion that predicts the circumstances that must exist in an accelerator for particles to reach maximum energy [ 18 ]. In typical units, the maximum energy can be stated as follows: EKLM NOPPLQ=Z×10%2+eV+U+B+ µG+X+U+RJ+ +kpc+X. (1.3) Figure 1.4: The Hillas plot represents the position of the acceleration sources in a double logarithmic scale of the magnetic field intensity vs. the source size. The knee (blue dashed), ankle (red solid) and maximum energy (green dotted) lines are shown. (Reprinted from [8], with permission from Elsevier.) DAMIÁN GARCÍA CASTRO 22 1.4 SOLAR MODULATION The influence of the Sun upon the intensity of CRs is called solar modulation. The term “solar activity” accounts for all turbulences or non-stationary phenomena that are originated in the Sun’s atmosphere and is dominated by the combination of magnetic and radiation activity. The main cause of solar modulation is the fluctuation in the magnitude of the solar wind, because of the solar activity. Generally, the solar activity is evaluated according to the number of black spots, called sunspots, on the Sun’s surface. Sunspots are very strong magnetic fields that appear dark because they prevent some of the Sun’s heat from reaching the surface. Their interaction with each other causes eruptions of energy in the form of SF and CMEs coming off the Sun, which perturb the solar wind and the HMF. In periods of high solar activity, the solar wind causes a decrease of the CR flux detected at Earth compared to the flux in the ISM [ 31 ]. The most remarkable modulation due to solar activity is the 11-year cycle, which is reflected in the CR intensity observed at Earth’s surface since the 1960s and in the notes of the number of sunspots since the early 17th century. Figure 1.9 shows the negative correlation between the CR flux and the number of sunspots. This correlation was discovered by Forbush in 1954 [ 32 ]. It is well-known that the 11-year cycle is, in fact, a 22-year cycle, widely known as the Hale cycle, that is directly related to the reversal of the polarity of the HMF during each period of extreme solar activity [ 33 ]. This modulation is observed by all detectors that are sensitive to particles with rigidity lower than 20 GV, and the amplitude of the fluctuation increases with decreasing values of the rigidity. In addition to long-term variations of the CR flux, there are considerable short-term periodicities that are relatively easy to distinguish during solar minima (solar activity minima): the 27-day variation caused by the rotation of the Sun. It is a quasi-periodic effect of 25–27 days due to the differential rotation of the Sun close to the equator; the daily variation owing to the Earth’s rotation, and several oscillations due to the higher harmonics of the 27-day variation [ 34 ]. 1. Cosmic Rays 23 Figure 1.9: Top) Sunspot number. Vertical lines indicate the start of a new solar cycle. Bottom) CR intensity recorded by different neutron monitors. Vertical lines show approximately the solar magnetic field polarity reversal. (Used with permission from [ 35 ], Creative Commons CC-BY 4.0.) It is also important to highlight the short-term effects of SF and CMEs in the CR intensity. SF and solar wind might cause magnetic storms when hitting the Earth’s magnetosphere. If the arriving magnetic field direction is southward, it interacts powerfully with the geomagnetic field which is oppositely directed. The interaction causes a weakening of the Earth’s magnetic field that will recover gradually over several days. Thus, energetic particles are streamed down the field lines and hit the Earth’s atmosphere, normally at high latitudes, causing the auroras. The most intense SF are CMEs, which are massive emissions of x-rays and magnetized plasma into the ISM. The largest geomagnetic storms are a result of the interaction of this plasma with the Earth’s magnetic field. The effect of the above-mentioned interactions on the CR flux is a sudden drop by 3–20%, followed by a progressive recovery to normal DAMIÁN GARCÍA CASTRO 24 intensity, called Forbush decrease (FD). A FD is caused by the sweeping of CRs by the plasma in the ISM and is registered by particle detectors in space and the Earth’s surface [ 36 – 38 ]. The magnitude of the FD depends on the direction of propagation of the magnetized plasma and the strength of the CME that emitted it, and also on the energy of the CRs. The low-energy CRs experience larger drops than high-energy CRs. 1.5 INTERACTION WITH THE EARTH’S ATMOSPHERE CRs hit the Earth’s atmosphere continuously colliding with atmospheric target nuclei. If the energy of the primary CR is high enough, the collision produces many new energetic particles as secondaries. These new particles can interact again, adding more particles to the developing cascade until their energy is not enough to continue the process. The secondary particles are spread over large areas due to the interactions and they all arrive almost simultaneously. This phenomenon is known as EAS and the observed flux is affected by the barometric pressure and temperature of the atmosphere. 1.5.1 EAS A detailed study of how an EAS develops in the atmosphere is relevant for the estimation of the energy and mass of the primary CR. All particles of an EAS undergo energy losses through hadronic and/or electromagnetic processes. As a result, the particle flux increases with increasing atmospheric depth, reaching a maximum in the first 100 g+cm,$ ( ~+30+km altitude over the sea level). Afterward, the flux decreases due to energy loss, absorption and decay processes. The shower eventually dies out before reaching the surface, if the energy of the primary CR is not enough. So that, the composition of the radiation changes at different altitudes over the sea level and it depends on where the first interaction of the primary CR took place. The interaction and decay probabilities depend on several factors such as particle’s energy and mean lifetime, and atmospheric density. Three major CR components are distinguished in an EAS: hadronic, muonic and electromagnetic (Figure 1.10) [ 39 ]. 1. Cosmic Rays 25 Figure 1.10: EAS schematic representation from top of the atmosphere. (Reprinted from [ 40 ], with permission from Elsevier) 1.5.1.1 Hadronic component The hadronic component remains very close to the velocity vector of the primary CR and is the core of the shower. It contributes continually to the electromagnetic component producing mesons (mainly pions), which decay to muons, electrons and positrons. Charged pions, kaons, other mesons, hyperons and nucleon-antinucleon pairs resulting from strong interactions continue to propagate and feed the hadronic component. DAMIÁN GARCÍA CASTRO 26 1.5.1.2 Muonic component The decays of charged pions, kaons, and other mesons into muons supply the muonic component. Kaon production has a low probability of about 10% in comparison to pions, so that, most of the muons originate from pion decays. The most important decay channels are: π±→µ±+νá+ f νá à à à h + ( ~+100% ) Κ±→µ±+νá+ f νá à à à h + ( ~+63.5% ) The mean free path in air of charged pions is ãå+~+120 g+cm,$ . Even though the mean lifetime of muons is approximately 2+µs , they easily penetrate the atmosphere reaching sea level because of the relativistic time dilation: τ(E)=τ<+U E mèc$X=τ<+γ+, (1.6) where zë and íë are the mean lifetime and the mass of the particle at rest, E is the total energy and ì is the Lorentz factor. Muons and neutrinos are the dominant flux at the sea level, and only they can penetrate underground. Despite this, some of them may decay, helping to develop the electromagnetic component. 1.5.1.3 Eletromagnetic component Neutral pions have a very short mean life and decay almost instantly. The dominant decay mode is into two photons: π<→γ+γ+ ( ~+98.8% ) Photons can produce electron-positron pairs if their energy is higher than 1.02 MeV, which are subjected to produce bremsstrahlung photons leading again to pair production. The radiation length of electrons in air is ñ<=37 g+cm,$ . This process builds up the electromagnetic component of an EAS. In addition, at low energies the muon decay is also important: µ±→e±+νò+ ( νò ô) +νá à à à + f νá h + ( ~+98.6% ) 1. Cosmic Rays 27 1.5.1.4 Time and density microestructure The most representative properties of an EAS may be summarized by different parameterizations for the time profile, the density of particles and the energy of the primary CR (Figure 1.11). The use of these parameterizations was suggested by John Linsley in 1985 [ 41 ]. The time-width distribution of the particles in a shower is very narrow at short distances to the core and it becomes wider at long distances. The equation that describes this behavior is the following: σõ(r)=σõúU+1+r rõ+Xù, (1.7) where r is the distance to the core, ûüú is the time width or time dispersion at time zero (2.6 ns), sü is the dimension of the shower (30 m) and † is an empirical parameter (1.5) [41]. Another characteristic of an EAS is the density of particles or lateral density distribution. It depends on several variables such as the distance to the core (r), the shower size ( °< ) and the mass of the primary CR as follows: ρ ( r,N< ) =ϵ+N<+r,§+, (1.8) where both • and n changes for different primaries. For example, for a proton •=5.3×10,¶ and n =1.5 . Finally, the energy of the primary CR is a function of the size of the EAS: E<(N<)=α+N<®+, (1.9) where /=2.217×10%% and ©=0.798 for a proton [ 42 ]. Using all these parameterizations, the energy of the primary CR can be written as: E<=α+™+ρϵ+´rõ™¨+σõ σõú+≠% ù−1ÆاƮ. (1.10) DAMIÁN GARCÍA CASTRO 28 Figure 1.11: EAS front and lateral density distribution. 1.5.2 Atmospheric effects Meteorological effects on secondary CRs are well known, with pressure and temperature effects being the dominant ones. The correction of the data by these effects increases the sensitivity to variations of the CR flux due to different processes of non-atmospheric origin. Both pressure and temperature cause perturbations in the effective thickness and height of the atmospheric layers. 1.5.2.1 Pressure The barometric effect is determined experimentally by the following equation: ln U δI I X ≥=β+δP+, (1.11) where ( ∂∑/∑ ) π is the relative or normalized variation of the CR flux at the detection point, ∂∫ is the pressure variation which is calculated as ∂∫=∫−∫|ª{ being P and ∫|ª{ the current and reference pressure, respectively. The coefficient † , called barometric coefficient, depends on many factors including the kind of secondary particle and the altitude where the observation is performed. Hence, an increase (decrease) in 1. Cosmic Rays 29 the pressure compared to the reference value means that secondary CRs suffer more (less) collisions on their way to the surface, and so that the flux detected decreases (increases). The barometric effect explains the effect of the atmospheric mass above the detector [39]. 1.5.2.2 Temperature In addition to the pressure effect, temperature changes in the atmosphere also modulate the CR flux at the surface. This modulation is very important, in particular for muon detectors. The temperature effect is mainly a result of two contributions, the so-called positive and negative effects. On the one hand, the positive effect is related to the interaction probability of kaons and charged pions with atmospheric nuclei in the high atmosphere. The decay of these particles is favored over their disintegration when the temperature increases, and that implies a higher production of high-energy muons [ 43 ]. On the other hand, the negative effect is associated with the path traveled by muons toward the surface. The higher the temperature, the further muons will travel. That benefits their decay before reaching the Earth’s surface, causing a decrease of low-energy muons [ 44 ]. The temperature influence also affects neutron detectors, but this effect is less significant. Different methods can be used to describe the temperature effect. Some of them require the temperature profile of the entire atmosphere, whereas others use the temperature and altitude of the maximum muon production [ 45 ]. The theoretical or integral method takes into account the temperature profile along the whole vertical above a detector. The relative change of the flux of muons arriving with energy above ºΩæø and zenith angle ¿ when the temperature changes by ¡¬ , can be written in the following way: ¨ΔNƒ(EKO§,X,θ) N<(EKO§,X,θ)≠ƒ=«Wƒ … <(EKO§,X,h,θ)+ΔT(h)+dh+, (1.12) where h is the atmospheric depth in atm at the observation point (X) and Àà is the muon weighting function or differential temperature coefficient (DTC) [ 46 – 49 ]. DAMIÁN GARCÍA CASTRO 30 Figure 1.12: DTC for muons of different threshold energies arriving vertically at sea level. Values calculated by Dmitrieva in [49]. Figure 1.12 shows that high-energy muons are very sensitive to temperature variations in the stratosphere. A good and permanent monitoring of the muon flux and its correlation with the stratosphere temperature might improve the mid-long term weather forecast. A new variable, defined as the weighted average of temperatures from the top of the atmosphere to the surface, can be derived from Equation 1.12: ¨ ΔNƒ ( EKO§,X,θ ) N< ( EKO§,X,θ )≠ ƒ=αƒ+TÕoo+, (1.13) where /à is the atmospheric temperature coefficient and ¬Œ{{ is the effective temperature defined as: TÕoo=∫Wƒ … <(EKO§,X,h,θ)+ΔT(h)+dh ∫Wƒ … <(EKO§,X,h,θ)+dh +, (1.14) 1. Cosmic Rays 31 The effective temperature takes into account the temperature at all pressure levels and approximates the atmosphere as an isothermal body. The contribution of each level is weighted, giving more importance to those where the muon production is more relevant. This parameter has been studied in multiple experiments like for instance Double Chooz, Daya Bay, IceCube, MINOS and Borexino, among others. The energy threshold varies from 22 GeV in Double Chooz to around 1.3 TeV in Borexino. The effective temperature and the temperature of the stratosphere are similar for such energies and the high-energy muon flux is strongly correlated with the temperature of the stratosphere. On the contrary, the flux of low-energy secondaries ( ~+1+GeV+muons , MeV electrons and gammas) showed a negative correlation. Figure 1.13 shows the /à for various experiments. The lines represent the expected values for different assumptions of the ratio kaon-pion and the extreme cases of pure pion and kaon production [ 50 – 54 ]. Figure 1.13: Measurements of the effective temperature coefficient “” for different threshold energies and angles through 〈 ’÷◊ÿŸ⁄€ 〉. (Used with permission from [54], Creative Commons CC BY 3.0.) DAMIÁN GARCÍA CASTRO 38 term, C, accounts for the shell correction, noticeable when the velocity of the incident particle is low and close to the orbital velocity of the bound electrons of the target material. The maximum energy transferred per collision to an electron is given by: WKLM+=+ 2mòc$β$γ$ 1+2γmò M˙mò M˚$+. (2.4) Equation 2.3 can be integrated between the initial energy and zero to find the continuous slowing down approximation (CSDA) range neglecting any kind of energy loss fluctuation and assuming it is continuous. Figure 2.2 shows the mean energy loss in several materials. Figure 2.2: Mean stopping power as a function of ¸˝ in different materials. (Reprinted with permission from [58]. Copyright by the American Physical Society.) 2. Gaseous Ionization Detectors 39 In the case of detectors with moderate thickness, the most probable energy loss is generally less than the given by Equation 2.3 for the mean energy loss (Figure 2.3). In this case, the energy loss is well-described by the Landau-Vavilov-Bichsel distribution, and it depends on the thickness of the material: Δi+=ξ Ù ln ¨ 2mòc$β$γ$ I ≠ −ln U +ξI+ X +j−β$−δ ı , (2.5) where !=(ˆ"/2#)+$$+(%/†$) MeV for a detector of thickness x in g+cm,$ and j = 0.200. Figure 2.3: Energy loss distribution of a muon of 10 GeV crossing 1.7 mm of silicon. Comparison of Landau-Vavilov (dashed line) with Bichsel (solid line). Zeroth and first cumulative moments, full width at half maximum (FWHM), most probable energy loss &' , and mean energy loss 〈 & 〉 are shown. (Reprinted with permission from [58]. Copyright by the American Physical Society.) DAMIÁN GARCÍA CASTRO 40 2.1.1.2 Electrons and positrons Light particles, i.e., electrons and positrons, suffer energy loss as a result of two main processes: ionization and bremsstrahlung. However, at low energies, other mechanisms also play an important role such as positron annihilation and Moller and Bhabha scattering (Figure 2.4). The stopping power for electrons and positrons is slightly different, and both differ from heavy particles. Small mass, indistinguishability and deflection must be taken into account. Bremsstrahlung probability is inversely proportional to the squared mass of the particle, hence its importance for light particles. It is produced by the deceleration of the electron or positron, resulting in the emission of a real photon, when deflected in the Coulomb field of atoms. At energies of few MeV, bremsstrahlung is relatively small but, above a certain energy, called critical energy, it dominates completely. Regarding muons and pions, it becomes important at a few hundreds of GeV. Figure 2.4: Contribution of the different processes to the fractional energy loss per radiation length as a function of the electron or positron energy. (Reprinted with permission from [58]. Copyright by the American Physical Society.) 2. Gaseous Ionization Detectors 41 The introduction of a new variable that characterizes the mean energy loss due to bremsstrahlung is needed. Considering the high-energy limit, where the radiative loss dominates and the screening effect is complete (Coulomb field of the nucleus screened by the electron cloud), the stopping power can be written as follows: −dE dx≈E X<+→+E(x)=E<+expU−x X<X+, (2.6) where ñ< is the radiation length usually measured in g+cm,$ . In such a way, the radiation length is the distance x an electron or a positron traverse losing all but 1/e of its initial energy º< by bremstrahlung. It can be approximated by: 1 X<≈U4Z(Z+1)ρN) AXrò$α+*lnf183+Z,%/flh−f(Z),+, (2.7) where Z and A are the atomic and mass numbers, °¯ is Avogadro’s number, sª is classical electron radius and /=1/137 is the fine structure constant. An useful approximation of the mass thickness as a function of the density ( - ) multiplied by the thickness leads to: X<=A Z(Z+1)ln(287/Z,%/$)×716.4+(g+cm,$)+. (2.8) Thus, radiation energy loss can be expressed in terms of the radiation length making it independent of the material. For chemical compounds and mixed materials, the radiation length can be calculated using the element mass fraction .æ and radiation length ñ<,/ : 1 X<=0FO X<,2 2+. (2.9) DAMIÁN GARCÍA CASTRO 42 2.1.2 Interaction of neutral particles with matter Neutral particles such as photons and neutrons cannot interact through Coulomb forces within the detector’s material, so they do it indirectly. They may release a charged particle that loses energy due to electromagnetic interactions. 2.1.2.1 Photons The interaction of photons with matter may create or not secondary particles. The most important mechanisms of photon interaction with matter are the photoelectric effect, Compton and Rayleigh scatterings and pair production. The photoelectric effect is the dominant process for low-energy photons in the keV range. A photon interacts with an atomic electron, transferring all its energy. As a consequence, one or more atomic electrons can escape the nucleus influence, whereas the photon is absorbed. In addition, lower energy photons, or fluorescence photons, might be emitted by the de-exciting atoms. Compton and Rayleigh scatterings dominate at intermediate energies. In Compton scattering, an incident photon interacts with a free electron. If the energy of the photon is higher than the atomic binding energy, electrons are treated as free. The interaction can scatter an electron away in concurrence with a new and less energetic photon. In Rayleigh scattering, the interaction is with the atom, and the incident photon can be deflected. This is a coherent process, and the target atom is neither excited nor ionized. Pair production is the most important process at high energies. To produce an electron-positron pair the energy of the photon must be at least 1.02 MeV, the energy equivalent to the rest mass of two electrons. The radiation length is also defined as a ~+7/9 of the mean free path for pair production for photons [ 59 ]. 2.1.2.2 Neutrons Neutrons are highly penetrating particles that interact weakly with matter. They only deviate from their trajectory due to collisions with a nucleus. There are two major types of interaction: scattering and absorption. 2. Gaseous Ionization Detectors 43 Scattering can be elastic or inelastic depending on whether energy is transmitted or not between the neutron and the nucleus. The nucleus will have some recoil velocity. In the case of inelastic scattering, it may reach an excited level that leads to photon emission. A neutron loses energy due to scattering until a nucleus absorbs it. Absorption involves the capture of the neutron by a target nucleus. This can lead to the emission of a wide range of radiations or induce fission. The target nucleus absorbs the neutron and emits a charged particle or a neutron. If the nucleus is left in an excited state, photon emission might occur [ 60 ]. 2.2 OPERATION PRINCIPLE OF GAS DETECTORS Gaseous detectors are used to measure ionizing radiation. Electrons and ions move more freely in gas than in liquid or solid. Therefore, the space between electrodes is filled with gas. The operation principle is the collection of the ionization electrons and ions produced by radiation going through the detector. The distribution of electron-ion pairs follows a Poisson distribution with sigma equal to the square root of the number of pairs produced. Usually, the collection is done after some amplification. In absence of an electric field, the diffusion of pairs due to random thermal movement leads to collisions with gas molecules. Therefore, electrons and ions are not accelerated to the electrodes, and recombination may occur. To avoid that, a voltage is applied to the electrodes. The potential difference creates an electric field between them, and electrons and ions drift to the electrodes, resulting in an induced current that can be registered by an acquisition equipment. Electrons drift toward the anode and ions to the cathode, where they are collected. If they gain enough energy during the acceleration, they can produce secondary ionizations in the gas. The number of electron-ion pairs produced by constant incident radiation varies with the applied voltage, and the number of secondary ionizations is related to the mean free path and the energy transferred from the external field. Depending on the gas type, pressure, and geometry of the detector, a wide range of voltages can be applied. Gain is defined as the ratio between secondary and initial ionizations for a detector under specific conditions [ 61 ]. DAMIÁN GARCÍA CASTRO 44 2.2.1 Working regimes Based on the applied electric field, there are different working regimes for a detector. Figure 2.5 shows the most important operating regions known as recombination, ionization, proportional, limited proportional, Geiger-Müller, and continuous discharge [ 62 ]. Figure 2.5: Total charge collected as a function of the applied electric field for different radiation. At zero voltage, there is no charge collection due to the recombination of electron-ion pairs. The pulse size increases with increasing voltage, while the number of pairs that are lost due to recombination decreases to the point it becomes zero. The range from zero to this point is the recombination region. Next is the ionization region, in which all pairs are collected. Thereby, a saturation zone is reached, and the charge collected does not change when increasing the electric field strength. This is the operating region of ion chambers. It is worth mentioning that the applied voltage is not enough to start an avalanche. A further increase of field strength increments again the induced current, and the proportional region is entered. In this working regime, the field is high enough to accelerate electrons that produce secondary 2. Gaseous Ionization Detectors 45 ionizations in the gas. The avalanche or multiplication is proportional to the initial energy deposited. The limit of the proportional region marks the start of the limited proportional region. Nonlinearities appear as a consequence of the growing voltage. Electrons drift faster than ions. So that, if the concentration of ions is high enough, it leads to electric field distortion about the anode. Increasing the electric field even higher makes possible the appearance of discharge in the gas. Discharge refers to a chain of many secondary avalanches. To stop this effect a quenching gas must be present. This is the Geiger-Müller region which is characterized by a plateau and gives no direct information about the type and energy of the radiation. Finally, the continuous discharge region must be avoided to prevent damage inside the detector. The working regime determines the kind of measurements that can be performed with a detector. The transport of electron-ion pairs has already been summarized throughout this section. According to the type of detectors on which this work is based, it is necessary to study the physics of the avalanche in more detail. 2.2.2 Avalanche multiplication Gas amplification occurs when the electrons resulting from the primary interaction gain sufficient energy to produce new ionizations in the gas. Secondary electrons moving toward the anode can also cause more ionizations and so on. The result is an avalanche that can continue growing until all electrons are collected [ 63 , 64 ]. The probability per unit track length of a secondary ionization to happen is determined by the inverse of the ionization mean free path of electrons. This parameter is better known as the first Townsend coefficient ( / ), which depends on the electric field and the gas density [ 65 ]. In the simplest case of a uniform electric field in parallel plate geometry, one electron-ion pair is produced after 1/ +α . If there are n primary electrons, after a path ds there will be: dn=n+α+ds+. (2.10) DAMIÁN GARCÍA CASTRO 46 The total number of new electrons (n) integrated over a path (s) can be described mathematically by the following equation: n(s)=n<+exp+(αs)+, (2.11) where 3< is the original number of electrons. The gain or multiplication factor is the ratio between the total number of electrons and the initial number ( 4=3/3< ). Nevertheless, an electron not only has a probability of being multiplied. There is also a probability of attachment by gas molecules. Normally, these molecules are present as impurities or contamination due to air, water, etc. Neglecting the contribution of the diffusion due to high electric fields, the gain equation can be written as follows [ 66 ]: G=exp+ ¨« f α ( s ) −+η ( s )h +ds Q6 Q7 ≠ +, (2.12) where 8 is the attachment coefficient. In general, both / and 8 depend on the reduced electric field. These coefficients are constant in uniform electric fields. However, they are influenced by the electric field distortion caused by large avalanches. This is an important effect in resistive plate chambers (RPCs) and is called the space charge effect [ 67 ]. In addition, gas density, geometrical imperfections, and edge effects also alter the multiplication. Besides ionization, excitation occurs, and so does photon emission. Ultraviolet photons that ionize gas molecules outside the radius of the electron avalanche generate delayed avalanches. The absorption of these photons requires a quenching gas that drains their energy. A streamer may appear at high gain ( ~ 102 electron-ion pairs), whose main characteristic is a fast increase of the charge. Its formation process is complex. The photons emitted in the avalanche create secondary electrons by photo-ionization of the gas molecules, which produce secondary avalanches that lead to charges moving forward and backward, originating a streamer. They may evolve to a spark if they are not damped [ 68 ]. 2. Gaseous Ionization Detectors 47 2.3 RESISTIVE PLATE CHAMBERS The first detector of this kind was developed in 1981 [ 69 ]. RPCs are one of the most used detectors in high-energy physics. They are used as trigger detectors and also for time-of-flight measurements [ 70 – 72 ]. A large detection area can be covered due to their relatively low cost per information channel. RPCs belong to the family of gaseous ionizing detectors, whose operation principle has already been described thus far. An RPC consists of two parallel resistive plates separated by a gas volume (gas gap) of a few millimeters. The number of gas gaps may vary depending on the purpose of the detector. Increasing the number of gaps improves the efficiency and the time resolution. The thickness of the gap, and so the uniformity of the electric field, are preserved with the placement of a grid of spacers made of polycarbonate. Generally, the main used gas is tetra-fluorethane ( C$H$F¶ ), commercially known as Freon R134-a, mixed with other gases (quenchers) to control the avalanche process [ 73 ]. A high voltage (HV) is applied to the electrodes, giving rise to a uniform electric field inside the gas gaps. At least one must be coated with a high-resistivity material to prevent sparks and discharges, limiting the available charge that can be evacuated instantaneously (Figure 2.6). Figure 2.6: Schematic representation of the internal structure of an RPC made with three gaps, showing glass, spacers and read-out electrodes. DAMIÁN GARCÍA CASTRO 54 Freon R134-a. Even though this kind of detector is built to work as a stand-alone device, it can be arranged in sets covering large areas or pilling up on top of each other to improve the performance of the whole system (Figure 3.1). Figure 3.1: TRASGO with four RPC planes and some possible configurations. 3.2 DETECTORS Nowadays, four TRASGOs are either operative or under development, and they have three different designs. The most important concept of the project is that all tools created can be used regardless of the design. The RPC structure and layout of the four detectors will be explained throughout this chapter. This thesis is based on the first two, thus, the remaining components will be described, in detail, in the next chapter. Figure 3.2 shows the current location of all TRASGO detectors. Figure 3.2: TRASGO detectors around the world. 3. TRASGO Detectors 55 3.2.1 TRAGALDABAS The first TRASGO to be constructed has been TRAGALDABAS (TRAsGo for the AnaLysis of the nuclear matter Decay, the Atmosphere, the earth B-field And the Solar activity) [ 80 , 81 ]. The detector is located at the Faculty of Physics of the University of Santiago de Compostela (USC), Spain (42º52’34” N, 8º33’37” W) since 2015. A very close to it weather station operated by MeteoGalicia provides the atmospheric data such as pressure, temperature and relative humidity, needed for the data corrections (Figure 3.3) [ 82 ]. Figure 3.3: Left) TRAGALDABAS location in the Faculty of Physics of the USC (yellow box). Right) scheme of the weather station. The detector has four active RPC planes and one layer of lead of 0.56 cm thickness or one radiation length, between the third and fourth (counting from top to bottom). These RPCs are based on the design developed by the Laboratório de Instrumentação e Física Experimental de Partículas (LIP) of Coimbra, in Portugal, for the MARTA (Muon Array with RPCs for Tagging Air showers) extension of Pierre Auger Observatory [ 83 , 84 ]. Each plane has an active size of 150×120+cm$ and is encapsulated by an aluminium box. An example of the internal layout of the RPCs was given in Section 2.3. These RPCs have two gas DAMIÁN GARCÍA CASTRO 56 gaps of 1 mm width filled with Freon R134-a and operate at a gas flow of ~+8+cc+min,% . Three slides of glass of 2 mm thickness of high resistivity separate the gas gaps. The electric field inside the gas gaps is created by applying HV to the conductive coating of the external glass plates ( ~+5.6+kV ). Table 3.1 shows the different materials that compose each detection plane and the values of their radiation length. The foam is added for better isolation of the plane. Table 3.1: Internal structure of the TRAGALDABAS RPCs. RPC layer CD / cm z-thickness / mm Aluminium 8.9 3.0 Polyethylene Foam 167.7 8.7 Copper 1.4 0.03 FR4 Printed circuit board (PCB) 15.9 1.57 Polymethylmethacrylate 34.1 1.0 Glass 9.5 1.9 Gas (Freon R134-a) 946.4 1.0 Glass 9.5 1.9 Gas (Freon R134-a) 946.4 1.0 Glass 9.5 1.9 Polymethylmethacrylate 34.1 1.0 Aluminium 8.9 3.0 Sum - 26 The read-out is performed by 120 rectangular copper pads per plane, with a size of 116×111+mm$ at a distance of 10 mm. Between pads, a guard electrode of 6 mm width has been added to prevent the cross-talk, which is almost negligible (Figure 3.4). Figure 3.4: Sizes of TRAGALDABAS read-out pads and guard electrodes. 3. TRASGO Detectors 57 TRAGALDABAS is installed on the first of a two-floor building ( ~+260 m a.s.l.) that partially rejects the low-energy particles of the electromagnetic component of the EAS. Additionally, electrons and gammas interacting with the walls of the building may produce low-energy secondary particles, whose contribution is hard to estimate. The detector is taking data at a constant rate of approximately 7–9 million events per day ( ~+90+ Hz) depending on the planes that are in the trigger. The acquisition trigger is done by a coincidence between two planes. Figure 3.5 shows the current layout of TRAGALDABAS and the effects of the walls on the incoming secondary particles. Figure 3.5: TRAGALDABAS in the current layout and the effects of the building. As it was the first detector, it has been used to elaborate on some tools that future detectors of the TRASGO family might need. For instance, the ones used for calibration, monitoring or visualization, tracking, reconstruction, and particle identification, have been tested as part of the work done in this thesis. DAMIÁN GARCÍA CASTRO 58 3.2.2 TRISTAN TRISTAN (TRasgo para InveSTigaciones ANtárticas), as its name states, is a detector intended for studying CRs in Antarctica [ 85 , 86 ]. The principal objective is to improve the understanding of secondary CRs in a wide range of energies and study the correlation of their flux with different phenomena related to Earth's environment. Before being installed in Antarctica, the detector performed several latitudinal surveys onboard the Spanish oceanographic vessels Sarmiento de Gamboa and Buque de Investigación Oceanográfica (BIO) Hespérides (Figure 3.6) [ 87 ]. Onboard the Sarmiento de Gamboa, the detector performed, in late 2018 and early 2019, a two-way latitudinal CR survey from Vigo, Spain, (42º14’13” N, 8º43’59” W) to Punta Arenas, Chile, (53º09’17” S, 70º54’41” W). The last journey, on board of the BIO Hespérides, was performed in late 2019 from Cartagena, Spain, (37º36’00” N, 0º59’00” W) to Punta Arenas. Then, the data acquisition continued until the final destination, the Base Antártica Española-Juan Carlos I (BAE-JCI) (62º39’46” N, 60º23’20” W), where TRISTAN was finally installed. Between the second and the last latitudinal survey, the detector operated at the Faculty of Physics of the USC, located on the ground floor of the building, below TRAGALDABAS. Figure 3.6: TRISTAN left) onboard of BIO Hesperides, right) in the BAE-JCI. This thesis is based, essentially, on the tools created and tested for the data monitoring, calibration, reconstruction, and analysis of this detector. The RPCs were built in Coimbra with the expertise of the mechanical workshop of the LIP of Coimbra, including the HV power supplies and the gas system [83]. As the design of the RPCs is very 3. TRASGO Detectors 59 similar to the ones used for TRAGALDABAS, they share the internal layout, which can be found in Table 3.1 but uses polycarbonate instead of methacrylate. The electronics, provided by Hidronav Technologies, is described in detail in the next chapter together with the remaining components [ 88 ]. TRISTAN consists of three RPCs and one layer of lead of one radiation length enabling a better muon-electron separation. The lead covers the central area ( 40% of the total active area) and is placed between the second and third planes (counting from top to bottom). Each RPC plane has an active size of 150×120+cm$ , operating at a gas flow rate of ~+11+cc+min,% . The HV ( ~+5.9+kV ) applied to the conductive coating covering the external glass plates creates the uniform electric field inside the gas gaps. The read-out is done by 30 rectangular copper pads per plane, with a size of 242×232+mm$ , with each pair separated by a guard electrode of 6 mm width. The distance between pairs of pads is 10 mm, and the addition of the guard electrodes is to prevent the cross-talk between the read-out pads (Figure 3.7). Figure 3.7: Size of TRISTAN read-out pads and guard electrodes. The data acquisition registers a rate of about 11–13 million events per day ( ~+ 130–160 Hz), depending on the cutoff rigidity of its location. The trigger scheme is based on coincidences between the first and third planes (counting from top to bottom). Figure 3.8 shows TRISTAN in the current layout in Antarctica. DAMIÁN GARCÍA CASTRO 60 Figure 3.8: TRISTAN in the current layout, installed in the BAE-JCI. This detector was conceived as a part of the Observatorio de Rayos Cósmicos Antártico (ORCA) set up in BAE-JCI in late 2018. ORCA is made up of a set of detectors with different properties that measure the flux of secondary CRs at ground level. Two blocks shape the whole observatory. On the one hand, TRISTAN, whose targets are all charged particles. On the other, NEMO (NEutron MOnitor) and MITO (Muon Impact-Tracer Observer), installed inside a 20 feet container thermally isolated (Figure 3.9) [ 89 ]. Figure 3.9: NEMO and MITO detectors. (Used with permission from [120], Creative Commons CC-BY-NC-ND 4.0.) 3. TRASGO Detectors 61 3.2.3 muTT MacroScanner project is a CR tomography project for security applications, and muTT is the prototype. Muon tomography can be exploited to effectively detect hidden and suspicious materials, especially those of high atomic numbers, in containers, vehicles, etc. The target is driven through the scanning device, formed by two groups of detectors: upper and lower (Figure 3.10). Both are used to reconstruct the trajectory of the incident muons. The lower detectors can detect a change in muons trajectory. The angular changes of the tracks depend on the material that muons traverse, being larger for denser materials. Figure 3.10: MacroScanner scheme. muTT was mounted and tested in O Porriño, Spain, achieving the identification of materials with high atomic numbers. The detector has four RPC detection planes with an effective area of 150×120+cm$ . The RPCs were built by the LIP of Coimbra, and the electronics was provided by Hidronav Technologies [83, 88]. The main features are a high angular resolution ( ~+1 degree), and sub-nanosecond time resolution ( ~+100+ps ) [ 90 ]. Table 3.2 shows the layers of each RPC, the materials, and their radiation length. DAMIÁN GARCÍA CASTRO 62 Table 3.2: Internal structure of the muTT RPCs. RPC layer CD / cm z-thickness / mm Aluminium 8.9 3.0 Polyethylene Foam 167.7 3,1 PCB (FR4) 15.9 1.5 Copper 1.4 0.03 Polycarbonate 34.6 1.0 Glass 9.5 1.0 Gas (Freon R134-a) 946.4 0.3 Glass 9.5 1.0 Gas (Freon R134-a) 946.4 0.3 Glass 9.5 1.0 Gas (Freon R134-a) 946.4 0.3 Glass 9.5 1.0 Gas (Freon R134-a) 946.4 0.3 Glass 9.5 1.0 Gas (Freon R134-a) 946.4 0.3 Glass 9.5 1.0 Gas (Freon R134-a) 946.4 0.3 Glass 9.5 1.0 Polycarbonate 34.6 1.0 Copper 1.4 0.03 PCB (FR4) 15.9 1.5 Copper 1.4 0.03 Aluminium 8.9 3.0 Aluminium base 8.9 3.0 Sum - 26 The need for a very good spatial and temporal resolution required a different configuration of the RPCs. In contrast to the aforementioned detectors, muTT replaces the rectangular read-out pads with read-out strips and the double-gap by multi-gap. Two layers of strips per plane, one up with 20 strips and one down with 25 strips, are placed perpendicularly to each other. The induced signal is collected by two layers of copper electrodes: top and bottom. 3. TRASGO Detectors 63 3.2.4 STRATOS Continuous monitoring of the temperature changes in the stratosphere using a CR detector at ground level may lead to a new tool for a medium-long term weather forecast. For that purpose, Hidronav Technologies designed a new set of detectors as part of the STRATOS project. Two stations are being tested, one located in O Porriño, Spain, and the other in Coimbra, Portugal (Figure 3.11). Figure 3.11: STRATOS-2 during the commissioning in Coimbra, Portugal. The CR stations of STRATOS consist of four RPCs built by the LIP of Coimbra, and the electronics was provided by Hidronav Technologies [83, 88]. The RPCs have been designed to optimize the identification capability of clusters of particles. They offer a very good angular and temporal resolution of ~+1 degree and ~+300+ps , respectively, due to the high granularity (64 read-out strips). The external design of the detection planes is different from any other TRASGO detector as the pre-amplifying, acquisition electronics and power supplies are enclosed in a single Faraday cage. In addition, the gas consumption is lower ( ~+5+cc+min,% ) than for the other detectors because DAMIÁN GARCÍA CASTRO 70 4.3 DATA ACQUISITION SYSTEM The data acquisition system (DAQ) and the FEE are the most important electronic systems. They determine the final time resolution of the detector, being the intrinsic resolution the limiting factor. The DAQ is based on the time-to-digital converter board (TDC read-out board), better known as TRB [95]. The signal from the FEE is transmitted to the TRB, where each MBO is connected via a flat cable. The acquisition starts after an external trigger signal is registered. The trigger is based on coincidences between planes within a certain time window. After a valid trigger, the TRB collects the data of the fired channels and applies several algorithms to decide whether an event is stored or not. Events that pass the filters are moved to external massive storage for offline analysis. 4.3.1 TRB The TRB has been developed at GSI for the HADES experiment. The design and main features have been improved with the release of the different versions. Until now, there are three versions, but only the last two are installed in the two detectors of the TRASGO project described throughout this chapter. The schematic of the TRB versions 2 and 3, which are explained in this section, is displayed in Figure 4.4. Figure 4.4: TRB layout left) TRBv2, right) TRBv3. Size: HD+ÿF×HI+ÿF . 4. Electronic Systems 71 4.3.1.1 TRB version 2 The DAQ and slow control of the TRBv2 are done by an ETRAX-FS processor running Linux and connected via ethernet of 100 Mb J,% . All components are fed by a 48 V DC/DC converter. The TRBv2 has four 32-channel High-Performance TDC (HPTDC) where the MBOs are connected [ 94 ]. Each HPTDC has 31 LVDS timing signals among other inputs and outputs for general purposes. An external time signal, used as the reference for synchronization, is connected to the 32nd channel of an HPTDC per plane. The TDCs have multi-hit capabilities that offer the possibility to differentiate simultaneous signals in multiple cells. The data selection in the HPTDCs is started by an external trigger signal. Then, the board-controller field-programmable gate array (FPGA) initiates the read-out. The event-builder receives the date, formatted date via User Datagram Protocol (UDP) internet protocol, collects, and orders the individual sub-events from all read-out chains. In addition, the optical link of the TRBv2 offers high-speed data transfer of 2 Gb J,% . The time resolution of the TRBv2 is 40 ps per channel [ 95 ]. 4.3.1.2 TRB version 3 The TRBv3, like its predecessor, is a multi-purpose device with on-board DAQ functionality. The TRBv3 replaces the HPTDCs with ECP3-150 FPGAs, which improves the time resolution per channel to below 15 ps. Each one of them can support up to 64 high-rate multi-hit TDC channels, allowing up to 256 in total with add-on cards. FPGAs have all required algorithms implemented [ 96 ]. The central FPGA gathers and sends all data via 8 small form-factor pluggable (SFP) transceivers that support data transmission at speeds up to 3 Gb s,% . Slow control information is transferred over the same links. A 48 V DC/DC provides power to all components. 4.3.2 Trigger system The trigger logic is configurable and implemented in an FPGA-based system. The low-level trigger signal is transported from the MBOs to the trigger logic via MMCX cable (Figure 4.5). The system is programmed DAMIÁN GARCÍA CASTRO 72 with a single-board computer (SBC) running Linux (ODROID, Raspberry Pi, …) and programs ctsrun, ctslog and ctschk. ctsrun is used to program the operating mode of the trigger system, which is done by defining the acquisition time window, the number of planes in coincidence, the trigger width and dead time, the synchronization frequency, and the logic gates. This program calls also the ctschk, which checks the correct programming of the hardware of this system. ctslog is used to start the DAQ and is also used to read and store the information given by the counters in log files. The low-level trigger signals from the MBOs (i.e., the number of cells fired per MBO and plane, even if they are not enabled for trigger generation), the total trigger signals generated by the system, and the trigger signals successfully sent to the TRBs, are the counters in this case. Figure 4.5: Left) Trigger board ( K+ÿF×8D+ÿF ). Right) Trigger logic. The scheme of the system is shown in Figure 4.5. Each line (L1 and L2) is fully programmable (coded in decimal) so it can be enabled/disabled, and also its polarity can be changed. The gates (1 and 2) can be configured as “and/or”. The condition that starts the acquisition is based on coincidences between the number of planes determined by the majority block. If there is a coincidence, the signal passes the stretcher and the trigger system generates a signal that is sent to the TRBs. A new output trigger signal will not be generated until the trigger dead time has expired. Even though the DAQ records all data of events 4. Electronic Systems 73 satisfying the trigger condition, the log file of the ctslog shows the counts in Hz (averaged over a custom time window). Additionally, a synchronization trigger signal with a custom frequency is sent to all TRBs simultaneously to ensure the correct data taking. 4.4 ENVIRONMENTAL SENSORS Measuring the environmental variables (pressure, temperature and relative humidity) of the RPCs gives information about the gas conditions, enables the HV dynamic correction explained in Section 5.5, and allows one to do the CR data correction. RPCs are manufactured in a broad variety of layouts. Some include the environmental sensors inside the aluminium boxes, whereas others are installed outside. For both designs, all sensors are connected to an i2c-bus of an i2c-board controlled by an SBC which runs a Python code via cron. The data is saved in log files for analysis. The sensors used for the different variables are described in this section (Figure 4.6). 4.4.1 Presure The pressure is measured by one MPL115A2 sensor per plane with an operative range from 50 to 115 kPa. The main features are an accuracy of ± 1 kPa and a resolution of 0.15 kPa (10 bits). The sensor also gives the temperature used to calculate the compensated pressure, a barometric pressure value compensated for changes in the sensor linearity. The 10-bit compensated pressure is calculated as follows: PLèKi=a<+ ( b%+c%$+T)@N ) +P)@N+b$+T)@N+, (4.1) where ∫¯BO is the 10-bit pressure analog-to-digital converter (ADC) output, ¬¯BO is the 10-bit temperature ADC output, P< is the pressure offset coefficient, ©% is the pressure sensitivity coefficient, ©$ is the temperature coefficient of offset, and Ó%$ is the temperature coefficient of sensitivity. Pressure in kPa is obtained by Equation 4.2 (the maximum for 10-bit is 1023 decimal). P=PLèKi+U+115−50 1023 +X+50+. (4.2) DAMIÁN GARCÍA CASTRO 74 4.4.2 Relative humidity SHT21 is the sensor that reads the information of relative humidity (RH). There is one sensor for each RPC plane. The most important properties are its accuracy of ± 2% (from 20% to 80% RH) and its resolution of 0.04% (12 bits). The functional range goes from 0 to 100% RH. The ADC output signal QRS is converted to relative humidity (result in % RH) by the following equation independently of the resolution: RH=−6+125 U +SUN 2%V+ X +. (4.3) Furthermore, this sensor measures the temperature within the limits of –40 and 125 ℃ , with an accuracy of ± 0.3 ℃ and a resolution of 0.01 ℃ (14 bits). The temperature conversion of the ADC output signal Qà is done as follows (result in ℃ ), regardless the resolution: T=−46.85+175.72U+Sƒ 2%V+X+. (4.4) 4.4.3 Temperature Multiple TMP75 sensors are settled on all RPCs to measure the temperature. The operating regime extends from 40 to 125 ℃ , with an accuracy of ± 1 ℃ and a resolution of about 0.0625 ℃ (12 bits). The output-to-temperature ratio depends on the chosen resolution, but it is always a power of two in the denominator. In the 12 bits resolution, each output “unit” equals 1/16th of ℃ (for 11 bits, equals 1/8th and so on). Figure 4.6: MPL115A2, SHT21 and TMP75 i2c sensors. Size: 8X+FF×8K+FF . 4. Electronic Systems 75 4.5 POWER SUPPLY The power supply (PS) regulates and gives a smooth voltage to the components of a detector. Diverse PS devices bring the low voltage (LV) to the FEE and the DAQ, and the HV to the RPCs. 4.5.1 LV The FEE and the DAQ are connected to individual LV PS that convert the 220 V input to 48 V. The LV provided to the FEE is about 5 V per MBO, so a maximum of 8 MBOs can be fed by a unique PS of this kind (Figure 4.7) [92]. Each TRB is supplied with 5 V by a different LV PS. Figure 4.7: Components of the LV PS of the FEE. 4.5.2 HV RPCs operate at HV to generate the avalanches inside the gas gaps. Each RPC plane is connected to a PS that sets the desired HV values (Figure 4.8). All HV PS of the detector are connected to an i2c-board. The voltage is set passing the information through an Ethernet cable. The same cable also carries the electrical power to the PS, what is called power over ethernet (PoE). The input voltage of an HV PS is 5 V. Then, it is converted to a value determined by the mode of operation of the RPC (around 5–6 kV for the avalanche mode). HV and background currents are monitored DAMIÁN GARCÍA CASTRO 76 every minute via the i2c-bus, and the data is recorded in log files for online and offline analysis. Figure 4.8: HV PS + ( 99+ÿF×8E+ÿF ). A dynamic adjustment of the HV values is managed by an SBC (ODROID, Raspberry Pi, …) to compensate for the variations of temperature and pressure that modify the reduced electric field applied inside the gas gaps. The gain of the RPC is kept constant during the whole period of data taking by adapting the HV to the environmental conditions as follows: VQòõ=EpòY+dZLi+P 0.0138068748+T+(V)+, (4.5) where º|ª[=º/° is the reduced electric field in Townsend (Td) being E the applied electric field and N the gas density, ‡\Ïy is the thickness of the gas gap in cm, P is the pressure in hPa, and T the temperature in K [ 97 ]. The data (P, T) of the environmental sensors, described in Section 4.4, is taken from the log files and averaged over a number n of measurements by a Python script. Then, the voltage is set to a value that keeps the EpòY constant, whose value is calculated to operate within the efficiency plateau. This method is the HV dynamic correction and is performed via cron. The limits or minimum and maximum voltages are calculated for extreme conditions of 900 hPa and 328 K and 1100 hPa and 273 K, respectively. 4. Electronic Systems 77 4.6 GAS SYSTEM The gaps of the RPC are filled with pure Freon R-134a. Freon is an electronegative gas, so the majority of the free electrons in the gas are attached to its molecules. Only a small fraction of them contributes to the avalanche process. Moreover, other gases (quenchers) can be mixed with Freon to control the formation of secondary avalanches and streamers by absorbing the emitted photons. The gas is continuously flowing in an open loop. At the end of the loop, there is a one-way valve or bubbler partially filled with liquid vaseline. The gas from the RPC bubbles through the vaseline before being vented to the atmosphere. In recent years, many studies have been carried out to find a gas with similar properties to R-134a and an acceptable Global Warming Power (GWP) [ 98 ]. Tetra-fluorethane has a GWP around 1430 being the reference the carbon dioxide with a GWP equal to 1. Nevertheless, none of the findings achieved the needed performances in terms of efficiency, time resolution, rate capability and aging. The gas emission can be reduced for indoor experiments by gas recirculation, while outdoor experiments, with stations covering large areas, are not suitable for such a technique [ 99 ]. 4.6.1 Bubbler The equipment of the bubblers has been improved considerably since the first version. First designs are used only as visual indicators of the number of bubbles produced at the gas outlet. Thus, to keep the gas flow constant, the bubblers needed regular on-site observations. Newest versions are more sophisticated and implement two different sensors that enable remote or online supervision of the gas conditions. Pressure and optical sensors quantify the flow at the gas outlet (Figure 4.9). The gas is introduced into the bubbler through a dip pipe, immersed at a fixed depth into vaseline. A pressure sensor installed at the gas inlet gives information of the gas flow and temperature. At the gas outlet, optical or photoelectric sensors detect the light changes when a bubble is produced. Since in the absence of bubbles the light reaches the photogate through vaseline with no interference, there is a reduction of the light intensity when a bubble is created. The pressure at the gas outlet is measured by the changes in the vaseline level a bubble causes. DAMIÁN GARCÍA CASTRO 78 Figure 4.9: Left) Bubbler sensors. Right) Linear correlation between the number of bubbles registered and the gas flow in ÿÿ+F7],8 . 4.7 TRISTAN-TRAGALDABAS EQUIPMENT The equipment of the TRISTAN and TRAGALDABAS detectors is slightly different, being the latter the one with the newest versions of the aforementioned electronic devices. For both detectors, the size of the pads and the dimensions of the guard electrode were explained in Chapter 3. The active size per plane is the same for both detectors, and only the cell size changes. Both detectors work in avalanche mode, so the induced signal needs to be amplified by the FEE. 4.7.1 TRISTAN The RPC planes of TRISTAN have 30 cells each, so 8 DBOs are needed for the read-out. The threshold of the DBOs is set to 40 mV by the TRB. Figure 4.10 presents the DBO channel configuration and cell mapping. The channels of the DBO start counting from the left, if we look at them from the front, and their corresponding number is written inside the rectangular pads. The cells are divided into groups of 30 as it is the maximum number of cells a single MBO can connect. Therefore, TRISTAN requires one MBO per RPC plane. 4. Electronic Systems 79 Figure 4.10: TRISTAN cell mapping and DBO-MBO-TRB connection. TRISTAN is an almost completely autonomous detector designed to operate in Antarctica. In case of failure, the multiple programmed alarms give precise information about the cause via email. Hence, these alarms allow one to have a fast and effective response to guarantee the correct data taking and save the components in case of a major failure. The DAQ is fully autonomous and based on a single TRBv3, to which the MBOs and the trigger logic are connected via TDC add-on cards. For the trigger logic, several frequencies have to be defined apart from the line-gate configuration, such as the window size (40 ns), trigger dead time (0.1 ms), trigger width (300 ns), synchronization frequency (1 s), and acquisition time (10 s). The first and third planes of TRISTAN measure in coincidence, so the majority value in the trigger system is set to 2. Event data recording starts when a coincidence occurs and the TRB gets the trigger signal. In addition to the data taken in coincidence, every RPC runs in self-trigger mode every six hours. Self-trigger enables a good diagnostic of the status of the RPCs. In this mode, the DAQ registers all signals originated in an RPC, independently of others. It takes three minutes to run the self-trigger in all planes, one minute each. Concerning the alerts and the self-controlled DAQ, a watchdog (WD) reboots the entire system in case of a computer crash or communication failure. A reboot is performed weekly to check the detector status, keeping the HV PS at the operating value. Besides, a daily analysis of all log files searches for out-of-range values. Lastly, DAMIÁN GARCÍA CASTRO 86 the temperature independently (numbers from 2 to 6), and the last one gives the pressure (number 7). Figure 4.17: Top view of the location of the environmental sensors (1-7) and the connections of the HV PS and the bubbler. The gas system consists of two gas flow regulators and one bubbler per plane. TRAGALDABAS operates at an almost constant gas flow rate of ~+8+cc+min,% . Nevertheless, the gas system is not monitored because the bubblers don’t have an integrated digital system. Even though the gas control has to be done in situ, some parameters, like the background currents, may give information about the gas conditions. The power is supplied to the remaining electronic components by various LV PS placed inside the control box. The HV PS gets the power via PoE and converts it to the value requested by the script of the dynamic adjustment. TRAGALDABAS CR data taking follows the same chain as for TRISTAN, from the FEE to the HDD. A new file is created for every 50 MB of data, and it needs to be unpacked and calibrated before performing any analysis. Data calibration is explained later in this manuscript. Besides local HDD storage, a copy of the data is sent to the Centro de Supercomputación de Galicia (CESGA) [ 100 ]. Figures 4.18 and 4.19 show the power and data flow diagrams for a better understanding of the equipment. 4. Electronic Systems 87 Figure 4.18: TRAGALDABAS power diagram. Figure 4.19: TRAGALDABAS data flow diagram. 5. Slow Control and Monitoring 89 5 SLOW CONTROL AND MONITORING Since particle physics detectors have become progressively more sophisticated and demanding, the interest in monitoring the numerous system variables has been increased to guarantee detectors’ integrity and stability. In this chapter, the slow control and monitoring systems of TRISTAN and TRAGALDABAS will be described in detail. 5.1 OVERVIEW Reliable control and monitoring of the operational status is very important to guarantee detector’s integrity and stability by early detection of system failures. The slow control and monitoring system (SCMS) refers to a fully autonomous system that controls different processes and gives information about their operational status. The SCMS is responsible for the periodic verification and display of the variables of the multiple systems that make up a detector. The experimental conditions are of special interest for future knowledge and offline data correction. For such a purpose, the SCMS controls, periodically, variables such as pressure, relative humidity, temperature, background currents, gas flow, disk space, and communication, among many others. Deviations from the predefined parameter range require immediate maintenance either with an automatic procedure or by operator-driven action. The SCMS also issues an alarm via email if any of the monitored variables exceed a preset acceptable working range. The SCMS of the detectors TRISTAN and TRAGALDABAS will be described in detail in the following sections. The detectors have been designed to operate under different conditions. Hence, the SCMS differs slightly concerning the visualization and control of some specific parameters. DAMIÁN GARCÍA CASTRO 90 5.2 PARAMETERS CONTROLLED BY THE SCMS The SCMS provides information about the conditions in which the experiments have been carried out. One or several parameters are controlled/monitored for each sub-system of the detectors. Depending on the sub-system, the monitoring is done via different processes. Some of them are fully monitored, whereas others require checking the log files manually. A summary of all sub-systems and parameters controlled by the SCMS for both detectors is given in Table 5.1. Table 5.1: Summary of the sub-systems controlled in the detectors. Sub-system Parameters TRISTAN TRAGALDABAS Environment Pressure, relative humidity, and temperature Yes Yes Gas system Gas flow, temperature, relative humidity, and pressure Yes No LV - No No HV Voltage and background currents Yes Yes FEE Threshold setting and read-out Yes Yes DAQ Data recording, rates and charges Yes Yes The data acquired from the multiple sub-systems are delivered to the SBC that controls every detector via the i2c-protocol and local area network (LAN). Only one sub-system is not implemented in the SCMS yet, which is the LV. LV control requires operator-driven action to check that the correct voltage is applied to the different devices. The LV PS status can be given indirectly by the status of the connected components because a failure of the PS causes the lack of their operability, and the SCMS issues an alert. Client programs are used to check the experimental parameters, look for alarm situations and provide a graphical output of the progression of the variables. The core of the SCMS was implemented on a computer running Linux for both detectors. Several codes run periodically to verify the optimal working range of the parameters. Visualization is done via either daily report or continuous display at the laboratory facilities, depending on the detector (Section 5.5). 5. Slow Control and Monitoring 91 5.3 SENSOR READING Data from each sub-system is stored in log files and transmitted to the computer in which the SCMS codes run systematically. The recording frequency of the log files depends on the variable impact on the detector’s performance, and it can be seen in Table 5.2. This section gives an overview of the SCMS integration in every sub-system listed in Table 5.1. The electronic components of each sub-system have been explained in detail in Chapter 4. Table 5.2: Recording frequencies of the log data used by the SCMS. Sub-system Parameters TRISTAN TRAGALDABAS Environment Pressure, relative humidity, and temperature 5 min 1 min Gas system Gas pressure at the gas inlet 5 min - Gas system Gas flow, temperature, and relative humidity at gas outlet 5 min - LV - - - HV Voltage and background currents 1 min 1 min HV HV dynamic setting 15 min 15 min FEE Threshold setting and read-out DAQ start DAQ start DAQ Selfand concidence trigger rates 2 min 1 min DAQ Data recording 5 min 5 min 5.3.1 Environment Environmental sensors provide information about the pressure, relative humidity, and temperature of the RPCs via the i2c-protocol. Sensor reading and digital signal output conversion have been programmed in Python following the specifications of each device. The equations used for the signal conversion can be found in Chapter 4. The control computer runs the code via cron on a five and one-minute basis for TRISTAN and TRAGALDABAS, respectively. Several measurements are performed for each sensor to avoid a possible reading failure. The averaged values over the total number of measurements are stored in log files line-by-line. DAMIÁN GARCÍA CASTRO 92 5.3.2 Gas system The gas system maintenance requires operator-driven action to replace the gas cylinder, modify the gas flow, and fill the bubblers with liquid vaseline. Gas flow monitoring is limited to on-site observation due to the version of the bubblers installed in TRAGALDABAS. The gas conditions are fully monitored in TRISTAN. Two independent sensors provide information about the gas pressure, gas flow, temperature, and relative humidity via the i2c-protocol. The gas flow is given by the number of bubbles produced per unit time. Sensor reading is programmed in Python. The code runs via cron every 5 minutes, and the data is stored line-by-line in a unique log file per day for the whole gas system. 5.3.3 HV HV PS are controlled via i2c-connectors by the computer, which sets the operational voltages and registers the information in daily log files. The SCMS has access to the minute information about the positive and negative voltages and background currents, set voltages, set maximum current, and several control flags. The HV dynamics performs, every 15 minutes, a series of new measurements of the environmental sensors to adapt to the new conditions. The data from all measurements are registered in a log file together with the command used to set the HV. 5.3.4 FEE Threshold setting is done by the TRBs via LTC2600 DACs with Serial Peripheral Interface (SPI) implemented in the MBOs. Eight DACs are connected in Daisy Chain per MBO. The TRB processor communicates with the DACs via a set of three differential-pair-pins plus ground. The data is sent to the first DAC via Serial Data Input (SDI) pins and clocked over the remaining DACs. After each programming operation, the data is clocked out via Serial Data Output (SDO) pins and read back by the TRB processor to verify the correct setting of the threshold voltages. TRBs are initialized at the start of the data acquisition. The information about the threshold writing and reading is registered in a log file for control purposes. 5. Slow Control and Monitoring 93 5.3.5 DAQ Data acquisition programs provide information about the detected events. The data is transported via Gbit-Ethernet UDP from the TRBs to event-builder processes. TRISTAN DAQ operates with Data Acquisition Backbone Core (DABC) [ 101 , 102 ]. DABC replaces the previous HADES building software hadaq, which is currently used in TRAGALDABAS. Data from the MBOs connected to the TRB are combined with an UDP frame and sent to the event-builder. The event building consists of the combination of Ethernet packets received by one or many TRBs, to coherent events based on the event identification generated in the first place by the trigger system. The resulting events are written in the standard HADES list data (HLD) format to an external HDD. Log files with self-trigger and coincidence trigger rates are created for monitoring purposes. Figure 5.1 illustrates the event building and storage chain. Figure 5.1: The acquisition chain from read-out to storage. The data in the HLD files created by the DAQ contains the event information (Figure 5.2). Events consist of a header and sub-events. Sub-events are the signals sent by each TRB and consist of a header and the data, whose format is defined by the sub-event decoding. Figure 5.2: Structure of an HLD file. DAMIÁN GARCÍA CASTRO 94 In order to process the event information, the data is unpacked and calibrated before the analysis. Data calibration, reconstruction, and analysis are described in the next chapters. The unpacking is done either with the existing C++ (TRAGALDABAS) or MATLAB (TRISTAN) classes and methods. Time and charge signals of all cells in a detector are stored in units of TDC. Therefore, before recovering the information, the TDC bin units are converted to time units (ns) by multiplying by the TDC conversion factor. FEE channels behave slightly differently, so the ToT pedestal is substracted to homogenize the response. The SCMS reads the unpacked raw data to check its quality and also gives information about the operative, noisy and inactive channels. 5.4 ALARMS Alarm programs periodically check the parameters from the log files of the aforementioned sub-systems and create a status report. Check intervals depend on the parameter and range from a few seconds to around one hour. The upper and lower limits of the working range of any parameter are predefined in a local configuration file. Alarms are issued via email either if a variable falls outside the allowed range, if the connection to a device cannot be established, or if a sub-system log file is not updated. TRISTAN and TRAGALDABAS alarms are configured in two different ways, but both have been implemented in the Python programming language. TRISTAN SCMS runs a check of all log files every half an hour via cron. If everything is correct or within the optimal range, the averages are written in a daily log file, which is the reference for the next day. In case of error, the information about the issue is sent via email. Occasionally, emails are not sent due to communication failures, so the email sending success is checked via cron every hour, and the system retries to send the alert. TRAGALDABAS is connected to a LAN with no band-width limits at the USC. Data from the sub-systems are delivered via LAN to a workstation. The SCMS of this detector is based on Nagios, which is an open-source software used for continuous monitoring and sending 5. Slow Control and Monitoring 95 of alerts [ 103 ]. A series of Nagios sensors (Python scripts) have been implemented to gather the data from the sub-system log files like pressure, relative humidity, temperature, HV, background currents, and trigger rates. The data is extracted periodically using regular expressions. Nagios connects to Raspberry01 to obtain the coincidence trigger rates and the self-trigger rates of each MBO and RPC. Environmental and power data access is done simultaneously via Raspberry02. Figure 5.3: Nagios alarms and host status. Figure 5.4: Nagios alarms and sub-system status. DAMIÁN GARCÍA CASTRO 102 5.5.2.4 Cell Viewer A custom GUI, called Cell Viewer, has been developed within the LabCaF group to display stats about TRAGALDABAS. Nevertheless, it can be adapted to any detector of the TRASGO family. Cell Viewer is programmed in Python with ROOT libraries to extract the data from the different Trees. ROOT is a high-performance software for data analysis widely used in the particle physics field [ 106 ]. Data quality can be checked after the unpacking and/or reconstruction have been performed. Cell Viewer displays the cell rate for the different data levels, from raw to reconstructed tracks, and the time period is customizable. The detector is divided into four sections according to the number of MBOs. Figure 5.12 shows Cell Viewer GUI and cell and MBOs counting rates. Figure 5.12: Cell Viewer interface. 6. Calibration and Reconstruction 105 6 CALIBRATION AND RECONSTRUCTION Particle identification requires well-calibrated data to provide reliable information about CRs. Calibrating detectors ensure their operation in the best possible conditions giving the best performance. The calibration and validation of TRISTAN and TRAGALDABAS data have been assessed in this research. This chapter is dedicated to the calibration and reconstruction algorithms and methods. 6.1 STRUCTURE OF UNPACKING AND CALIBRATION PROCESSES The correct understanding of the physics behind the CR data taken by the two detectors relies on a good characterization and calibration of the registered signals. Before performing any analysis, CR data stored in HLD files are unpacked with the existing C++ or MATLAB classes and methods. The unpacked data contains the event information like the event header and the signals measured by the TDCs. Events have at least as many signals as MBOs are connected to the TRBs. These signals are the trigger reference on channel 32 of each TDC. The appearance of more signals indicates that CR particles crossed the cells of the RPC, producing the so-called hits. A hit is a fired cell whose detected signal passed all thresholds. The time signals expected in a hit are the leading and trailing edges of the pulses. Hits with just one of those signals are rejected a posteriori. Times are in TDC bin units, and the TDC conversion factor converts them to nanoseconds. One TDC bin corresponds to 0.098 ns. Charge (in ns) is obtained by the difference between leading and trailing and times, and the algorithm is called charge-to-width (Q2W) [ 107 ]. The calibration process converts the raw data into hits for which the calibration constants, like time and charge, are needed. These constants are obtained by calculating the pedestals, which are subtracted from the original data to homogenize the response DAMIÁN GARCÍA CASTRO 106 of each FEE channel. Due to the fact that threshold voltages are set and fixed in the DBOs, the differences in rise-time or amplitude of the pulses can lead to differences in the digitizing time (Figure 6.1). This effect is known as amplitude or rise walk, and the walk correction is needed to generate the hits. Figure 6.1: Walk correction effect. Signals with the same shape but different amplitude cross the threshold at nonidentical times T1, and T2. Unpacked data also contains information about the TRB number, the channel, and the number of hits. The channel information used to unpack and calibrate the CR data is given by the look-up tables. These tables consist of one row per channel and the eight following columns: TDC channel number (1–128), MBO number (1-total number of MBOs), DBOs channel (1–32), MBO channel (1–30), Kx (1-RPC rows), Ky (1-RPC columns), and the xand y-coordinates of the cell center, respectively. In TRAGALDABAS, the interconnection of multiple TRBs implies the addition of an external synchronization signal from the FPGA-based system (Table 4.1). This signal is used to check that all TRBs are synchronized and recording the same event. The script called checksync reads the event information to find that signal on channel 32 of the second TDC in all TRBs. The arrival direction of the primary particle to the Earth’s atmosphere can be derived from events of high hit-multiplicity (number of hits). Hence, it is essential to perform an accurate time calibration, whose 6. Calibration and Reconstruction 107 algorithms account for several effects such as fixed time delays due to cables, configurations, etc., in a unique constant per cell. The relative arrival times, together with the recorded charge, are important to determine the position of the shower axis on the ground. The calibration of the detectors includes the estimation of the efficiency and the noise rate of each RPC plane. Detectors’ performance has a direct relation to the operation parameters. Thus, the production techniques can not guarantee the same performance and long-term stability. RPC performance varies from chamber to chamber and from time to time. Currently, calibration is generally performed once per day, and the calibration constants are stored in ASCII files. These constants have to be subtracted from the measured values to study the CR data. The calibration algorithms and methods developed in this work will be explained in the following sections. 6.2 GEOMETRIC ACCEPTANCE Primary CRs can be assumed that arrive isotropically at the top of the Earth’s atmosphere. At sea level, muons are the most abundant charged particles in secondary CRs. The general angular distribution of CR muons at a certain distance from the sea level depends on several factors, such as the incident zenith angle and energy as follows [39]: I(θ)=I<+cos§¿+, (6.1) where ∑< is defined as the integrated vertical muon flux in cm,$+s,%+sr,% and ¿+ is the zenith angle of the muon. The exponent n varies over a wide range depending on the latitude, altitude, muon cutoff momentum, etc. Integrating the angular distribution in the downward direction or vertical component of the velocity vector over the solid angle gives the downward flux as: J(θ,ϕ)=«I(θ)+cosθ+dΩ=« «I(θ)+cosθ+sinθ+dθdϕ ` < $a <. (6.2) DAMIÁN GARCÍA CASTRO 108 The acceptance of the detector depends on the active area, the zenith-angle distribution of the incident muons, and the solid angle subtended by the RPC planes. The steepest angle between the planes that are in coincidence is determined by the path from one edge of the top plane to the opposite edge of the bottom plane. A flat detector of active area A will see a muon spectrum approximately proportional to cos$θ+ at sea level. To estimate the muon flux, a couple of simplifying assumptions have to be made. On the one hand, we assume that all cells of the RPC planes see the same solid angle, which is equal to the angle seen by the element at the center of the bottom cells. On the other hand, we assume that cells of rectangular shape can be modeled as circular cells with the same area. This assumption makes the calculation of the flux per unit area easier because of the cylindrical geometry, for which the solid angle is subtended by a cone. Therefore, the estimated muon flux is modulated by the cos¶θ and given by the following equation: J(θ)≈π 2+I<+(1−cos¶θ)+. (6.3) A simulation using Monte Carlo techniques has been carried out to determine the acceptance of both detectors. The trigger is based on coincidences between the first and third planes for both cases. A random position is generated in the top trigger plane. Similarly, the zenith angle of the incident CR is generated using a cos$θ distribution, and the azimuth angle is generated randomly between 0 and 2π . The generated particle is extrapolated to the bottom trigger plane and the acceptance is computed. Basically, the Python script that performs the calculation determines if a CR passing through the active region of the top trigger plane is also detected by the bottom plane or not. The program tacceptance takes the name of the detector as an argument and imports its geometry from tdetectors class. The required geometric parameters are the number of cells and their size in both directions of the RPC plane, the width of the guard electrodes to compute the dead zones, and the vertical distance between the trigger planes. Table 6.1 shows the geometry of TRISTAN and TRAGALDABAS detectors used to obtain the acceptance and angular distribution of the particles that are accepted. 6. Calibration and Reconstruction 109 Table 6.1: Geometric parameters. Parameter TRISTAN TRAGALDABAS Cells x-axis 6 12 Cells y-axis 5 10 Cell size x-axis 242 mm 116 mm Cell size y-axis 232 mm 111 mm Width of dead zones 10 mm 10 mm Vertical distance 484 mm 902 mm In Table 6.2, the distances between RPC planes for both detectors are presented. Trigger configuration allows any combination of planes, and it was set to the first and third planes, counting from top to bottom, for this work. Hereinafter, planes are labeled starting from the top of the detectors as T1, T2, etc. Table 6.2: RPCs z-coordinate in mm. Plane TRISTAN TRAGALDABAS T1 484 1739 T2 271 1217 T3 0 837 T4 - 0 Ten million CR particles have been generated. The zenithal angular distributions of generated and accepted events are shown in Figure 6.2. The acceptance, or the percentage of particles that crossed both planes over the total generated, is 57.89±0.02(stat) for TRISTAN and 34.18±0.02(stat) for TRAGALDABAS. Uncertainties have been calculated by taking the square root of the accepted events. Figure 6.2: Zenithal angular distribution of generated and accepted events for left) TRISTAN and right) TRAGALDABAS. DAMIÁN GARCÍA CASTRO 110 Acceptance cell maps show the events with a hit in the active area of the top trigger plane, that have been detected also in the bottom trigger plane. The lower the incident zenith angle, the higher the acceptance. Central cells have a higher acceptance rate due to the detector’s geometry (Figure 6.3). Figure 6.3: Acceptance cell maps left) TRISTAN and right) TRAGALDABAS. Colorbar shows the percentage of accepted events. The acceptance or accepted CR fraction for a given zenith angle is plotted together with the zenith-angle distribution of the accepted events in Figure 6.4. TRISTAN cells have around four times the area of TRAGALDABAS cells. Therefore, a particle crossing the same cell in the upper and lower trigger planes can have a maximum zenith angle of about 35 degrees, whereas for TRAGALDABAS the maximum zenith is around 10 degrees. Figure 6.4: Theta distributions and acceptance of the detectors left) TRISTAN and right) TRAGALDABAS. 6. Calibration and Reconstruction 111 An important test is to verify the cos$θ distribution of CRs arriving at the Earth’s surface using the real reconstructed data from both detectors. Reconstruction algorithms will be described in Section 6.7. 6.3 SIGNAL CALIBRATION Correct calibration of the CR data involves both charge and time-of-flight signals. In this section, the algorithms and results used for the signal calibration will be discussed. TRISTAN programs have been developed in MATLAB, whereas for TRAGALDABAS the already existing C++ classes within the ROOT framework have been used. 6.3.1 Charge The charge spectrum of raw data is characterized by four regions (Figure 6.5). The first is the low-charge region, with no signals due to the fixed threshold on the FEE, which is delimited by the pedestal peak. The charge pedestal region separates the low and intermediate charge regions. Signals with a charge higher than a certain value obtained by fitting the pedestal peak correspond to CR particles, and the signals below that value are mainly noise. Finally, the high-charge region is associated with streamers produced in the detector due to the interaction of high ionizing particles. It is important to bear in mind that the measured charge is given in nanoseconds so that, to perform a detailed charge analysis it must be converted to femtocoulomb. Figure 6.5: Charge measured in a cell. Vertical lines separate different regions. DAMIÁN GARCÍA CASTRO 118 4) The iterative process consists of repeating the aforementioned steps until it converges. Convergence is achieved once the constants of both planes differ less than 1% with respect to the previous iteration. The result of the iterative process is a narrow time distribution centered at 0 ns. Normally, the process converges in no more than three iterations. Figure 6.14 shows the comparison of the distribution before and after the calibration process. Figure 6.14: Comparison between the distributions before and after the calibration for all cells of left) top and right) bottom planes. In TRAGALDABAS, the time calibration is performed using the C++ classes and methods already developed. The process followed is the same as for TRISTAN. A Gaussian fit is applied to the time differences distributions for all combinations of cells between two 6. Calibration and Reconstruction 119 planes. The mean and bin center of the histogram are extracted and then subtracted to the time differences of the measured data, which centers the distribution. Repeating the same steps a few times makes the distribution narrower after each step until it converges. Figure 6.15 presents an example of TRAGALDABAS time calibration. Figure 6.15: Time differences left) 2D map and right) projection. The time calibration parameters of the detectors are stored in ASCII files. These constants are subtracted online from the measured times before performing the analysis of a CR shower. 6.3.3 Slewing correction Signals produced when a CR particle interacts within the detector’s active volume are sent to the read-out electronics. The charge integrated on the pads is related to the amplitude of the signals. As it was mentioned in Section 6.1, the differences in rise-time or amplitude can lead to differences in the digitizing time. This time shift depends on the ratio between the charge and amplitude of the signal, being the large signals the ones arriving first. The slewing correction is then an effect produced by the read-out electronics. The correction of the charge to time correlations can improve the time resolution considerably [ 108 , 109 ]. Slewing correction consists of the mean deviation in time for each charge value, and its application to particles with different masses could improve the time resolution because the charge is also related to the mass and the velocity of the incident particle. Slewing effect is removed in TRAGALDABAS by fitting the two regions of the spectrum to two polynomials [108]. Due to the large size of TRISTAN pads this effect don’t improve considerably the time resolution. DAMIÁN GARCÍA CASTRO 120 6.4 RANDOM COINCIDENCES Accidental or random coincidences occur when unrelated pulses coincide by change, and they affect the rate of CRs measured by the detectors. The effect of the accidental coincidences has to be taken into account when correcting the rates because the efficiency correction, as will be explained in Section 6.6, is not enough when the environmental conditions suffer dramatic changes. An estimation of the expected random coincidence rate can be done by using simple probability arguments [ 110 , 111 ]. If we assume a time window of size uA within which the acquisition is open after a trigger signal is sent, a pulse arriving within a time interval of 2uA represents a coincidence. The trigger configuration of TRISTAN and TRAGALDABAS is based on coincidences between two planes. However, the analysis will be extended to three planes in order to compare the results. In the simplest case of two RPCs in coincidence, an RPC producing s¯ pulses per second means that the available time for the second RPC to produce a coincidence is the fraction 2s¯uA of a second. If the rate of the second RPC is sf , then the rate of accidental coincidences s¯g after a long period is determined the following equation: r)L=r)×P ( t>;B ) ++ri+×P ( t>;A ) , (6.5) where ∫(uA;j) is the probability of plane B delivering a pulse within uA when a pulse is sent by plane A, and ∫(uA;#) is the probability of plane A delivering a pulse within uA when a pulse is sent by plane B. P ( t> ) =1−exp ( −r+t> ) ≈r+t>+. (6.6) The probability when the window size uA is much shorter than the individual rates is given in first order by Equation 6.6. Therefore, the rate of accidental coincidences is calculated as follows: r)L=2+r)+ri+t>+. (6.7) 6. Calibration and Reconstruction 121 Extending the argument to three planes it is easy to demonstrate that the rate is given by: r)L=3+r)+ri+rN+t>+. (6.8) Figure 6.16: Random coincidences for two samples of TRISTAN data left) unstable and right) stable environmental conditions. TRISTAN window size is set to 40 ns, whereas for TRAGALDABAS, it is 50 ns. The effect of the random coincidences is dominant under unstable environmental conditions such as extreme temperature changes. An increase in the temperature also produces an increase in the electronic noise in the detector. In Figure 6.16, the left plot corresponds to a period of TRISTAN data where the working conditions changed from stable to unstable due to a drastic temperature increase caused by an air conditioning issue. The average trigger rate for such period was about 110 Hz, which makes the effect of the random coincidences very important, reaching 18%. On the other side, a period of stable conditions is shown, and the effect of the random coincidences is below 3% of the total coincidences rate for a trigger rate of around 120 Hz. 6.5 ACTIVE AND DEAD TIMES Additional corrections to the data due to active and dead times might be required. The active time accounts for the seconds the detector takes data without any interruption. Data averaging over certain periods DAMIÁN GARCÍA CASTRO 122 require the active time correction due to the fact that the acquisition time might differ per interval. The dead time correction becomes important when operating at very high trigger rates. The relationship between real and measured counting rates, considering that the non-dead time disturbed distribution is Poissonian, is given by the next equation for the non-paralyzable dead time case: Rp=RK+ 1−τ+RK+, (6.9) where @| and @Ω are the real and measured counting rates, respectively, and z is the dead time [111]. In this case, its effect is less than 0.5% for a measured trigger rate of around 100 Hz and a dead time of 4 µs , making it almost negligible. 6.6 EFFICIENCY RPCs are used in high-energy physics experiments due to their high efficiency. The peak of the efficiency distribution aims to be around 99%, while the tail at lower efficiency values is due to RPCs working out of the range of the optimal parameters. Normally, the efficiency drops are originated by dramatic temperature changes. These changes cause the saturation of the HV and the background currents, which may increase the number of streamer signals, and so the recovery time of the electrodes. TRISTAN and TRAGALDABAS RPCs operate in avalanche mode at the edge of the voltage plateau. Thus, HV changes cause major changes in the working conditions affecting the measured CRs rate. RPCs at their optimum involves a high efficiency and low noise level. Several methods, labeled as tefficiency, have been developed to study the detection efficiency. The efficiency of the whole detector is calculated by multiplying the individual efficiencies of each RPC. Comparing the different methods described in this section the information about the systematic uncertainties can be inferred. 6. Calibration and Reconstruction 123 6.6.1 Tracking method Usually, the CR detection efficiency is calculated by the tracking method. This method consists of finding the particles going through an RPC plane that is not in trigger using the information given by the RPCs that are in coincidence trigger. Hence, the reason why the random coincidences effect is important. The efficiencies for each plane can be obtained by changing the coincidence trigger configuration, but we assume that all RPC planes behave similarly. Therefore, all RPCs have the same efficiency given by the tracking method ( •Ã| ) for the plane T2 when T1 and T3 are in coincidence. To determine the efficiency of unpacked HLD files, the look-up table, and the charge and time calibration constants are needed. CR events are processed individually, starting by filtering the hits according to the charge calibration constants. A second filter using the time calibration constants can be added to reduce noise contamination. However, the charge filter is enough to remove most of the random coincidences, which probability for three planes is less than 2%, as it was shown in Section 6.4. For events with a hit multiplicity equal to one in T1 and T3, the algorithm searches for hits in T2. The information of the fired cells in T1 and T3, i.e., the Kx and Ky coordinates, defines the searching grid in T2. T2 efficiency, for the incident angles defined by T1-T3 cell centers, is given by the ratio between the number of events with and without at least one hit in T2 during a certain time. TRISTAN and TRAGALDABAS efficiencies are calculated on a two-hour basis. Data averaging over a certain period requires a correction related to the active time of the detector. The tracking method of TRISTAN has been developed in MATLAB whereas for TRAGALDABAS it was implemented in C++. In Figure 6.17, a comparison between the efficiency for vertical incident particles with and without the random coincidences correction is presented. This correction is of special interest for the period of the first latitudinal survey performed by TRISTAN, which will be described in Chapter 7, due to the air conditioning issues that caused extreme temperatures where the detector was located. For other periods the correction is included but is less significant. DAMIÁN GARCÍA CASTRO 124 Figure 6.17: Efficiency for vertical incident particles with and without the random coincidences correction. TRISTAN data sample. 6.6.2 Principal component analysis RPC performance depends on many factors such as HV, background currents, environmental conditions, gas flow, among others related to the building process. Changes in the conditions have a different impact on RPC efficiency. Knowing the efficiency of T2, we can estimate the efficiency of the remaining planes by performing a principal component analysis (PCA) [ 112 ]. The main goal of the PCA is to understand the relationship between a group of slow control variables and the efficiency calculated by the tracking method for the T2 plane. This technique consists of a dimensionality reduction by linearly transforming the original variables into a new set of uncorrelated variables, which are called principal components (PCs). The first PC accounts for the maximum variance and so on. Taking the HV, background currents, pressure, temperature, and humidity of T2 as inputs or features, the PCA provides their relationship with the target variable, which is the efficiency of the T2 plane. The resulting equations that describe the target variable as a function of the slow control variables are used to obtain the efficiency of the other planes. PCA algorithm has been implemented in Python from scratch, and the steps will be described below. 6. Calibration and Reconstruction 125 Since the majority of optimization or machine learning algorithms, like PCA, perform better when all the features are along the same scale, data has to be standardized. It makes sense because the feature subspace given by the PCA maximizes the variance along the axis. Standardization of a feature value is given by the following calculation: xQõY O=xO−µM+ σM+, (6.10) where kw and ûw are the mean and the standard deviation of the feature variable. As a result of the standardization, feature values have a mean of 0 and standard deviation of 1 so they have the same parameters as a normal distribution. Correlation between pairs of feature variables measures how they vary with each other. The covariance û/l for two features %/+ and %l with n values is obtained as follows: σ2m=1 n−10fx2O−µ2hfxm O−µmh § Oc%+. (6.11) As a consequence of the standardization, the means are zero, and the covariance matrix of the standardized data ( n ) can be calculated by Equation 6.12. o=1 n−1C”C+. (6.12) Directions and magnitudes of maximum variance, or the PCs, are represented by the eigenvectors and eigenvalues of the covariance matrix. Eigenvector Ì and eigenvalue ã of the covariance matrix, satisfy the condition pÌ=ãÌ . The eigenvalues of q are the roots of the following characteristic equation: det(o−λr)=0+, (6.13) and the eigenvectors are calculated for the correspondent eigenvalues. DAMIÁN GARCÍA CASTRO 126 Eigenpairs are sorted based on the magnitude of their eigenvalues to find the PCs with the highest variability. Eigenvectors of symmetric matrices are orthogonal which means that the first PC explains most of the variance and is orthogonal to the second, and so on. The number of PCs selected for the dimensionality reduction is based on the cumulative explained variance. An example of a data set of TRISTAN is shown in Figure 6.18. The first two PCs are selected to reduce a 5-dimensional feature space to a 2-dimensional feature subspace, as they explain almost 90% of the variance. Figure 6.18: PCs individual and cumulative explained variance representation. Correlation matrices before and after performing the PCA are shown in Figure 6.19 for the same data set. Figure 6.19: Correlation matrices left) before, and right) after the PCA. Inputs: temperature (T), pressure (P), humidity (H), HV (V), and currents (I). 6. Calibration and Reconstruction 127 The projection matrix W is constructed with the eigenvectors of the highest explained variance and is used to transform the original feature data onto the new reduced feature subspace. The transformation is done via Equation 6.14. s=C∙t+, (6.14) where Y is the matrix of the transformed feature data. Figure 6.20 presents the PCs corresponding to the aforementioned set of data. In this case, the 5-dimensional subspace is plotted to show the importance of the first two PCs and how higher components account for small oscillations or short-term variability. Figure 6.20: Example of PCs behavior for the above-mentioned data set. The first two components describe almost 90% of the feature data variability. It is important to bear in mind that the target variable for the PCA is the efficiency of T2 from the tracking method. Several methods have been developed to find the best criteria for estimating the efficiency of the remaining planes. The best results are given by a 2-dimensional fit of the first two PCs as a function of the efficiency (Figure 6.21) and a running PCs linear regression method. The running method consists of a first linear regression of PC1 and efficiency,