Modelovanje gasnih detektora čestica visokih energija primenom tehnike elektronskih rojeva

Abstract

Zahvaljujući svojim dobrim performansama i niskoj ceni po jedinici zapremine, gasni detektori su najčešće korišćeni detektori u eksperimentalnoj fizici visokih energija. Pored fizike visokih energija, ovi detektori nalaze primene u mnogim drugim oblastima, poput dozimetrije i zaštite od zračenja, medicine, fizike kosmičkog zračenja i geofizike. Postoje brojni modeli ovih uređaja. Bez obzira da li su analitički ili numerički, stohastički ili deterministrički, svi ovi modeli koriste transportne i/ili sudarne podatke za elektrone u gasovima. Nažalost, uobičajeno je da se unutar detektorske zajednice, ovi podaci kao i tehnike za njihov proračun primenjuju nekritički. Ova praksa, kao što je diskutovano u ovoj disertaciji, veoma često vodi ka pojednostavljenim modelima detektora i neadekvatnoj metodologiji za pristup i analizu. Imajući ove činjenice u vidu, osnovni cilj ove disertacije je da na osnovama transportne teorije rojeva elektrona, ukaže na čitav spektar važnih aspekata u proračunu i implemetanciji transportnih podataka u modelovanju kao i da na konkretnim modelima detektora pokaže kako podaci i njihova implementacija utiču na izračunate signale i performanse detektora. Osim toga, u ovom radu su detaljno analizirane netipične pojave u transportu elektrona indukovane eksplicitnim efektima nekonzervativnih sudara i njihove potencijalne implikacije u modelima. Specifičnosti transporta elektrona u ukrštenom električnom i magnetskom polju, ilustrovane su na primeru detektora tipa Time Projection Chamber (TPC) koji se koriste za trodimenzionalnu rekonstrukciju putanje čestica. Kod ovih detektora magnetsko polje ima ulogu u redukciji bočne difuzije od koje direktno zavisi prostorna rezolucija dok npr. linearnost rekonstrukcije zavisi od osetljivosti brzine drifta na temperaturu i nehomogenost magnetskog polja. U ovom kontekstu potencijalne optimizacije radnih uslova, a takođe imajući u vidu i neželjene varijacije parametara tokom rada, sistematski je razmotren uticaj električnog i magnetskog polja, temperature i pritiska gasa kao i udela nečistoća u gasnoj smeši, na transportne osobine elektrona u TPC detektoru. Posebna pažnja posvećena je detektoru sa pločastim elektrodama visoke otpornosti (Resistive Plate Chamber, RPC) koji se koriste za timing i triggering u brojnim eksperimentima fizike visokih energija kao i u drugim oblastima. Rešavanjem Boltzmannove jednačine i primenom Monte Karlo tehnike, koju smo sa jedne strane koristili da proverimo rezultate dobijene Boltzmannovom jednačinom, a sa druge strane za dobijanje prostorno razloženih transportnih parametara elektrona, identifikovani su iobjašnjeni transportni fenomeni elektrona poput negativne diferencijalne provodnosti i grejanja zahvatom elektrona koji su uočeni u gasnim smešama RPC detektora koji se primenjuju na eksperimentima u CERN-u. U ovoj disertaciji, razmotreni su teorijski principi klasičnog fluidnog modela i modela zasnovanog na difuzionoj jednačini i hidrodinamičkoj aproksimaciji na osnovu kojih je razvijen numerički 1.5-dimenizionalni fluidni model RPC detektora. Ovim modelom, ispitivan je razvoj elektronske lavine i strimera pod dejstvom efekata prostornog naelektrisanja i fotojonizacije u gasu. Pokazano je da nepravilna implementacija transportnih podataka, zanemarivanjem eksplicitnih efektata nekonzervativnih sudara, može dovesti do greške od nekoliko stotina procenata u proračunu indukovanog signala. Razmatrana je i osetljivost izračunatog signala detektora na promene setova preseka za rasejanje elektrona u individualnim gasovima gasnih smeša. Konačno, u ovoj disertaciji razvijen je i mikroskopski Monte Karlo model RPC detektora koji se zasniva na praćenju pojedinačnih trajektorija elektrona i njihovih sudara sa molekulima gasa. Pomoću ovog modela, ipitivana je stohastika elektronskog lavinskog procesa. Takođe, koristeći različite setove preseka za rasejanje elektrona u individualnim gasovima gasne smeše, izračunate su vremenska rezolucija i efikasnost RPC detektora koje se dobro slažu sa eksperimentalnim vrednostima.

Owing to their good performance characteristics and low price per unit volume, gaseous particle detectors remained the most commonly used detectors in high energy physics experiments. In addition to high energy physics, these detectors have also found applications in other fields such as radiation protection and dosimetry, medicine, cosmic ray physics and geophysics. A number of methods to model particle detectors have been developed. Being analytical or numerical, stochastic or deterministic, detailed knowledge of electron swarm transport properties as well as reliable cross sections for electron scattering are required as an input in modeling. The highly applied nature of the field, has inevitably driven the modeling of these systems more towards empiricism, and unfortunately often away from its roots in the fundamental transport theory of electron swarms. Thus, the main goal of this work is to bridge the gap between the fundamental transport theory of electron swarms and applications in the field of particle detectors. This goal is achieved by considering many elements of the theory which are important for accurate calculation and correct implementation of electron transport data in modeling. In addition, we provide the examples of specific detector models in which the incorrect implementation of data affects the calculated signal and detector performance characteristics. In this work, we discuss atypical manifestation of electron transport phenomena induced by the explicit effects of non-conservative collisions and potential implications arising from their inclusion in the models. The peculiarities of electron transport in crossed electric and magnetic fields are illustrated using the example of Time Projection Chamber (TPC), a detector employed for three-dimensional reconstruction of particle trajectories. In this detector, the magnetic field suppresses the transverse diffusion, which directly affects the spatial resolution. On the other hand, the reconstruction linearity depends on the sensitivity of drift velocity on the gas temperature and non-uniformity of the magnetic field. With this as one of the motivating factors, and also having in mind the unwanted variation of detector parameters with time, we systematically study the influence of the electric and magnetic fields, gas pressure and temperature, as well as the impact of impurities in the gaseous mixture, on the electron transport properties in TPC. Special attention is given to the Resistive Plate Chambers (RPCs) which are used for timing and triggering purposes in many high energy physics experiments and elsewhere. The Boltzmann equation is used for the determination of electron swarm transport properties under conditions when transport is greatly affected by nonconservative collisions. A Monte Carlo simulation technique has been used with the aim of verifying the results based on the Boltzmann equation as well as for the evaluation of spatially resolved electron transport data. This segment of data is used to explain the existence of certain kinetic phenomena, including negative differential conductivity and attachment heating, which are important for the detector behavior. Within the framework of the classical fluid model and using the diffusion equation in association with the hydrodynamic approximation, we have developed a numerical 1.5-dimension fluid model of an RPC. This model is used to study the electron avalanche and streamer development under the influence of space charge effects and photoionization. We have shown that improper use of the data, especially the lack of correct representation of the explicit effects of non-conservative collisions, can lead to errors of a several hundred percents for the calculated signals. In addition, we discuss the sensitivity of the output detector signals with respect to the sets of cross sections for electron scattering. Finally, in this thesis we present our microscopic Monte Carlo model of RPC based on the tracking of individual electron trajectories and their collisions with the gas molecules. Using this model, we study the electron avalanche fluctuations and the related processes. The detection efficiency and timing resolution are calculated using different sets of cross sections for electron scattering. We have found that our results agree very well with the measured data.