ENGINEERING AND TECHNOLOGY
ISTANBUL TECHNICAL UNIVERSITYF GRADUATE SCHOOL OF SCIENCE
OPTIMIZATION OF GEOMETRY OF THE DRIVING ELECTRIC FIELD FOR BETTER DETECTION EFFICIENCY OF
RADON DECAY PRODUCTS
M.Sc. THESIS Esra BARLAS
Department of Phyiscs Engineering Phyiscs Engineering Programme
ENGINEERING AND TECHNOLOGY
ISTANBUL TECHNICAL UNIVERSITYF GRADUATE SCHOOL OF SCIENCE
OPTIMIZATION OF GEOMETRY OF THE DRIVING ELECTRIC FIELD FOR BETTER DETECTION EFFICIENCY OF
RADON DECAY PRODUCTS
M.Sc. THESIS Esra BARLAS (509091125)
Department of Phyiscs Engineering Phyiscs Engineering Programme
Thesis Advisor: Prof. Dr. Cenap ÖZBEN
˙ISTANBUL TEKN˙IK ÜN˙IVERS˙ITES˙IF FEN B˙IL˙IMLER˙I ENST˙ITÜSÜ
RADON BOZUNUM ÜRÜNLER˙IN˙IN DAHA ˙IY˙I B˙IR VER˙IM ˙ILE DETEKTE ED˙ILEB˙ILMES˙I ˙IÇ˙IN RADON DETEKS˙IYON S˙ISTEM˙IN
ELEKTR˙IK ALAN GEOMETR˙IS˙IN˙IN OPT˙IM˙IZASYONU
YÜKSEK L˙ISANS TEZ˙I Esra BARLAS
(509091125)
Fizik Mühendisli˘gi Fizik Mühendisli˘gi
Tez Danı¸smanı: Prof. Dr. Cenap ÖZBEN
Esra BARLAS, a M.Sc. student of ITU Graduate School of Science 509091125 suc-cessfully defended the thesis entitled “OPTIMIZATION OF GEOMETRY OF THE DRIVING ELECTRIC FIELD FOR BETTER DETECTION EFFICIENCY OF RADON DECAY PRODUCTS”, which she prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below.
Thesis Advisor : Prof. Dr. Cenap ÖZBEN ... Istanbul Technical University
Jury Members : Prof. Dr. Serkant Ali ÇET˙IN ... Do˘gu¸s University
Assoc. Prof. Dr. ˙Iskender REYHANCAN ... Istanbul Technical University
Date of Submission : 4 May 2012 Date of Defense : 8 June 2012
To my beloved family,
FOREWORD
I would like to express my sincere gratitude to my advisor Professor Dr. Cenap Özben. His many years of experience in the field of Nuclear Physics gave me the opportunity to learn how to make a scientific research. He always had time and energy to work even though he had lots of duties in the management of the faculty. Without his suggestions and guidance, there wouldn’t be any results to present in this project. I am very grateful to him for being so much supportive.
I would also like to thank to my co-workers Ahmet Bayrak and Mehmet Erhan Emirhan for being helpful and supportive in this research and Selçuk Hacıömero˘glu for letting us use his Geant4 interface which was very helpfull to build different simulations easily. I would like to thank to Mete Yücel, who is also a research assistant in physics department, for helping me in every aspect of my work and life.
In addition I would like to thank to TUBITAK for supporting our project financially. Finally I would like to thank to my family for encouraging me to do the job I want to do, and for being always supportive about my education. Without them I wouldn’t be here.
May 2012 Esra BARLAS
(Physics Engineer)
TABLE OF CONTENTS Page FOREWORD... ix TABLE OF CONTENTS... xi ABBREVIATIONS ... xiii LIST OF TABLES ... xv
LIST OF FIGURES ...xvii
LIST OF SYMBOLS ... xix
SUMMARY ... xxi
ÖZET ...xxiii
1. NATURAL RADIOACTIVITY AND RADON... 1
1.1 Natural Radioactivity... 1
1.2 Radioactive Decay ... 2
1.2.1 α Decay ... 3
1.2.2 β Decay ... 3
1.2.3 γ Decay ... 3
1.3 Uranium Decay Series ... 4
1.4 Radon-222 and Its Decay Products ... 5
1.5 Radon Health Effects... 7
1.6 Radon Measurements Methods ... 8
1.7 Interaction of Alpha Particles with Matter ... 10
1.8 Radon vs Earthquakes ... 11 2. SIMULATION SOFTWARES... 15 2.1 SRIM ... 15 2.2 Poisson Superfish... 16 2.3 COMSOL Multiphysics... 17 2.4 GEANT4... 19 2.4.1 Design overview ... 20
2.4.2 Geometry and detector representation... 20
2.4.3 Tracking... 20
2.4.4 Physics ... 20
2.4.5 Particles and materials ... 21
2.4.6 User actions ... 21
3. SIMULATIONS AND RESULTS... 23
3.1 Introduction ... 23
3.2 Optimizations of Electric Field Geometry ... 23
3.2.1 Choosing the best electric field geometry ... 25
3.2.2 Geant4 simulation of the detector with electric field... 25 xi
3.2.2.2 Calculation of radon concentration... 27
3.2.2.3 Building the geometry ... 28
3.2.2.4 Including the electric field algorithm... 28
3.2.2.5 Alpha particle in an electric field... 29
3.2.2.6 Motion of alpha particles in an electric field ... 30
3.2.3 Comparison of Geant4 simulations and experiment for radium source . 32 3.2.4 Comparison of Geant4 simulations and experiment for radon source ... 34
3.3 Optimizations of the Detector Geometry ... 35
3.3.1 Optimization of the photodiode location in the detector ... 35
3.3.2 Optimization of radious of the hemisphere ... 36
3.3.3 Other issues in the design of the optimum geometry ... 37
3.4 Systematic Effects of Radon Detection ... 38
3.4.1 Humidity... 38 3.4.2 Ion/Dust density... 39 4. CONCLUSIONS ... 41 REFERENCES... 43 CURRICULUM VITAE ... 45 xii
ABBREVIATIONS
FFT :Fast Fourier Transform
SRIM :Stopping and Range of Ions in Matter
LIST OF TABLES
Page Table 3.1 : Electric field values for three Geometries while photodiode is in
(0,0,0) and placed in x-y plane (z is distance above the photodiode). 26 Table 3.2 : Number of alpha particles reached to the photodiode in various
geometries. ... 30 Table 3.3 : Number of alpha particles reached to photodiode in radon
concentrations. ... 32 Table 3.4 : The relation between the radius of hemisphere and electric field
above the photodiode. ... 36 Table 3.5 : Ratio of components of air elements for different humidity. ... 39
LIST OF FIGURES
Page
Figure 1.1 : Uranium decay series . ... 4
Figure 1.2 : Radon decay products [1]... 6
Figure 1.3 : Relative activity concentration of222Rn and its decay products as a function of time [1]. ... 7
Figure 1.4 : Arithmetic mean radon level by country [2] ... 8
Figure 1.5 : Range of alpha particles in silicon for different energies. [3] ... 11
Figure 1.6 : Radon concentration before, after and during after shocks of Tashkent earthquake [4] ... 12
Figure 2.1 : SRIM User Interface. ... 15
Figure 2.2 : SRIM Software: Simulation of Helium nucleus in the silicon target layer... 16
Figure 2.3 : Stopping power of silicon from SRIM examples. ... 17
Figure 2.4 : Poisson ... 18
Figure 2.5 : Comsol: Electric Sensor Example ... 18
Figure 2.6 : Flow chart of how Geant4 works [5] ... 22
Figure 3.1 : Electric field geometries... 24
Figure 3.2 : COMSOL simulations of electric field for hemisphere geometry ... 30
Figure 3.3 : Locations on the radium source where the particle were first located in the simulation. ... 32
Figure 3.4 : Radium spectrum drawn with the results of the simulation. ... 33
Figure 3.5 : Experimental radium spectrum. ... 33
Figure 3.6 : Simple drawing of the simulation geometry. ... 34
Figure 3.7 : Energy spectrum of alpha particles reaching to the detector surface under the influence of 2.7× 105V/m electric field... 35
Figure 3.8 : Energy Spectrum of alpha particles measured with the radon detector. ... 36
Figure 3.9 : Optional caption for list of figures ... 37
Figure 3.10: Design of electrostatic collection geometry. ... 38
Figure 3.11: Comparison of the electric field with and without the conducting base plate... 39
Figure 3.12: Influence of conducting bottom layer to the electric field strength for the axis through the detector center... 40
Figure 3.13: Spectrum of energy of alpha particles taken with radon detector. ... 40
LIST OF SYMBOLS α : Alpha β : Beta νe : Electron neutrino γ : Gamma λ : Lambda τ : Tau xix
OPTIMIZATION OF GEOMETRY OF THE DRIVING ELECTRIC FIELD FOR BETTER DETECTION EFFICIENCY OF
RADON DECAY PRODUCTS SUMMARY
222Rn is a radioactive isotope which is formed in uranium decay series. It also
decays to other radioactive isotopes as polonium with alpha and beta decay. Radon is a noble gas and it has no color or odor. That’s the only way to detect it to use a radon detector.Although it is possible to measure radon itself with detectors, radon concentration is usually measured by detecting the alpha particles which are the products of radon’s alpha decay. It can be measured with active or passive methods. The main purpose of this research is optimizing the electric field of the radon detector we built in Nuclear Physics Laboratory of Istanbul Technical University which is supported by TÜB˙ITAK. Optimizing processes included the simulations of the geometries of the electric field and the location of photodiode in the radon monitoring system. There were three prototypes of the geometry which were considered to be proper: linear, half-cylindrical and hemispherical type of geometries. These geometries were simulated in order to compare the electric field generated. As a result, the hemispherical electric field was found to be the most efficient method to collect alpha particles in silicon photodiode of the detector.It is especially more effective at collecting the particles not just above the photodiode but also the ones which are on the edge of hemisphere’s base plate. The main part of the simulations were accomplished with the software package Geant4 which includes several tools to be able to simulate the particles through matter. Electric field information which was obtained from COMSOL simulations were imported into Geant4 code. These behavior of radon atom and its decay products were investigated in a volume with these electric field geometries applied. The optimized location of photodiode was simulated with the help of POISSON software which is a package that calculates the electromagnetic field in matter. The base layer of the hemisphere material was included after the simulations indicated that it was necessary in order to collect the particles far away from the photodiode. Measurements taken with radon detector using radon and radium sources were compared with the Geant4 simulations and they were consistent with each other. They weren’t full simulations that describes the whole events and geometries in radon monitor system, but each simulations had a specific task to understand the behavior of particles and to crosscheck the measurements that were taken with radon detector. The effects of humidity and dust particles were investigated whether they change the count of alpha particles detected in the detector or not. As a result it showed that humidity and counts did not have a linear relationship with each other. However the effect of dust particles in the volume with electric field is known to change the number of counts, since positively charged polonium particles attach themselves on the dust particles and be drifted toward the photodiode with the help of electric field. So the effect of charge number to the counts was investigated briefly in Geant4 simulations without knowing the exact behavior of dust particles which is actually hard to know.
RADON BOZUNUM ÜRÜNLER˙IN˙IN DAHA ˙IY˙I B˙IR VER˙IM ˙ILE DETEKTE ED˙ILEB˙ILMES˙I ˙IÇ˙IN RADON DETEKS˙IYON S˙ISTEM˙IN
ELEKTR˙IK ALAN GEOMETR˙IS˙IN˙IN OPT˙IM˙IZASYONU ÖZET
222Rn uranyum bozunum serisi içerisinde yer alan radyoaktif bir izotoptur. Alfa, beta
ve gama bozunumları ile kendisi gibi radyoaktif olan izotoplar olan218Po ve214Po’ u olu¸sturur. Radon gazı aktif ve pasif dedi˘gimiz iki çe¸sit ölçüm tekni˘giyle de ölçülebilir. Pasif ölçümlerde radon veya ürünleri farklı detektörler yardımıyla toplandıktan sonra laboratuvarlara götürülüp, analizlerinin buralarda gerçekle¸stirilmesi tekni˘gini içerir. Aktif ölçüm yöntemlerinde ise radon veya ürünlerinin konsantrasyonlarının ölçümden hemen sonra veya e¸s zamanlı olarak kullanıcıya aktarması metodu kullanılmaktadır. Radon konsantrasyonu ölçümü genelde bozunum ürünleri olan alfa parçacıklarının detekte edilmesi ile gerçekle¸stirilir. Bu çalı¸smanın ana konusu ˙Istanbul Teknik Üniversitesi Nükleer Fizik Laboratuvarında, TÜB˙ITAK deste˘gi ile üretilen radon dedektörünün elektrik alan optimizasyonunu içermektedir. Ayrıca dedektörün asıl ölçüm yapan kısmı olan silikon foto diyotunun sistem içerisindeki lokasyonu da incelenmi¸stir. Öte yandan ölçümleri etkileyecek sistematik etkiler olan nem, basınç, sıcaklık, toz parçacıklarının ölçümlerde yaptıkları de˘gi¸siklikler de simülasyonlar yardımıyla incelenmi¸stir. Ayrıca radon ve radyum kaynaklarıyla alınan ölçümlerden elde edilen spektrumlar ile simülasyon sonuçları kar¸sıla¸stırılmı¸stır. Bütün bu simülasyonlara geçmeden önce ise alfa parçacı˘gının havada veya vakumda ne kadar yol aldı˘gını, havada nasıl çarpı¸smalar ya¸sadı˘gını, radon ve ürünlerinin bozunma sonucu olu¸sturdu˘gu alfa parçacıklarının enerjileri için incelenmi¸stir.
Çalı¸sma boyunca kullanılan yazılımlardan ilki SRIM olmakla birlikte bu program ile alfanın herhangi bir materyal içerisinde aldı˘gı yol hakkında bilgi edinilmi¸stir. COMSOL ise sonlu elemanlar yöntemi kullanarak sınır-de˘ger problemi çözebilen bir simülasyon paketidir. Bu çalı¸smada ise 3 boyutta tanımlanan geometriler için istenilen koordinatlarda elektrik alan vektörlerini bulmak için kullanılmı¸stır. Geant4 ise parçacıkların madde içerisindeki etkile¸simlerini inceleyen ve bunları simüle edebilen c++ kaynaklı bir yazılım paketidir. Son olarak Poisson yazılımı 2 boyutta elektrik ve manyetik alan hesaplamaları yapabilen bir pakt yazılımdır.
Çalı¸smanın ba¸slangıcında iyi bir toplama etkisi yapaca˘gını tahmin edilen üç farklı geometri mevcut idi. Bunlar hemen hemen do˘grusal bir elektrik alan yaratacak olan diskli sistem, yarım silindirik sistem ve yarımküre sistemiydi. Bu geometrilerden diskli ve yarım küreli geometriler öncelikle azimuthal olarak simetrik olduklarından tercih edilmi¸slerdir (Bu tarz bir simetrinin merkeze do˘gru olan bir elektrik alanın ¸siddetini ve yönünü etkileyece˘gi a¸sikardır). ˙Iletken olarak tanımlanan bu materyaller COMSOL programı ile yaratılıp yüzeylerine yüksek +3500 V gerilim verildi. Bu gerilim, yapılan hesaplamalar sonucu gerekli elektrik alanı elde edebilmek için yeterli görünmü¸stür. Fotodiyot ise topraklandı˘gı için bu materyallerin yüzeyinde fotodiyota do˘gru yönelen bir elektrik alan meydan getirildi.
COMSOL ile yapılan üç farklı simülasyon sonucu elde edilen farklı koordinatlardaki elektrik alan vektörleri, radon, polonyum ve alfa parçacıklarının madde içerisinde davranı¸sını simüle edecek olan Geant4 koduna enjekte edilmi¸stir. COMSOL sonuçlarından yapılan analizlere göre farklı noktalardaki elektrik alan bilgileri kar¸sıla¸stırılmı¸s, sonuçlar fotodiyotun üstende veya hacmin yan kısımlarında en iyi sonucu yarım küre geometrinin verdi˘gini göstermi¸stir. Di˘ger iki geometriler bazı koordinatlarda yarım kürenin elektrik alanına yakla¸smı¸s olsalar da, sonuçta her noktada yarım küre di˘gerlerinden daha iyi bir sonuç vermi¸stir. Diskli ve yarım silindirik geometrilerin ise birbirleriyle kar¸sıla¸stıracak olunursa diyot yakınlarında diskli sistemin yarım silindire göre daha iyi sonuçlar verdi˘gi sonucuna ula¸sılmı¸stır. Geant4 içerisine bu üç farklı elektrik alan bilgisi, radon parçacıklarının yaydı˘gı alfa parçacıklarını detekte edecek olan fotodiyot geometrisi ve ortamdaki hava bilgisi tanımlandı. Havayı olu¸sturan elementler olarak oksijen, argon, hidrojen ve azot elementlerinin oranları oda sıcaklı˘gında ve 1 atmosfer basınçta tanımlandı. Her bir parçacı˘gın hangi fiziksel olaylardan geçece˘gi, hangi bozunumları yapaca˘gı, hangi ortamların nelere kar¸sı duyarlı oldu˘gu tanımlanmı¸stır. Ayrıca ortama bırakılacak parçacı˘gın sayısı, enerjisi, çe¸sidi gibi bilgilerde Geant4 kodu içerisinde tanımlanmı¸stır. Bu kodlar her bir çalı¸smada farklı amaca hizmet ettiklerinden, her seferinde ortamın yeni ko¸sulları koda tanımlanmı¸stır. Kısacası yapılan simülasyonlar farklı radon konsantrasyonları ve elektrik alan de˘gerleri için gerçekle¸stirilmi¸s, sonuçta detektörün alfa parçacı˘gı toplama verimi en fazla olan durum olarak yarım küre metodu bulunmu¸stur. Bu sonuçlar daha önce her bir elektrik alan geometrisi için ayrı ayrı ko¸sulmu¸s olan COMSOL simülasyon sonuçlarıyla da tutarlıdır.
Radon detektörüyle yapılan ölçümler ile simülasyon sonuçlarını kar¸sıla¸stırmak ve birbirleri ile tutarlı olup olmadı˘gını görmek amacıyla radon ve radyum kaynaklarıyla ölçümler alınmı¸stır. Bu ölçümler laboratuvarda, oda sıcaklı˘gında, kayna˘gın geometri içerisine koyulmasıyla alınmı¸stır. Farklı geometrilerdeki bu kaynakların fiziksel yapıları Geant4 koduna eklenip ölçümlerin yapıldı˘gı aynı ko¸sullar altında simülasyonlar yapılmı¸stır. Detektör ile alınan radon ve radyum spektrumları ile Geant4 simülasyon sonuçlarının analiz edilmesiyle elde edilen spektrumların birbirleriyle tutarlı oldu˘gu görülmü¸stür. Literatürdeki makaleler ile yapılan radon spektrum kar¸sıla¸stırması da sonuçları do˘grulamaktadır.
x-y düzleminde tabanı olan yarım kürenin azimuthal simetriye sahip olmasından dolayı tam merkezin üzerinde x ve y yönünden gelen elektrik alan bile¸senleri birbirini götürür. ˙I¸ste bu yüzden yarım küre sistemindeφ simetrisi oldu˘gu göz önüne alarak fotodiyotun sistem içerisindeki yeri için Poisson ile 2 boyutta simülasyonlar yapılmı¸stır. Bu simülasyonlar sonucu fotodiyotun sistemdeki optimum lokasyonu belirlenmi¸stir. Poisson sonuçlarından farklı noktalardaki elektrik alanları kar¸sıla¸stırılmı¸s ve sonuç olarak silikon fotodiyotun tabandan 1-2 cm içeride gömülü olmasının elektrik alanı arttırıcı bir faktör oldu˘gu çıkarılmı¸stır. Öte yandan yarım küre elektrik alan sisteminde yarım kürenin tabanına eklenecek +3500 V’luk bir iletkenin, sadece fotodiyot üzerindeki parçacıkları de˘gil, fotodiyota uzak olan kenardaki parçacıkları da sürükleyecek bir elektrik alan yarataca˘gı dü¸sünülerek, böyle bir iletkenin olması durumunda nasıl bir fark yarataca˘gı Poisson ile simüle edilmi¸stir. Sonuçta elde edilen elektrik alan ¸siddeti önceki halinden bazı noktalarda 1000 V/cm e kadar varan de˘gerlerde daha fazla bulunmu¸stur. Aynı sonuçları yapılan COMSOL simülasyonları ile de elde edilmi¸stir.
Deteksiyonu etkileyen bazı sistematik etkiler olan basınç, sıcaklık ve nem gibi etkenlerin parçacıkların ilerledi˘gi havanın yo˘gunlu˘gunu ve içindeki elementlerin oranını de˘gi¸stirdi˘gi göz önüne alınarak yapılan simülasyonlarda bu etkenlerin sayımla lineer bir ili¸ski içerisinde olmadı˘gı sonucuna varılmı¸stır. Yapılan simülasyonlar sonucu hava yo˘gunlu˘gunun etkisi tam olarak gözlenememekle birlikte asıl önemli olanın havadaki su moleküllerinin polonyumları tutması sonucu deteksiyonun de˘gi¸sip de˘gi¸smedi˘gini ara¸stırmak oldu˘gu sonucuna varılmı¸stır. Öte yandan radon monitör sistemi içerisinde yer alan devrelerin içerisindeki elemanların farklı sıcaklıklarda farklı tepkiler verdi˘gi göz önüne alınırsa, sayımda de˘gi¸sece˘ginden, kalibrasyon yaparken detektörün sıcaklık, basınç ve nem ile korelasyonuna bakılması gerekmektedir. Tabi bu çalı¸smada elektronik elemanların verdi˘gi tepki simüle edilmemi¸stir. Genel olarak tam bir simülasyon de˘gil de ara¸stırılmak istenilen konulara yönelik geometriler yaratılıp, buna göre parçacıklar olu¸sturulmu¸s, hızlı ve kısmi simülasyonlar yapılarak sadece istenilen bilgilere ula¸sılmı¸stır. ¸Sayet sistemdeki bütün hacimler tanımlanıp, çevredeki bütün fiziksel olayları simülasyona yansıtmak istenilirse, çok az olay için bile yapılsa günler sürecek simülasyonlar yapılmak zorunda kalınırdı. Yapılan kısmi simülasyonlar ile istenilen analizler yapılmı¸s ve bu analizler kar¸sıla¸stırma yapmaya olanak sa˘glamı¸stır.
Literatürdeki radon ölçme tekniklerinin incelendi˘gi bir çok makalede, elektrik alan içerisinde sürüklenen parçacıklarının yüklü parçacıklar olan Po ve alfa parçacıkları oldu˘gu gösterilmi¸stir. Radon alfa bozunumu yaparken % 80 olasılıkla +2 yüklü bir polonyum atomu, % 20 olasılıkla ise nötr bir polonyum atomu olu¸sturmaktadır. Ortamın tozlu oldu˘gunu da göz önüne alırsak burada bulunan toz parçacıklarına yapı¸san yüklü polonyum atomları elektrik alan yardımıyla detektör yakınlarına ta¸sınıp alfa bozunumu yaptıklarında, bu alfa parçacıkları detektör etrafında daha da güçlü olan elektrik alan yardımıyla silikon fotodiyot içine sürüklenip detekte edilirler. Dolayısıyla iyon oranı yüksek olan bir ortamda alınan ölçümler ile verim oranı yükselmi¸s oluyor. Öte yandan tozun fotodiyot üzerinde toplanması da radon deteksiyonu sırasında istenilen bir olay de˘gildir.
Geant4 ile yüklü parçacık tanımlayıp bunun hareketini incelemek mümkün olsa da, toz üzerinde ta¸sınan polonyum atomunun simüle edilmesi henüz mümkün olmamı¸stır. Bu konu hakkında deney düzenekleri olu¸sturularak ortamdaki yük oranının deteksiyon verimini yükseltmesi hakkında çalı¸smalar yapılmı¸s olsa da toz parçacıklarının içeri˘gi bilinmedi˘ginden kesin sonuçlar verecek bir simülasyon yapılması ¸simdilik mümkün gözükmemektedir. Fakat farklı yük oranına sahip atomlar ile yapılan denemelerde her ne kadar polonyumun bu yüklü atomlara yapı¸sması sa˘glanamasa da yük oranının deteksiyona olan pozitif etkisi gözlemlenebilmi¸stir.
Son olarak, simülasyon sonuçlarına göre yapılan radon detektörünün test denemeleri ba¸sarılı olup, elektrik alan ile yapılan ölçümlerde beklenildi˘gi gibi yüksek verim artı¸sı gözlenmi¸stir. Elektrik alan yoklu˘gunda farklı ortam ko¸sullarında saatlerce birkaç sayım alınabiliyorken, aynı ortam ko¸sulları altında elektrik alan varlı˘gıyla yapılan ölçümlerde fark edilebilecek miktarda artı¸sı gözlenmi¸stir.
Detektörler test a¸samasında iken alınan ölçümler analiz edildikten sonra, simülasyon sonuçlarıyla detektörle alınan spektrumların daha do˘gru bir kar¸sıla¸stırması yapılması planlanmaktadır. Böylece detektörün bulundu˘gu ortamı birebir olmasa da gerekli parametreleri programlarda tanımlayarak olayları simüle etme olana˘gı sa˘glanmı¸s olacaktır.
1. NATURAL RADIOACTIVITY AND RADON
In this chapter natural radioactivity will be explained in order to explain the radioactive decay of radon atoms. Then its decay products and the methods to measure them will be explained very briefly. At the end, radon and earthquake prediction will be explained with some examples from literature.
1.1 Natural Radioactivity
Radiation is energy that travels through medium or space. Universe is filled with radiation and all things on Earth are exposed to radiation which caused by natural events or man made sources. Man made radiation is caused by X-rays and other medical procedures. Natural radiation comes from radioactive atoms in rocks and soils from radon, outer space or human body [5]. There are three main forms of natural radioactive atoms that are found on Earth and they are called radionuclides. These atoms are uranium, thorium and potassium. They have been around since the beginning of Earth.
The Earth and other planets of our solar system formed about 4.5 billion years ago out of material rich in iron, carbon, oxygen, silicon and other heavy elements. These elements were formed by lighter elements; hydrogen and helium. Most of these elements are radioactive. A large part of them decay into stable nuclei immediately, but a few of them, like thorium, neptunium, uranium and actinium, have longer half-lives than the age of earth, so their radioactivity can still be observed [6].
Even though potassium atoms decay to nonradioactive atoms, uranium and thorium decays to radioactive atoms, and then these atoms decay to another radioactive atoms. This keeps going until they decay into lead atoms, which are stable [6]. These decays are called uranium, radium and thorium natural decay series. Decaying is a process for an radioactive element to get rid of the extra energy that it has to be stable.
1.2 Radioactive Decay
When an atom has too much energy, it needs to get rid of that energy and it also needs to have the right numbers of neutrons and protons to stay together. To accomplish that, it usually converts a proton to a neutron or a neutron to a proton or does both of them. This process is called radioactive decay [5].
Decay rate of a radioactive substance decreases with time according to the law of radioactive decay law. If N is the radioactive nuclei number presented at time t and there is no new nuclei in the sample, then decay constantλ can be found with;
λ =−( dN
dt )
N (1.1)
and it gives the probability for the decay of an atom per unit time. This probability is constant and it is independent from the age of atoms. Integrating the equation (1.1), one can easily obtain the exponential law of radioactive decay:
N(t) = N0e−λt (1.2)
where N0 is the number of nuclei present at time t=0. Half life t1/2 gives the time
necessary for the nuclei to decay and can be found by putting N = N0/2,
t1/2= 0.693
λ (1.3)
Mean lifetime of a nuclei is average time that a nucleus is likely to survive before it decays and it can also be found with the equation [6]:
τ= ∫∞ 0 t|dN/dt|dt ∫∞ 0 |dN/dt|dt (1.4) where|dN/dt|dt is the the number of decay between t and t+dt. As the result of the integral it can be shown thatτ = λ1.
There are three primary radioactive decay types:
Alpha decay is the most probable decay type because of emitting alpha can make a huge difference on the energy of atom. Radioactive atoms also decay beta and gamma radiation to be stable.
1.2.1 α Decay
In alpha decay the nucleus emits an alpha particle which is actually nucleus of helium,
4
2He2. Many of heavy nuclei, especially naturally occurring ones decay through α
emission. It can be presented with the following equation:
A
ZX→AZ−4−2X’ +
4
2He2 (1.5)
where X is the initial nuclei and X’ is the final form of the nuclei. The reason that an alpha particle is emitted from a nuclei, when it needs to carry the positive charge away, is because alpha particle is a very stable and tightly bound structure, has relatively small mass compared with the mass of its constituents. It is favored when the disintegration product is needed to be as light as possible and get the largest possible energy out of the system [6].
1.2.2 β Decay
In beta decay, the nucleus becomes stable by converting a proton into a neutron or a neutron into a proton and while this is happening,the mass and stays the same and electric charge is conserved. Beta decay process can be observed in three ways as it is showned in the following lines:
A
ZX→ AZ+1X’ + e−+νe β−decay A
ZX→ AZ−1X’ + e++νe β+ decay
First process is known asβ− decay involves emitting an e− andνe. Second process,
β+ decay, involves emitting a positron andν
e. There is also electron capturing which includes the event of capturing an electron and emitting a neutrino [6].
1.2.3 γ Decay
Radioactive γ decay is a process in which an excited state decays to a lower excited state of ground state by emitting a photon of gamma radiation with an energy equal to difference between these two states. It can be observed with all nuclei which have excited state and have mass number larger than 5. It usually occurs after alpha and beta decay, since they often cause to excited states in the daughter nucleus. [6].
1.3 Uranium Decay Series
Radioactive decay is a process which an unstable atom releases particulate radiation or electromagnetic radiation. The radioactive decay of a naturally occurring isotope changes the number of protons in a nucleus by doing alpha and beta decays. If the decay is a one step process, it means that a stable atom is formed, but on the other hand; nucleus of the decay product, which is called its daughter, might be unstable and this results to another decay till the daughter nuclei is stable. This multiple step is called a decay series. The decay of238U to206Pb is a decay series which involves 14 steps and includes several α and β decays. As it is seen from Figure 1.1 some part of the decay series has branchings where it is possible to observe different radioactive daughters formed by one nuclei. But in the end, path always rejoin and there is usually one decay daughter which is likely to be formed, like218Po will undergoα decay with a possibility of 99.97% and yet it is possible for aβ decay to occur with a possibility of 0.03% [7].
Figure 1.1: Uranium decay series .
Uranium is a radioactive isotope that spontaneously decays to lighter “daughter” elements by losing high-energy particles at a predictable rate, known as a half-life. Uranium decays to radium through a long series of steps with a half-life of 4.4 billion years. During these steps, intermediate daughter products are produced, and
high-energy particles including alpha particles are released. The daughter mineral radium is itself radioactive, and it decays with a half-life of 1,620 years with an alpha decay, forming the heavy gas radon. Radon is also radioactive and it decays with a half-life of 3.8 days, producing daughter products of polonium, bismuth, and lead.
1.4 Radon-222 and Its Decay Products
222Rn is produced continuously from the decay of radium in the ground. It dissolves
in groundwater, which often carries it in high concentrations and releases it to areas inhabited by humans.
An important characteristic of radon is that it gives more radiological significance than other members of uranium decay series, is that it is a noble gas. It is colorless and odorless. It is the heaviest of the noble gases in the zeroth group of the periodic table and it has no stable isotopic form, instead all of its isotopes are radioactive. Once it is formed, it is possible for it to move in space by molecular diffusion or by flow of the fluid.
222Rn is the most important radon isotope in uranium decay chain, because it has the
longest half-life, 3.8 days. That makes it easier for radon to travel in air before it decays.
Other important characteristic of radon is that its decay products are also chemically active radionuclides and relatively short-lived. As it is shown in Figure 1.2 four decay products following radon decay have half-life less than 30 minutes. So if they are collected in lung, they will all decay before lungs get them out and as a result of alpha and beta decay, lungs will absorb the emitted alpha and beta particles. 212Pb has the most significance radiation since it has a half-life of 10.6 hours.
The equations about the radioactive growth and decay equilibrium between two or more species are based on law of radioactive decay, although they are much more complicated [1]. For a general case as A→ B the differential equation which describes the production of B from the decay of A is:
dNB
dt = NAλA− NBλB (1.6)
Figure 1.2: Radon decay products [1].
For the progeny relations like between radon and its progeny, similar equations can be derived and they are called as Bateman equations. Bateman equations can be simplified for specific cases like NB0 = 0 or NA= NA0. So it becomes like:
NB= λA λB−λA NA0 [ e−λAt− e−λBt ] (1.7) or using activity definition I = Nλ and t1/2= 0.693λ , one can easily obtain the equation:
IB IA0 = t1/2(A) t1/2(A)−t1/2(B) [ e−λAt− e−λBt ] (1.8)
Using these equations time dependent activity concentrations can be calculated for each radon products. The relative activity concentration of radon-222 and its decay products as a function of time, can be seen in Figure 1.3. It shows the conditions of radioactive equilibrium which is achieved after nearly 3 hours. After 3 hours short-lived product concentration will be equal to the radon concentration. It is called second equilibrium.
It also can be seen from Figure 1.3 that218Po concentration increases rapidly in222Rn sample, so 90% of equilibrium between radon and its first decay product is obtained within 10 minutes.
By knowing the concentration equation and decay constants of radon and its decay products, total alpha activity can be found with:
Figure 1.3: Relative activity concentration of 222Rn and its decay products as a function of time [1].
(total alpha activity) IRn222(initial) =
3.010exp(−λRn−222t)− 1.024exp(−λPo−218t)− 4.404exp(−λPb−214t) + 3.418exp(−λBi−214t)
These equations actually are the main equations for measurements of radon concentration using samples taken with a scintillation cell [1].
1.5 Radon Health Effects
Since radon-222 is a descendant of long half-lived nuclide, it represents a long term hazard although it has a short half-life. It is a noble gas resulting free motion in the ground and surface waters.
The most dangerous thing about Radon-222 is that it could be inhaled by human and its radioactive products are deposited directly in the lung. Since the decay products have relatively short half-lives, they will cause ionizing radiation and induce cancer in the lung tissue [8]. Radon exposure is the second major cause of lung cancer, after smoking with the risk increasing 8-16 % for every 100 Bq/m3increase in radon concentration. The radiation dose, caused by Radon-222 and its decay products,forms the most part of the natural radiation exposures in general. Monitoring of radon in various countries
shows that average concentration changes from 10 to 100 Bq/m3(0.3-3 pCi/L) although some part of America have high dose of radon (Figure 1.4) [9].
Figure 1.4: Arithmetic mean radon level by country [2]
Radon concentration changes from house to house, depending how they are built and ventilated. It gets into the houses through cracks in solid floors, construction joints, cracks in walls, gaps around pipes and with water. It can fill one room within 3 hours if it doesn’t have air circulation. That’s why houses have to be ventilated regularly in order to prevent the high radon concentration in rooms.
1.6 Radon Measurements Methods
The detection of radon particle is based on detecting the radiation caused by radioactive decay. It includes not only alpha and beta detection, but also detecting gamma radiation caused by transition of the decay product from the excited state in which it is left to its ground or unexcited state. Alpha, beta and gamma radiation creates ions in materials while passing through it, so the measurement methods are based on detecting the ionization.
Specific techniques are designed to measure the radon concentration. If a grab sample of air is taken, there are some short-term measurement techniques which are suitable. On the other hand some techniques need long-term sampling in order
to measure average concentration. While some techniques are self-contained which needs requiring a moderate and equipment to measure the concentration, some of the techniques includes collecting the sample and taking it back to the laboratory to be analyzed.
An important point to distinguish the methods from each other is that whether they measure radon concentration or its decay products. While some of the techniques measure decay product concentration, others measure the alpha-energy concentration. Time resolution is also a characteristic feature on detection methods. There are three classes according to sampling time. First one is called grab-sample technique which includes collecting a sample of air over a short time at a single point and taken back to laboratory to be analyzed. Second method is continuous technique which enables to give the information of concentration with time dependence. Third method is called integrating methods which provides the average concentration obtained from the measurements of sampling for a period of a few days to a year.
These techniques are basically called passive methods since radon is measured with the detector, but it must be taken to a laboratory to be analyzed later. There are 3 methods to measure the concentration of radon with grab-sample methods.These methods are also known as passive methods to measure radon concentration. First method is grab-sample monitoring for radon and its decay products can be formed with a portable-self-contained detector that uses scintillation material to measure the alpha particles emitted in a collection cell. The measurements can be completed in some tens of minutes, but it only gives concentration in a specific time, it does not give a direct measure of the average rate in the location. Second method can be performed with a charcoal sampler. The technique includes gathering Radon-222 over a period of a day to a week and taking it back to laboratory where the gamma radiation from decay products can be measured. But this technique is not suitable for collecting the sample for more than 1 week, because222Rn has 3.8 days of half-life and by the time
it gets back to laboratory, collected 222Rn will be gone. Third method includes an
etched-track detector. The detector can be placed in a home for periods from weeks to a year, then returned to the laboratory where the plastic detector material is etched, showing the tracks made by alpha particle from the decay of 222Rn and its decay
products [9].
However there are some active methods where the detector can be located to the place where radon concentration will be determined and results are obtained in Situ. These detectors could either measure the concentration of radon or the concentration of radon products and they include the other systems to be able to observe the concentration simultaneously. An active radon or radon decay product measurement device uses a sampling device, a detector and an analysis system (optional integration) to measure the concentration and it could have a monitoring system to observe the results simultaneously. It could also give an option not only to observe the results but also to record them to be analyzed deeply later.
Silicon photo diodes usually are used to create a radon detector. Basically the system has a silicon photodiode where an alpha particle creates a signal.Then this signal is fed to an preamplifier before being sent to an voltage amplifier. After this process the signal becomes amplified enough to be read. The output could be put into an multi-channel analyzer (MCA) where the signal produced by detector is reshaped into a gaussian or trapezoidal shape. This gives a chance to see the energy spectrum of the alpha particles detected. There are other ways of detecting radon or its decay products such as a gas-flow counter or a scintillation detector.
1.7 Interaction of Alpha Particles with Matter
Most of the interaction of charged particles are due to scatterings from a nuclei or an electron. Coulomb scattering of an alpha particle by nuclei (Rutherford Scattering) costs a very little energy loss to the alpha particle. Since the nuclei of an atom occupies only 10−15 of the volume of its atoms, the probability of an alpha particle to collide with an electron is nearly 1015 times more probable than colliding with a nucleus. That’s why Coulomb scattering is usually responsible for energy loss of charged particles [6].
For an alpha particle with energy of 5 MeV, the energy loss after colliding with an electron is nearly 2.7 KeV. Alpha particle loses its energy after thousands of colliding and colliding with an electron causes a negligible angle change on the direction of the alpha particle. Since Coulomb force is effective from infinite distance, alpha particles interact continuously with electrons till they lose all of their energies and stop at a range. This distance is called range of that particle and it depends on energy of the
particle and the type of the material. Collision with electrons gives enough energy (10 eV) to the electrons to be ionized, if it is not enough to liberate the electrons from the atom, then the atoms is placed into an excited state (then de-excites back immediately to the ground state) [6].
Theoretical relationship between range and energy can be obtained from solving the Bethe equations. Then range can be calculated by integrating;
R = ∫ 0 T (−dE dx) −1dE (1.9)
The range of alpha particles in silicon material for different energies can be seen in Figure: 1.5.
Figure 1.5: Range of alpha particles in silicon for different energies. [3]
1.8 Radon vs Earthquakes
Earthquakes appear when the pressure between colliding parts of earth’s crust increases and these fault lines houses the earthquakes all along them and make them carried away by increasing the magnitude of them. Most of the rocks in earth’s crust contain Uranium and since radon-222 is a part of the uranium decay series, most of radon emissions can be detected from within few meters of Earth’s crust [10] .
Since radon is a noble gas and its isotopes are mobile, they can travel large distances within the earth and in the atmosphere [11]. It has been reported that radon emission from the Earth’s crust changes from the average value before the earthquake. Concentration of radon in soil and ground water have been found to be anomalously high along active line faults [10].
First observation of increasing radon concentration before an earthquake was observed in 1966 Tashkent earthquake (Figure: 1.6).Also, before the earthquake of Gasli (1976) and some strong earthquakes in China, unusual radon changes was detected. This led the way to research the relation between radon concentration and earthquakes [4].
Figure 1.6: Radon concentration before, after and during after shocks of Tashkent earthquake [4]
Although it has been a long time since the research has started, there is no certain way of prediction earthquakes with radon monitoring. On the other hand, there are several ways of analyzing the radon-earthquake correlation. It is not fair to say that there is going to be an earthquake after every increase in the radon concentration since environmental effects changing the radon concentration is also part of the game. A research that is about the Fast Fourier Transform based Earthquake Precursor Analysis of Radon uses a technique of FFT to analyze the results from radon concentration [10]. The technique they used is basically; measuring the radon concentration of a base where several earthquakes happen, taking the averages of radon emission over different time periods obtained by FFT processing of time series and analyzing the results. As a result of the analysis they claimed that possibility of predicting the earthquakes for short periods is 80%.
Another research method about predicting the earthquake with monitoring radon is; building artificial network models [12]. Apart from trying to get a linear relationship between radon and earthquake, this method uses several parameters observed during the earthquake like longitude, latitude, pressure or temperature. As a result, the average relative error between the calculated magnitude of earthquake with this method and measured data is about 2.3% and relative error varies from 0% to 12%. This method is considered a potential alternative model for predicting the earthquakes with complex mathematical operations.
There are also researches that uses GPS and SAR imaging to provide surface deformation data, ASTER and ETM to detect the surface temperature, ground passive stations to detect electromagnetic and ionosphere anomalies, solid ground detectors to measure radon gas emission and finally use these parameters all together to predict the earthquakes [11].
All of these researches indicate that with necessary parameters and right analysis tools, earthquake prediction with radon monitoring could be accomplished with a fair accuracy.
2. SIMULATION SOFTWARES
In this chapter, the simulation software packages that were used for this research, will be explained very briefly. It will also be explained which characteristic features of these packages were used.
2.1 SRIM
SRIM (Stopping and Range of Ions in Matter) is a program which calculates the range of ions in matter by taking into account the interaction mechanisms of ions with matter (Figure 2.1).
The method is based on a Monte Carlo simulation, which uses the binary collision approximation with a randomly selected impact parameter of the next colliding particle. As input, it needs the type of the ion, energy (in the range 10 eV - 2 GeV) and the material information for several target layers.
Figure 2.1: SRIM User Interface.
As a result of the simulation, it provides three-dimensional distribution of the ions which can be plotted for several parameters such as penetration depth or spread along the ion beam. Other output information about the interaction are concentration of vacancies, sputtering rate, ionization, phonon production in the target material, energy deposition or ion ranges as it is showed in Figure 2.2. It also gives the opportunity of ion implantation which actually means using ion beams to modify samples by injecting atoms to change the target’s chemical structure and electronic properties.
Figure 2.2: SRIM Software: Simulation of Helium nucleus in the silicon target layer. Experimental measurements of stopping power is a difficult task and SRIM gives an opportunity to compare the results of stopping power with experimental data. (Figure 2.3)
2.2 Poisson Superfish
POISSON/SUPERFISH codes are a groups of programs that makes the calculation of magneto static and electrostatic fields in two dimensional Cartesian coordinates or three dimensional cylindrical coordinates (Figure 2.4) [14]. The program has AUTOMESH and LATTICE which generate the mesh for the given geometry and TEKPLOT generates graphical output for electric and magnetic field [14].
Figure 2.3: Stopping power of silicon from SRIM examples.
After the geometry, material boundary conditions have been defined, the mesh is generated and the finite difference equations are solved by equation-solving programs like POISSON(electrostatic) or SUPERFISH (magnetostatic).
POISSON uses "successive point over-relaxation" (SPOR) method which is very efficient for solving discretized problems which converge rapidly in this method.
2.3 COMSOL Multiphysics
COMSOl Multiphysics is a simulation program which uses finite element method to solve partial differential equations used to define physics and engineering applications. The package offers to the user to build a geometry in three dimension with a chosen material, apply any physical laws to the material, give boundary and initial conditions, mesh it as preferred, then solve it using finite element method(FEM). User can choose
Figure 2.4: Poisson
which results or simulations to observe(Figure 2.5). The results can be asked for electric field, magnetic field or electric potential. Although most of the physical laws and material information exist in the module, user can create his/her own material or physical law by defining the parameters and the formula that defines the law. It is also possible to import an Autocad, Solidworks or Matlab geometry into Comsol software [15].
Figure 2.5: Comsol: Electric Sensor Example
2.4 GEANT4
Geant4 is a free software package including tools which can be used to simulate the passage of particle through matter. The package includes defining the geometry of the system, the materials involved, fundamental particles, generation of primary events, tracking particles through materials and electromagnetic fields, the physics processes, response of sensitive detectors, generation of event data and finally visualization of the detector and particle trajectories while capturing them in different levels of detail. It has been used in particle physics, nuclear physics, accelerator design, space engineering, astrophysics, medical physics and the number of fields that it has been used is increasing day by day.
Geant4 is written in C++ and offers advanced software-engineering techniques with object-oriented technology. The output can be changed into alternative or complementary models according to energy range or the particle type by the user. The detail of the output can be adjusted by the user. User can build specific application by choosing from these options and write the code in user action classes using the toolkit. Since Geant4 is an object-oriented program, adding new physics models and making the code more complex aren’t going to be a problem. In contrast it helps manage the complexity of the situation by defining uniform interface for all physics models. It also gives the opportunity to define new physics. In this framework, models can be more easily used without making any modification in the code and user has chance to pick up only the components that he or she needs [16].
The main parts of the simulation of a particle passing through material are basically the following parts: geometry and materials, particle information, particle interaction in matter, tracking management, digitization and hit management, event and track management, visualization and visualization framework, user interface [16].
These parts naturally led to the creation of class categories with adaptable interfaces and a corresponding working group with a well defined responsibility for each category of Geant4. It also led the way to the concept of a ”toolkit”, which implies that a user may assemble his/her program at compiling time from components chosen from the toolkit or from the components that he or she build with his or her own parameters(Figure 2.6) [16].
2.4.1 Design overview
Geant4 has some design pattern with its defined classes to be able to work properly. Event category is a part of this pattern which enables the user generating the primary particles with physical events. The class named G4Event stores the information of the primary particles before the event begin. Hits, digitizations, trajectories of the particles also can be stored after the processing [5].
2.4.2 Geometry and detector representation
Geometry category describes the geometrical structure of the materials and controls the movements of particles in matter. Although it is possible to create a geometry from zero, a CAD file could be imported to the system. There are two kinds of volumes as logical and physical. A logical volume can host other volumes in it and a physical volume represents the position of the logical volume and the information about its place in the coordinate system [5] .
2.4.3 Tracking
Another category is tracking which duty is to follow the particle’s each movements in the simulations. In Geant4, particles get transported instead of moving with the transportation process. Tracking follows these process and steer them. Transportation does not depend on any kind of particle or physics information. All physics process is defined with a step length with the information of the particle in that process [5].
2.4.4 Physics
All physics process defined in the simulation are confirmed by this category. For example; in particle decay, step length is calculated with the mean life of that particle. Decay product forming needs more information as branching ratios and some distribution knowledge to create new particles.
Another physics process is electromagnetic physics which manages the electro-magnetic interaction between particles. Other physics processes are ionization, Bremsstrahlung, multiple scattering, Compton scattering, Rayleigh scattering, photo-electric effect, pair conversion, scintillation, refraction, reflection, absorption and Cherenkov radiation [5].
2.4.5 Particles and materials
These categories describe the information about the particles and the materials in the simulation. G4ParticleDefinition class carries the information about the particle like charge, mass or cut information. There is also a class for each particle for specific properties. Material category includes the information of what the materials are made of knowing that materials are made of single elements or a mixture of elements. The classes include the information of what kind of elements to be used, the ratio of elements in the material and the density of that material.
There is also a class named G4DynamicParticle which has the definition of an atom, not just a nuclide. It has the information of atom number, mass number, electron number, charge number. It is also possible to learn the information of spin number of that atom if it is needed. Other information are momentum direction, kinetic energy, dynamical magnetic moment, electron occupancy. [5].
2.4.6 User actions
User must define the physical processes to be used, since it would be hard to use each and every process in the Geant4. There are 8 classes which must be defined by the user. 3 of them are mandatory and they are G4VUserDetectorConstruction to define the detector, G4VUserPhysicsList to define the particles and physical process, G4VUserPrimaryGeneratorAction to generate the primary particles. 5 of them are optional and they are: G4UserRunAction for action at the beginning and end of runs, G4UserEventAction for action at the beginning and end of each event, G4UserStackingAction for arranging the access to the tracks, G4UserTrackingAction action at the beginning and end of each track, G4UserSteppingAction for arranging the behavior at each step [5].
Figure 2.6: Flow chart of how Geant4 works [5] .
3. SIMULATIONS AND RESULTS
This chapter includes the information of how the simulations were made and which software package was used for each one. Also the results that were obtained from these simulations will be explained in detail.
3.1 Introduction
In this chapter, the simulations for the radon detector system, which has been building in our laboratory for the TUBITAK project (110T261), will be explained. The simulations are based on two sections. First and the main part of the simulations is made to optimize the electric field geometry for increasing the efficiency of the detector.
Second part is actually based on the optimization of the relative location of the silicon PIN photodiode. The simulations guided us to build the radon detector with optimum collection efficiency.
3.2 Optimizations of Electric Field Geometry
Since alpha particles which are emitted from radon-222 have the energy of 5.49 MeV, they can only travel a few centimeters in air. So, to get the best efficiency in an alpha detector, one simply should drive the particles towards the photo-diode with an electric field.
At the beginning of the electric field optimization study, three types of electric field geometry were used. They were half cylindrical, hemispherical and linear electric fields (Figure 3.1). These three simple geometries were chosen simply because they are symmetrical to work and they provide intense electric field near the photodiode region.
The simulations were run under the same conditions in order to find which one is the best after following simulations.
Figur e 3.1 : Electric field geometries. 24
These results will be discussed in the following sections in detail and comparison will be held for both Comsol and Geant4 simulations.
3.2.1 Choosing the best electric field geometry
In this section, COMSOL software was used to create different geometries from materials to generate electric field. As it is explained in second chapter, COMSOL uses finite element method to find the approximate solution of Poisson equation in order to determine the electric field with given initial conditions of that geometrical shape.
To make a realistic comparison between the chosen geometries, the area of the plates were made equal. As it is seen from Figure: 3.1 in first picture +3500 V is applied to the disk. In the second picture +3500 V is applied to the side surface of the cylinder. At third picture, +3500 V is applied to the hemisphere surface. In all cases, there will be an electric field from the surface with high voltage to the ground point where the photodiode is located. With this electric field, positive ions will drift to the photodiode. In 3 different COMSOL programs, these three geometries were simulated to get the electric field information within the volume. Since COMSOL gives electric field results in the defined volume, electric field information for the interested volume was extracted from the COMSOL output data. Before implementing this information into Geant4, the electric field near the zero point was compared for all three geometries to get a rough idea about the magnitude of the electric field in different region (Table 3.1 ). Hemispherical electric field is the best option to get better efficiency on collecting the particles above the photodiode. Although in some coordinates disk or cylinder type geometry gives a better result, in general hemisphere type electric field is better at collecting the particles towards the photodiode.
3.2.2 Geant4 simulation of the detector with electric field
In this part of the research, the primary purpose is to apply the electric field to alpha particles and simulate their motion with this electric field in the Geant4 geometry. The Geant4 used the electric field vectors from the COMSOL output for estimating the track of the particle. An algorithm was written to apply electric field to the particles. Using Geant4, alpha range in air, electric fields or detector geometries were simulated.
Table 3.1: Electric field values for three Geometries while photodiode is in (0,0,0) and placed in x-y plane (z is distance above the photodiode).
Coordinate Electric field Electric field Electric field (m,m,m) for disk (V/m) for hemisphere (V/m) for cylinder (V/m)
(0.02-0.02-0.001) 32915 36900 16078 (0.05-0.05-0.001) 4878 6037 2521 (0.05-0.05-0.03) 3849 3176 2139 (0.03-0.03-0.03) 8800 9136 4698 (0-0-0.03) 50950 51844 30794 (0-0-0.01) 76524 117775 94839 (0.02-0.02-0.02) 2522 20728 10197 (0.01-0.01-0.01) 74681 85956 42888 3.2.2.1 Geant4 code
The Geant4 code basically must insert definition of:
• all the particles that could exist after decays or interactions • the elements that forms the materials
• compounds of the materials
• the geometries that compose the detector and the environment • defining the necessary volumes
• defining the sensitive volumes
• placing the particle iterator and the materials in the volumes • physical events that is defined for each particle type
• output type to get the necessary information
• number of particles generated at the beginning of simulation • electric field functions and which particles to be applied
Initial energy of particles, initial coordinates of the particles or number of particles generated can be modified from interactive mod tool of Geant4 after the simulation is started. Even the geometries of the materials can be changed during the simulation and the result can be seen immediately.
3.2.2.2 Calculation of radon concentration
Radon measurements usually express in terms of Bq/m3 and since we have to give Geant4 how many particles will be simulated, the dose should be represented in terms of number of radon particles in our monitoring volume. To be able to calculate it, one should be aware of following units and conversions:
• Bq: decays per second • Ci = 3.7 ∗ 1010 Bq
• 1µCi = 37000 Bq =37000 cps (count per second)
The box of the detector is in size of 30× 30 × 30 cm3. Let’s say one would like to calculate the number of radon in this volume if radon concentration is measured to be 100 Bq/m3.
Volume of the box is: 30× 30 × 30 cm3= 0.027 m3
If there are 100 Bq in 1 m3; the concentration must be 0.027× 100 = 2.7 Bq in 0.027 m3.
Specific activity means number of decays per second per amount of substance and specific activity of radon is: SA(222Rn)= 1.5× 105Ci/gr
If SA= 1, it means 37× 109decay happens in 1 second in 1 gr of that element. So;
2.7 Bq = 2.7
3.7× 1010 = 7.3× 10
−11Ci (3.1)
If there are 1.5× 105particles in 1 gr, there are:
7.3× 10−11
1.5× 105 = 4.87× 10
−16gr in concentration of 7.3× 10−11Ci (3.2)
To calculate the number of particle in this mass;
We know that 1 mole of222Rn is 222 gr; then 4.87× 10−16gr becomes 4.87× 10−16/222 = 2.19× 10−18mole
At the end; number of radon particle in 0.027 m3is: 27
6.02× 1023× 2.19 × 10−18= 1.32× 106 (3.3) If we generalize the formula:
while N = number of atoms in given volume in given concentration
N = (concentration[Bq/m
3]× volume[m3])
(3.7× 1010)(speci f icactivity[Ci/gr]× molecularmass)(6.02 × 1023) (3.4)
3.2.2.3 Building the geometry
The Geant4 volume is assumed to be a box with the dimension of 30x30x30 cm3. Geant4 volume is filled with air(H-O-N-Ar). The photodiode is defined as 10x10x0.5 mm3 sizes and made of Silicon. The geometry is simple as it seems in Figure 3.1. The particles outside of the electric field volume won’t reach to the detector, therefore they would only create electrons that has no effect on the detection of alpha particles on the silicon photodiode. That’s why, this work investigated only the particles within the electric field region.
3.2.2.4 Including the electric field algorithm
Normally the functional form of the electric field (E=E(x,y,z)) is known, the electric field on the particle can be determined easily if the location of the particle is known. However in some cases determining the functional form of the electric field analytically is not possible. In this case numerical look up table with the values of the electric field for certain coordinates (grid points) can be used for determining the approximate electric field which the particle is under the influence of, if its coordinates are known. For that reason, instead of going through detailed theoretical calculations for determining the analytical form of the electric field geometry for three mentioned cases, COMSOL software is used for creating look up tables filled with electric field vector for specific grid coordinates.
At the beginning of every simulation these electric field information is imported to an array with 6 columns(x-y-z-Ex-Ey-Ez)for once, and then it’s used during the Geant4 simulations.
Briefly, the algorithm can be given as follows: 28
• Electric field information for the coordinates within the electric field region, was imported into an array.
• During the simulation, right after first particle was shot from the gun, the electric field algorithm takes the information of location of the particle ( xi, yi, zi).
• Looks into the array for every new position of particle (xk, yk, zk, Exk, Eyk, Ezk).
• Finds the closest position between (xi, yi, zi) and (xk, yk, zk). • Apply the value of E(xk, yk, zk) to E(xi, yi, zi).
• Do it again while (i=1,N) N is decided by Geant4 until the particle stops or decays to another particle.
Electric field is applied with G4ElectricField class which is defined in Geant4. 3.2.2.5 Alpha particle in an electric field
The electric field values from three geometries imported in Geant4 and three simulations were started with the conditions of:
• 1000 alpha decay locations were determined randomly in the volume,
• Alpha particles were distributed randomly with the energy of 5.49 MeV, natural decay energy of222Rn,
• Medium of the volume was made vacuum to distinguish the effect of electric field, • Electric field was applied to the volume with three different geometries,
• Number of alpha particles reached into the photodiode was counted for each geometry.
These simulations were also performed with and without electric field to observe the effect of the electric field. Table 3.2 shows the results. As one can see from the table, the most efficient collection happens in the hemisphere case.
As a result of this analysis, the effect of electric field is obvious, disk method is not enough to get a better efficiency. Cylindrical and hemispherical method is much more efficient and it seems that hemispherical geometry is the best choice to get a
Table 3.2: Number of alpha particles reached to the photodiode in various geometries. N(initial) N(disk) N(half-cylinder) N(hemisphere)
1000 0 13 35
good efficiency on driving the particles towards the target. It is acceptable because of the azimuthal symmetry in this geometry stops the particles from going to other directions, it drifts them right onto photodiode as it can be seen from COMSOL results (Figure: 3.2).
Figure 3.2: COMSOL simulations of electric field for hemisphere geometry
3.2.2.6 Motion of alpha particles in an electric field
Alpha particle with an energy of 5.49 MeV can only move few cm in air. The effect of the strength of the electric field on the range of alpha was also studied. An alpha particle was created with an energy of 5.49 MeV and the direction of the electric field was chosen with the same direction of the alpha particle’s momentum.
As a result, when there is no electric field, particle stopped after going 40 mm, when the electric field was 105V/m, it moved 40.07 mm in the air. Finally when the electric field value was 5∗107V/m, it moved 46.72 mm in the air which makes a difference of 6.72 mm compared to the one with no electric field option.
When we take a particle in vacuum which starts with an energy of 1 MeV, It goes 10 mm in vacuum and its kinetic energy increases from 1 MeV to 1.8 MeV in existing of an electric field (5∗ 107V/m) in the same direction with particle’s momentum. With a quick and dirty calculation: Energy loss of the particle is:
∆T = Tf inal− Tinitial= W = F∆x = qE∆x (3.5) If we put the energy values into equation, energy difference can be calculated with:
∆T = 1.8 − 1 = 0.8MeV
If we put the values into first equation:
2× 1.6 × 10−19× E × 10 × 10−3= 0.8× 106× 1.6 × 10−19 We can find energy of that particle:
Ecalculated≈ 4 × 107V /m (3.6)
Applied electric field was:
Eapplied = 5× 107V/m (3.7)
So one can easily see that the calculation and the simulation results are in the same order of magnitude.
Another study is about the correlation between the number of alpha particles reached to the detector and radon concentration of the volume. In this work, the conditions of the study is given as follows:
• Radon atoms are located randomly in the volume.
• Number of radon atoms were changed depended on their concentrations • The volume is chosen to be air.
• Electric field is set to be 105V/m in Z direction(towards the photodiode)
After the simulations, number of alpha particles released and detected in the photodiode is shown in Table 3.3.
Table 3.3: Number of alpha particles reached to photodiode in radon concentrations. Number of event Radon concentration Number of alpha detected
(Bq/m3) in the photodiode 131920 10 18 263842 20 27 395763 30 56 527684 40 69 659606 50 87 791527 60 108
3.2.3 Comparison of Geant4 simulations and experiment for radium source First test of the radon monitor system was performed with a radium source. The simulation of this source was made with Geant4. Since our radium source was inside a metal jacket, we had to build a new geometry for this source to include the scatterings from this metal jacket which will obviously effect the energy spectrum of the detected alphas. Radium decay appears emitting an alpha particle with energy of 4.78 MeV as a result of following decay.
226
88 Ra→42α+22286 Rn
In the study; radium particles were positioned at 16 different locations in the source as it is shown in Figure 3.3. The radium source is in a shape of disk and inside a metal pipe. In the simulations, 900000 radon particles were released from the 16 locations of the source and the energy of alpha particles deposited in the photodiode was recorded to be for constructing the energy spectrum.
Figure 3.3: Locations on the radium source where the particle were first located in the simulation.
Spectrum consist of alpha particles from Radium and its decay products. Figure 3.4 shows the energy spectrum obtained from Geant4 study. Figure 3.5 shows detected experimental radium spectrum.
Figure 3.4: Radium spectrum drawn with the results of the simulation.
Geant4 simulations weren’t run as real time simulation. That’s why radon and its decay products can be seen in the spectrum even though radium has thousand of years half life. And the reason every energy has two peaks is because of some of the particles scatter from the metal jacket of the source.
Figure 3.5: Experimental radium spectrum.
