Iranian Journal of Siene & Tehnology, Transation A, Vol. 33, o. A3 Printed in the Islami Republi of Iran, 9 Shiraz University "Researh ote" AALYSIS AD OPTIMIZATIO OF A FISSIO CHAMBER DETECTOR USIG MCP4C AD SRIM MOTE CARLO CODES * K. HADAD 1** AD M. HASHEMI 1 Shool of Mehanial Engineering, Shiraz University, Shiraz, I. R. of Iran Email: hadadk@shirazu.a.ir Islami Azad University, Siene and Researh Division, Tehran, I. R. of Iran Abstrat In this study, a general theoretial model to foresee and alulate the urrent-voltage harateristis in a plateau zone and the assoiated effiieny of the neutron detetor (sensitivity) is presented. This study is to omplete the previous studies in this field. The model also onsiders eletri field distortion resulting from the harge olletion effet. The harateristis urve is obtained as a funtion of fission rate, hamber geometry, and filling gas pressure. The output urrent at the saturation domain is alulated. The applied voltages about two phenomena, reombination and avalanhe, for working the hamber in an ionization zone are an important part of the alulation. In developing the theoretial model, the MCP ode for fission rate, the SRIM ode for eletron-ion pair and GEAT4 for gamma sensitivity alulations were used. Keywords Fission hamber, MCP, GEAT4, SRIM, optimization 1. ITRODUCTIO Fission ionization hambers are widely used as neutron detetors in irradiating environments suh as nulear reators, aelerators, and physi laboratories. They an be used in pulse mode, urrent mode or Mean Square Voltage (MSV) mode [1]. Cylindrial fission hambers are made of two oaxial eletrodes, whih are separated by a filling gas. The filling gas that is used in ATO TYPE 81 is a ombination of argon (95%), and nitrogen (5%) []. The anode is usually oated with a fissile element (our model s fissile oating has 9% U-35). Under irradiation, neutrons indue fission reations inside the fissile element (the probability is proportional to the fission reation ross setion) and two fission fragments (FF) with a range of energy of about 6 MeV to 9 MeV are emitted in opposite diretions. If the energy of the inident neutron is negligible ompared to 9 MeV and 6 MeV, it is aurate to say those FF emerge in opposite diretions. Thus, on average only one FF partiipates in the gas ionization, the other one being absorbed by the anode. The FF emitted to a gas ionizes the filling gas and as a result, generates a high number of eletronion pairs. Of ourse, there is a probability that the two fragments remain in the fissile element and do not enter into the surrounding environments (gas and anode). The fissile element layer should be thin enough for fission fragments to have a hane to enter into the filling gas. When a voltage is applied, an eletri field is generated between the two eletrodes. The anode ollets the negative harge, while the athode ollets the positive one. The olleted harges are responsible for the reation of an eletri urrent. The Reeived by the editor January 9, 8 and in final revised form June 13, 1 Corresponding author
7 K. Hadad / M. Hashemi layout of this urrent, aording to the voltage applied gives a harateristi urve, known as the alibration urve. In the alibration urve the saturation urrent is proportional to the neutron flux, whih is why it is important to know when the hamber works in saturation onditions. Therefore, the main aim of this study is to determine the relevant parameters of the hamber and the optimal voltages whih answer the neutron flux requirements. Also, the saturation urrent and sensitivity of the modeled hamber are alulated.. AALYTICAL AALYSIS a) Fission made from neutron ollision with fissile element Suppose µ s is the area density of a fissile element (for ATO TYPE 81 µ s =68 µg.m - []). This parameter dereases during the life of the hamber beause fissile nulei are depleted. The fission reation rate per unit surfae is given by [3, 4]: s fst AE M U ( E) ( E) de (1) Where fst stands for fission per unit surfae per unit time, σ(e) is an effetive fission ross setion for the neutron of energy E, M U is the molar mass of U-35, A is the Avogadro s number and E( E ) is the neutron flux at energy E. Realling that the fission rate is given by [3]: ( E ) ( E ) de () To verify the auray of the fission rate alulation by MCP, the neutron soure was evaluated in two different methods. In the first method, a neutron soure with an energy range of to MeV was defined and the fission rate was evaluated using MCP. In the seond method, the fission hamber was assumed to be plaed in a ritial nulear reator ore, and using the KCODE option, the fission rate was evaluated. The results of both methods were omparable and the auray of the fission rate evaluation was onfirmed. The fission rate was found to be: b) Eletron-ion pair prodution rate alulation E 15 1.4818 1 fission se After generating fission fragments nearly all entered into the filling gas and ionized the atoms of the gas, generating the ions (Ar + and e - ). Thus, fission fragments make an eletron-ion pair. We onsider I (r) the average number of eletron-ion pairs reated by a fission fragment per unit of length travelled in the radius path. However, in the ase of a fission hamber with small dimensions, the trajetory of the fission fragments is short enough that I (r) an be onsidered onstant, on average, equal to I in the eletrodes spae. By using the SRIM program [5, 6] of J. F Ziegler whih omputes the stopping range of the ions in solids, liquid and gases, we alulate the I, onsidering the lightest fission fragment with an energy of 9 MeV ( 95 Mo, Molybdenum) as an inident partile in the hamber s gas. Iranian Journal of Siene & Tehnology, Trans. A, Volume 33, umber A3 Summer 9
Analysis and optimization of a fission 71 For the ionization hamber, the energy loss by ionization omputed by SRIM was obtained as 4.5469E-1 (ev/a.ion) with a gas pressure of 1.1 bar. If the required ionization energy of the ombined gas atoms is about 3 ev [3], we an alulate I by dividing the ionization energy loss by the gas atoms ionization energy: I ev A ion ev ion pair m bar 3 6 454.691 (. ) 3 1.9769131. We need to alulate the density of the eletron-ion pair reated per unit time at a distane r from the anode axis, (r). For a fission hamber with small dimensions we ould write [3]: where p is the pressure of the filling gas. ) Saturation Current, I sat ( r) fst pi (3) The saturation urrent orresponding to the olletion of all eletrons reated by the primary ionization, I sat, is obtained by: I el r r (4) ( ) sat a where L is the sensitive length, e is the harge of the eletron, r is the athode radius, and r a is the anode radius. The limitations of the saturation plateau zone are due to the reombination and threshold ondition where the reombination modifies the saturation urrent. With some theoretial assumptions the beginning voltage of the saturation plateau, V re, is equal to the minimum voltage of the plateau zone. d) Minimum Voltage, V min For a voltage less than the minimum value, the eletri field is not strong enough to evauate the harges reated by the primary ionization. Below this minimum voltage a steady state ondition ould not exist. Minimum voltage is alulated by integrating the eletri field between the anode and athode distane [3]: r e ( r ra ) ( r r ) Cmin Vmin ( ) [ ( ) ] 4 r ra 1 dr (5) Where µ + and µ - are the mobility of positive and negative ions respetively and C min is integral onstant (µ + 1.3 m.bar.v -1.se -1, µ - 13 m.bar.v -1.se -1 ). Using equation 1 and and the MCP result for the fission rate, the fission reation rate per unit surfae is: fst s M U g 68 # 1 #. m 4 atom 15 atom A.61 1.481 585 g mole se m.se 35.534 mole and the density of the eletron-ion pair reated per unit time is obtained from equation 3: fst pi # atom 585 1.1bar 1 m.se 6 ion pair m. bar 8.1781 9 ion pair 3 m.se Summer 9 Iranian Journal of Siene & Tehnology, Trans. A, Volume 33, umber A3
7 K. Hadad / M. Hashemi By substituting ε = 8.85 1-16 (.m /C ), e = 1.6 1-19 C, r a =.8595 m, r =.5695 m, and alulating C min to be about 1585.45 in equation 5, the minimum voltage for the fission hamber is obtained as: V ( ) 357.71volts. min e) Maximum voltage, V max In the plateau zone the maximum voltage should be limited. The relationship between V max and the hamber parameters is [3]: V r 1 e ( r ra ) ( r r ) ES ra Cmin max ( ) [ ( ) ] 4 r r ra dr (6) By substituting the parameters from setion.4 and E s =.5 1 6 V/m in equation 6, the maximum voltage for the fission hamber is obtained as: f) Sensitivity (effiieny) of fission hamber V max 634. 81 volts. The sensitivity is obtained by dividing the urrent delivered by the hamber to the thermal neutron flux: S= I sat / Ф th (7) By replaing I sat from equation 4 and from equation 3, we an write S as S el s M U A pi ( r th r a ) (8) Where, σ th is the effetive thermal neutron ross setion and its value is onsidered about 57 barns [7]. Therefore, substituting L =15.4 m in Equation 8 gives: S 13 ampere 1.4114 1 ( n / m. se) Having the sensitivity, the saturation urrent ould be obtained in any neutron flux from the ATO TYPE 81 datasheet []. For example, in a flux of 3 1 9 n/(m.se), using the equation 7, the urrent I sat is obtained as.46634 ma. 4. GAMMA SESITIVITY CALCULATIO USIG GEAT4 CODE The fission hamber was modeled with GEAT4 [8, 9] to estimate eletron-ion pair prodution by γ- radiation from different soures and the gamma sensitivity. The gamma sensitivity threshold energy to produe the eletron-ion pair was obtained as 1.451 KeV in GEAT modeling. Therefore, taking into aount the range of energies of γ-rays in a thermal reator, the gamma threshold energy is negligible and ould be onsidered as noise. a) The Gas Pressure 5. THE OPTIMIZATIO PROCESS Iranian Journal of Siene & Tehnology, Trans. A, Volume 33, umber A3 Summer 9
Analysis and optimization of a fission 73 The inner-eletrodes gas pressure was varied to analyze the eletron-ion pair generation. Ionization energy at eah pressure was omputed by SRIM program. Inreasing the gas pressure results in an inrease in eletron-ion pair generation. Figures 1 and illustrate the effets of pressure variation in eletron-ion pair generation and the detetor s operating voltage plateau, respetively. Fig. 1. The variation of eletron-ion pair prodution vs. pressure Fig.. The variation of Vmin- Vmax plateau voltage vs. internal gas pressure Summer 9 Iranian Journal of Siene & Tehnology, Trans. A, Volume 33, umber A3
74 K. Hadad / M. Hashemi b) Area density and enrihment variation of Fissile Element The area density variation inreases min-max plateau voltages. The results are shown in Fig. 3. Fig. 3. The variation of Vmin-Vmax plateau voltage vs. surfae mass Besides the original enrihment used in analysis (9% for U-35), two different enrihments (95% and 85%) were used to investigate their effet on the fission rate and min-max voltages. Figures 4 and 5 illustrate these variations, respetively. Fig. 4. The variation of fission rate vs. enrihment Iranian Journal of Siene & Tehnology, Trans. A, Volume 33, umber A3 Summer 9
Analysis and optimization of a fission 75 ) The Inter-Eletrodes Gap Fig. 5. The variation of min-max plateau voltage vs. enrihment Anode radius varied with the fixed athode radius. The major effet appears in the numerial alulation and has an ignorable effet on the fission rate resulting from the MCP ode. Figure 6 shows the voltage variation for different inter-eletrode gaps. Fig. 6. The variation of min and max plateau voltages vs. inter-eletrodes gap Summer 9 Iranian Journal of Siene & Tehnology, Trans. A, Volume 33, umber A3
76 K. Hadad / M. Hashemi 6. COCLUSIO This study revealed three important results about the fission hamber. Firstly, the best approah for dereasing the minimum voltage in the plateau zone and retaining the hamber in the ionization zone is to redue the pressure of the filling gas in the hamber. However, by reduing the hamber gas pressure we derease the filling gas density whose net effet is eletron-ion pair rate redution. This eletron-ion pair redution would also affet the sensitivity (se 3.4). It was noted that at high pressure, the plateau zone width would extend. This extension would fore a higher eletri field requirement and a distortion of the eletri field due to the spae harge effet. Seondly, by hanging the area density and enrihment of the fissile element we dedue that inreasing the fissile element enrihment an be useful in a high flux neutron surrounding (Fig. 4) where the applied voltage and plateau zone width did not hange (Fig. 5). Inreasing the fissile element area density has no useful effet, and it requires higher voltage (Fig. 3). Thirdly, by dereasing the inter-eletrodes spae, the detetion sensitivity of the neutron flux would derease, whih inreases the width of the plateau zone (Figs 6 and 7), improving the hamber performane for high neutron flux and dereasing the resulting errors. Furthermore, by dereasing or inreasing the inter-eletrode gap, the fission hamber ould be used either in a high flux or low flux neutron surrounding respetively, providing a high resolution of neutron detetion. REFERECES 1. Knoll, G. F. (). Radiation detetion and measurement. John Wiley & Sons, In. 17.. Due-range sensitivity neutron (fission) ionization hamber, EIA type 6376, ATO TYPE 81 doument, ode: AEL-Cat-1. 3. Poujade, O. & Lebrun, A. (1999). Modeling of the Saturation Current of a Fission Chamber taking into Aount the Distortion of Eletri Field due to Spae Charge Effets. ul. Instr. and Meth. A433, 673-68. 4. Chabod, S., Fioni, G., Letourneau, A. & Marie, F. (6). Modeling of fission hambers in urrent Mode - Analytial approah. ul. Instr. and Meth. A566, 633-653. 5. Available in freeware at <http://www.srim.org> 6. Ziegler, J. F. & Manoyan, J. M. (1988). The stopping of ions in ompounds, ul. Instr. and Meth. B35, 15-8. 7. Lamarsh, J. R. (197). Introdution to ulear Reator Theory. Addison-Wesley Publishing Company, 577. 8. Geant4- A Simulation Toolkit. (3). ul. Instr. and Meth. A56, 5. 9. GEAT 4.8.. (6). Detetor desription and simulation Tool, CER Program Library Long Writeup W513, CER, Geneva. http://geant4.web.ern.h/geant4. Iranian Journal of Siene & Tehnology, Trans. A, Volume 33, umber A3 Summer 9