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Calhoun: The NPS Institutional Archive DSpace Repository Theses and Dissertations Thesis and Dissertation Collection 1969 Design of a cobalt-60 fueled thermionic power supply. Doherty, Brian J. Massachusetts Institute of Technology http://hdl.handle.net/10945/11956 Downloaded from NPS Archive: Calhoun N PS ARCHIVE 1969 DOHERTY, B. DESIGN OF A COBALT-60 FUELED THERMIONIC POWER SUPPLY by Brian J. Doherty . DUDLEY KNOX LIBRARY NAVAL POSTGRADUATE SCHOOL MONTEREY, CA 93943-51 01 DESIGN OF A COBALT-60 FUELED THERMIONIC POWER SUPPLY by Brian B. S. , J. Doherty United States Naval Academy (1965) .Submitted in Partial Fulfillment •of Requirements for the •Degrees of Master of the 'Science and Nuclear Engineer at the Massachusetts Institute of Technology June, 1969 »e2ts^4;t»34 LI3RARY NA y/AL POSTGRADUATE SCHOOfc MONTEREY. CALIF., 93940 DUDLEY KNOX LIBRARY ^OTI^*??**. MONTEREY, CA 93943-5101 DESIGN OF A COBALT- 60 FUELED THERMIONIC POWER SUPPLY by Brian J. Doherty Submitted to the Department of Nuclear Engineering on June 30, 1969 in partial fulfillment of the requirements for the degrees of Master of Science and Nuclear Engineer. ABSTRACT The objective of this thesis was to design a practical thermionic which would use cobalt-60 as a fuel and which would provide supply power 500 watts of electric power over a three year operating period. In order to make the cobalt-60 fuel, which has a low melting point, compatible with the high temperature required for efficient operation of a thermionic converter, a low temperature fuel concept was employed. This meant that the fuel would be insulated from the converter heat source by a multi-foil thermal insulation. The multi-foil insulation uses refractory metal foils separated by thin layers of refractory oxide particles to provide a highly efficient and compact thermal insulation. With this design it was desirable to minimize the gamma self absorption of the fuel. Most of the effort in this thesis was directed toward the optimization of the fuel supply. The final design uses fuel elements which are in the form of hollow cylinders and which have a thermal efficiency of 75. 6%. A power flattening device which operates on a moveable fuel concept was designed to overcome the problems posed by the relatively short half life of cobalt-60. The power supply was designed for terrestrial applications; accordingly it was not subjected to severe weight limitations. Nevertheless, every effort was made to keep its weight and size within reasonable limits. The power supply was also designed so that it could operate automatically, unattended, for the three year lifetime. An additional design criteria was that no significant advance in the present state of the art be required for the design to be feasible. The final design uses five thermionic converters operating at a fixed power point and a DC -DC regulated converter to provide 500 watts of electric power at 28 volts. The overall efficiency of the power supply system is 9. 7%. Thesis Supervisor: E. P. Gyftopoulos Title: Professor of Nuclear Engineering li TABLE OF CONTENTS Abstract Table of Contents List of Figures and Tables CHAPTER 1 ii iii v INTRODUCTION 1. 1 Objective 1.2 Design Concept Fuel Requirements 1. 2. 1 Low Temperature Fuel Concept 1. 2. 2 Preliminary Design Considerations Further Design Refinements 1. 3 1.4 CHAPTER 2. 1 2. 2 2 1 Intrinsic Efficiency Emitter And Collector Operating Temperatures 2.2.4 Output Voltage Thermionic Converter Designs Compatible With Power Flattening Requirements 2. 2. 3 2. 3 2. 3. 1 2. 3. 2 2. 3. 3 CHAPTER 3 3. 3. 3. 3. 3. 3. 3. 3. 4. 1 4. 2 4. 3 1 5 15 16 Converter Operation With Varying Cesium Reservoir Temperature Operation At A Fixed Power Point 18 21 FUEL ELEMENT OPTIMIZATION 26 26 29 30 30 31 31 36 38 40 SHIELDING General Remarks Method For Calculation Of Shield Thickness Shield Design CHAPTER 5. 4 8 8 8 9 18 18 General Remarks 2 Fuel Element Configuration 3 Energy Losses To The Fuel Elements 4 Fuel Element Efficiency 5 Calculation Of Ea 6 Calculation Of E^ F 7 Calculation Of e£ c And E^t 8 Calculation Of Eg^ 9 Calculation Of Qj 10 Evaluation Of Specific Fuel Elements CHAPTER 5 Power Flattening Requirements 3. 1 3. 2 4 SELECTION OF THEMIONIC CONVERTER DESIGN General Remarks Thermionic Converter Performance Characteristics Performance Characteristics Used As Design Basis 2. 2. 1 2. 2. 2 1 1 50 50 53 POWER CONDITIONING General Remarks 59 iii TABLE OF CONTENTS (CONT. 5. 2 5. 3 5.4 5. 5 Operating Principle Of The Power Flattening Mechanism Fuel Rod Positioning Mechanism Initial Fuel Rod Position Operation Of The Fuel Positioning Mechanism CHAPTER 6. 1 6. 2 6. 3 6. 4 6. 5 6. 6 7. 1 6 61 61 62 63 ADDITIONAL DESIGN CONSIDERATIONS General Remarks Lead Losses Insulation And Support Of The Emitter Heat Source Modifications Requires To Fuel Element Design Electrical Insulation Of Emitter And Collector Radiator Design CHAPTER 7. 2 ) 7 65 65 66 67 68 70 SUMMARY AND CONCLUSIONS Design Summary Conclusions 73 73 BIBLIOGRAPHY . IV 78 LIST OF FIGURES AND TABLES Figure 1. 2. 2. 1 Schematic Power Supply Design Figure 2. 2. 1. 1 Thermionic Converter Output Voltage Characteristics Figure 2. 2. 1. 2 Thermionic Converter Intrinsic Efficiency Characteristics Figure 2. 2. 1. 3 Thermionic Converter Output Power Characteristics Figure 2. 2. 1. 4 Thermionic Converter Intrinsic Efficiency Characteristics Figure 2. 2. 1. Thermionic Converter Output Power Characteristics Figure 2. 2.4. 1 Representative DC-DC Converter Efficiencies Table 2. 3. 2. 1 Characteristics Of Converter With Variable Cesium Reservoir Temperature Table 2. 3. 3. 1 Characteristics Of A Converter Operating At A Constant Power Point Figure 3. 2. Solid Fuel 3. 6. Self Absorption 3. 7. 1 Geometry Used Element In Factor 17 22 28 32 The Calculation Of 3^ 7. LP 34 35 37 3. 9. 1 W-ThO^ Multi-Foil Insulation Thermal Conductivity Figure ^.10. 3. 10. Solid Fuel Element Efficiencies 41 1 Components Of Heat Loss 3. 39 1 Comparison Of Table 14 27 Normalized Intensity Of Absorbed Radiation Figure 3. 8. 1 Isotropic Source Gamma Albedo For Tungsten Table 13 1 Figure Figure 12 3. 2. 2 Gamma Figure 11 24 Cross Section Of Tubular Fuel Element Figure 10 1 Cross Section Of Figure 3 In Solid Cylinder Fuel Elements 43 10.2 Components Of Heat Loss For Different Fuel Element 44 Configurations Table 3. 10. 3 Components Of Heat Loss Figure In Tubular Fuel Elements 45 3. 10. Comparison Of Solid and Tubular Fuel Element Efficiencies Figure 3. 10. Tubular Fuel Element Efficiency 46 47 LIST Figure 4. 2. OF FIGURES AND TABLES (CONT. ) 1 Geometry Used In The Calculation Of Shielding Figure 4. 3. 1 Emitter Heat Source Table 4. 3. 1 Required Shiel Thicknesses Figure 4. 3. 2 Cross Section Of Shield Assembly Figure 5. 1. 1 51 54 55 57 Power Flattening Mechanism 60 Figure 6. 5. 1 Thermionic Converter Configuration Table 7. 1. 1 Final Design Summary VI 69 75 CHAPTER 1 INTRODUCTION 1. 1 OBJECTIVE The objective of this thesis is to design a thermionic power supply which will be fueled with cobalt- 60 and which will provide 500 watts of electric power over of three years a three year operating period. was chosen because the required radioisotope power supplies Most is between one and of the effort in this thesis The design lifetime life of many five years. operational (Reference I. 1] has been directed toward the opti- mization of the fuel supply and toward the power flattening requirements. The final design has been formulated so that no significant advances the present state of the art are required for The power supply was designed ingly it is not effort has it to be feasible. for terrestrial applications, accord- subjected to severe weight limitations. been made to in Nevertheless every keep weight and size within reasonable limits. The power supply was also designed so that it could operate automatically, unattended, for the three year lifetime. 1. 2 DESIGN CONCEPT 1. 2. 1 FUEL REQUIREMENTS In order to operate a thermionic converter efficiently the tempera- ture of the thermionic emitter must be at least 1500°C. Most design concepts for radioisotope power generators require that the isotope fuel operate at temperatures higher than the thermionic emitter temperature in order for heat transfer to occur. Difficulties associated with the operation of isotope fuel at these high temperatures have proven to be the primary deterrent use of isotope fueled thermionic converters. to the The relative low cost and high power density make ed to other isotope fuels such as strontium- 90, fuel. (Reference and that is However, the melting point 1. 2) compar- of cobalt- 60, it attractive as a of cobalt-60 is MQS^, significantly below the melting point required for a useful thermionic converter To make fuel. this isotope compatible with ther- mionic converter requirements, alloys of cobalt and rhenium have been tested in an attempt to produce an isotopic fuel form with This approach has not been entirely successful. point. drawbacks is that the alloy must be formed after a high melting One of its major the cobalt has been ir- radiated. 1. 2. 2 LOW TEMPERATURE FUEL CONCEPT Considering the facts mentioned above the choice of cobalt-60 as a fuel for a thermionic power supply appears at best to be illadvised. However, an interesting concept has been proposed which isotope which emits energetic (Reference radiation to be used as a fuel. 1. 3) This design concept The design proposes fuel, gamma to presented schematically is thermally insulate the The gamma radiation from gamma converted into heat by the in gamma cobalt-60 in this case) from a surrounding absorber. will allow an Figure 1. 2. 2. 1. source (the isotope medium of gamma the fuel would be absorbed and absorber. The gamma absorber would then act as the heat source for the thermionic emitter. Since the cobalt-60 source (gamma is absorber), thermally insulated from the emitter heat it can operate at a temperature lower than the temperature of the emitter heat source and lower than its ing point. own melt- This design concept has recently become feasible due to the VAC HOD COLLECTOR RADIATOR SCHEMATIC POWER SUPPLY DESIGN FIGURE 1. 2. 2.1 develop^ment of a high temperature multi-foil insulation which uses refractory metal foils separated by thin layers of refractory oxide particles to provide a highly efficient and (Reference 1. 3 compact thermal insulation. 4) 1. PRELIMINARY DESIGN CONSIDERATIONS Several additional design requirements are illustrated in Figure Some 1. 2. 2. 1. of these have been selected for convenience, others are required by the operating conditions. Since the high operating temperature of the emitter heat source required the use of a refractory material, tungsten was selected as the The high atomic number material to be used. gamma of tungsten gives it good absorption properties. The high temperature of the thermionic converter and its heat source imposes a requirement that the system operate in a vacuum order to Thus the design in prevent rapid oxidation of the high temperature components. vacuum housing, shown in order to in Figure 1. 2. 2. 1, was included in the maintain a vacuum around the high temperature com- ponents. In order to facilitate fabrication of the heat source assembly it is thermionic converter and desirable to delay loading of the isotope fuel until all other steps in the fabrication process have been completed. This procedure will minimize the work which must be performed re- motely in a hot cell and thus greatly simplify assembly of the unit. was therefore decided to locate the fuel outside of the Approximately one to the collector of the power. It is fifth of the It vacuum housing. energy transfered from the emitter thermionic converter thus necessary to provide a is removed as electric means of removing the remainder order of this energy ture. A in the atmosphere. in maintain the collector to constant tempera- at a radiator is provided so that the excess energy can be dissipated Since the radiator area remains constant throughout the operating period, the collector temperature will be determined by the heat flux to it from the emitter and the output power. The hard gamma radiation from Mev and 1. 33 per disintegration) requires that the power supply be shielded in order the cobalt-60 (1. 17 personnel from the ionizing radiation. to protect Since there will be some heat generated in the fuel a means must be provided to remove the heat so that the fuel will remain at a low temperature. In Figure 1. 2. 2. 1 As conduction through the shield. necessary to the heat removal this design accomplished by is was modified, it provide the fuel with a radiator assembly similar became to the collector radiator. 1.4 FURTHER DESIGN REFINEMENTS The basic design matically in be modified Figure in is now qualitatively set and is represented sche- 1. 2. 2. 1. In the following an attempt to both optimize chapters the design will performance and its to remain within limits set by materials and the state of the art. The thermionic converter design practical output voltage for the obtaining output mine it A In Chapter of 3 power the fuel is in to fix the Power Chapter 2. A selected and methods of thermionic converter design the required input power. mode considered power supply power requirements are used ted and the imum discussed. is is selected and the operating point and deter- flattening concepts are investiga- flattening selected. element design is optimized so that the max- useful energy will be delieverd to the emitter heat source. An optimized fuel element design is selected to meet the converter input power requirements which were determined in Chapter The shielding requirements are discussed in 2. Chapter 4. The shielding calculations are explained and the shield design is finalized. Since no power flattening device found was compatible with this design's needs, one was designed. discussed in Chapter Chapter 6 The power flattening mechanism 5. contains an explanation of numerous heat losses which degrade the performance of the thermionic converter and cause operate at less is than the intrinsic efficiency. losses on the fuel element design is The it to effect of these heat Several additional also treated. design problems which were not treated in detail are summarized. The drawn. final design is summarized in Chapter 7 and conclusions are REFERENCES 1. 1 1. 2 W. R. and Harvey, D. G. Englewood Cliffs: Prentice Hall, Corliss, , Radioisotopic Inc. , Power Generation, 1964. Hilbom, H. S. "Savannah River Laboratory Isotopic Power and Heat Sources, Part I Co-60, " Quarterly Progress Report, July September, 1967, DP-1129-1. , "Description of a Cobalt-60 Fueled Thermionic Generator Experiment, " Conference Record of the Thermionic Conversion Specialist Conference, October, 1967. 1. 3 Dunlay, 1.4 "Quarterly Progress Report of Carvalho, J. and Dunlay, J. B. Research and Development of Vacuum Foil Type Insulation for Radioisotope Power Systems," Thermo Electron Corp., Report No. 4059-109-69, January 20, 1969. J. B. , , - CHAPTER 2 SELECTION OF THERMIONIC CONVERTER DESIGN 2. 1 GENERAL REMARKS Thermionic converter performance characteristics (i. e. , output current density, output power density and intrinsic efficiency) are functions of several that the desired different These parameters can be varied parameters. in a power output can be obtained using any one parameter combinations. In this manner such of several chapter a set of performance characteristics, which has been extracted from the literature, is discussed and the reasoning used in fixing the converter operating parameters is explained. Methods of obtaining a practical voltage output and their effects on converter design are explained. this power supply design The problem of The choice method to be used in made. is power flattening is also treated. ing concepts are proposed and discussed. to operate using of the Two power flatten- Thermionic converters designed each of the power flattening concepts are discussed and compared. Finally the thermionic converter design to be used in this power supply 2. 2 is selected. THERMIONIC CONVERTER PERFORMANCE CHARACTERISTICS 2. 2. 1 PERFORMANCE CHARACTERISTICS USED The performance characteristics output power density and reservoirtemperature T (i. e. , AS DESIGN BASIS output current density, intrinsic efficiency) are functions of the , emitter temperature T Tq, interelectrode spacing and electrode material. , cesium collector temperature In order to select the operating values of these parameter shows the functional dependence it is desirable to have data which of the thermionic converter performance characteristics on each of the variable parameters. Figures 2. 2. 1. 1 through 2.2.1.5 show the thermionic converter performance characteristics of a converter with tungsten emitter at 2000°K, molybdenium collector and an interelectrode spacing of mils 7. as a function of cesium reservoir temperature and collector temperature. These performance characteristics were calculated using an analytical These theoretical characteristics are converter model. with corresponding experimental characteristics. in The method used calculate these characteristics is explained in References Although the data presented in Figures 2. 2. 1. 1 for an emitter temperature of 2000°K, Reference good agreement 2. 1 2. and 1 through to 2. 2. 2. 2. 1. 5 is provides similar data for emitter temperatures ranging from 1600°K to 2100°K. As explained below, however, 2000°K is the emitter operating temperature K and 1000 is the proposed the collector operating temperature which were selected for power supply. INTRINSIC EFFICIENCY 2.2.2 The Figures intrinsic efficiency appears as the ordinate on the graph in 2. 2. 1. 2 and 2. 2. 1. 4; it intrinsic efficiency fl- is defined here so that no confusion will arise. The of a thermionic converter is defined as the efficiency in the absence of electrode, lead, and structural support losses. This efficiency considerations and ^i = is is independent of detailed converter design given by P/(Q e + Q t + Q r + Q g ) (2.2.2.1) 10 THERMIONIC CONVERTER OUTPUT VOLTAGE CHARACTERISTICS 0.4 0.8 1.2 1.6 OUTPUT VOLTAGE (VOLTS) FIGURE 2. 2. 1. 1 2. 11 THERMIONIC CONVERTER INTRINSIC EFFICIENCY CHARACTERISTICS 24. 20. ^ 16. O u — I 12. w o I— w I— 8. 4. 0. 4 0.8 1. 2 OUTPUT VOLTAGE (VOLTS) FIGURE 2. 2. 1. 2 TO 12 THERMIONIC CONVERTER OUTPUT POWER CHARACTERISTICS 24. 20. K Tn =64C TE = 2000 I Tq = 1000 I D i\ = MI 7. _,S 630 Y< 6: <>] O 16. H V 610 i— \j , xn § 12.0 K W 600 A o h !=> 8. P-i 590 H - ID O 4. ^*****™^^^i 0.4 1.2 0.8 OUTPUT VOLTAGE (VOLTS) FIGURE 2. 2. 1. 3 1.6 2. 13 THERMIONIC CONVERTER INTRINSIC EFFICIENCY CHARACTERISTICS 24. 0.4 0.8 1.2 OUTPUT VOLTAGE (VOLTS) FIGURE 2. 2. 1. 4 1.6 2. 14 THERMIONIC CONVERTER OUTPUT POWER CHARACTERISTICS 24. 20. CV) O 16. >i H i— CO W Q 12. o PL, Ph H O ID 4. 0.4 0.8 1.2 OUTPUT VOLTAGE (VOLTS) FIGURE 2. 2. 1. 5 1.6 2. 15 where P fluxes is the output removed from power density and Q c , QX Q., X and Q are the heat g the emitter due to electrons, ions, radiation, and gas conduction, respectively. Q flux is which 2. 2. 3 by far the most important term and Qr the only other heat is is significant. EMITTER AND COLLECTOR OPERATING TEMPERATURES It is generally true that the efficiency of an optimized thermionic converter increases monotonically with increasing emitter temperature. It is thus desirable to operate the converter at the highest allowable emitter temperature. The highest temperature allowed in the system is limited to 2270°K by the tungsten multi-foil insulation which is used to insulate the fuel elements and the emitter heat source. (Reference The highest temperature to which the multi-foil insulation will be subjected occurs at a point on the emitter heat source from the emitter. Using it was determined that the emitter temperature would be approximately 2100 K. that further refinement of the design the emitter from of end farthest (i. e. necessity maximum Since it allowable was expected to electrically insulate heat source) would lead to a larger temperature drop across the heat source, the at the first design iteration values for heat fluxes and emitter heat source size, its 2. 3) it was decided performance characteristics that the design would be of a converter with an emitter based on temperature 2000°K. The operating temperature of the collector was selected as 1000 K since this gives the highest intrinsic efficiency for an emitter temperature of 2000°K. Since the collector radiator the emitter to the collector is fixed in size, must be constant in the heat flux from order to maintain a constant 1G collector temperature for a given electric power output. OUTPUT VOLTAGE 2.2.4 Much of the equipment which power supplies of this type are designed to power require input voltages on the order of 28 volts. (Refer- ence 2. 4) It was therefore decided that in order to be practical this power supply should have an output voltage of 28 volts. Thermionic converters are classified as low voltage, high current devices. volt. The output of a single thermionic diode is on the Thus, in order to furnish power mionic diodes must be connected must be stepped up using more attractive since it a desired 28 volts, many ther- series or the output from a few diodes in DC-DC at the order of one converter. The second alternative is requires fewer diodes and, moreover, the electronics for the step up process are relatively simple. The circuitry and operating characteristics of low voltage input, regulated, current drive DC-DC described in Figure DC-DC in converters suitable for use with thermionic converters are References 2.4. 2. 1 2. 5, 2. 6 and 2. 7. shows representative efficiencies of current drive converters for various voltage inputs and power levels. Figure 2. 2. 4. 1 The data indicates that there is little to be gained by using an input voltage greater than 5 volts, but that the efficiency falls off rapidly for input voltages less than 5 volts. At a power level of 500 watts and an input voltage of representative DC-DC converter efficiency of 89% 2.2.4.1. Thus, necessary to supply 560 watts to the in order is a found from Figure to obtain 500 watts of useful DC-DC 5 volts, power converter. it will be Therefore the thermionic converters will be designed so that several connected in series 17 3 i *p G- r > > O C CM i o o U > 2 t > CD 1 CO W o o K- u lO w I— CO u I— Eh < o « w « > o o u u o o -* CO p £ J p > H J HH PS CM* r—t . CM a £ H o PS ID Pn o — 1 u 1— i u Q PS Eh o > CM i— < Eh u w H Eh p W Ph CO 1 H o o PL, H // PS o o o o CO A0NHI0MJ3 o 1— fe 18 DC-DC will provide 560 watts at 5 volts to a Now converter. that the thermionic converter output requirements have been established the power flattening problem must be investigated to determine whether or not it restricts the selection of the thermionic converter operating point. 2. 3 THERMIONIC CONVERTER DESIGNS COMPATIBLE WITH POWER FLATTENING REQUIREMENTS 2.3.1 POWER FLATTENING REQUIREMENTS Since the half life of cobalt- 60 is 5. 25 years, the energy supplied to the emitter heat source will decrease significantly over the three year life of the power supply. must be employed so This means that .some form of power flattening that constant power can be supplied to the load. Since a constant emitter operating temperature of 2000°K has been chosen for this design, the power flattening problem reduces maintaining the emitter heat source at a to one of constant temperature while the energy available from the cobalt-60 decreases. approaches to this power flattening problem. There are two general The first is to remove all the energy deposited in the emitter heat source through the thermionic This approach necessitates operating with a variable cesium converter. reservoir temperature. verter to operate current). In The second approach allows the thermionic con- at a fixed power point (i. e. constant output voltage and order to do this a variable heat removal system to the emitter heat source and operates in parallel with the is connected thermionic converters. 2. 3. 2 CONVERTER OPERATION WITH VARYING CESIUM RESERVOIR TEMPERATURE When operating near maximum efficiency the major fraction of the 19 heat transferred electrons. If from the emitter to the collector is carried by the the emitter is maintained at a constant temperature the only other significant heat transfer, that due to radiation, remains constant. Thus, order in be varied. to vary the emitter cooling rate, the output current must Figure 2. 2. 1. 1 shows that the output current can be varied by varying the cesium reservoir temperature. In order to maintain a constant power output the output voltage would also have to be varied. the current density and As can be seen from Figures 2.2.1.2 and power output are both functions 2.. 2. 1. 3 of the converter output voltage and cesium reservoir temperature. Over a three year period the energy released by the cobalt-60 decreases by 33%. to vary by 33% and This means that the current density would also have in order to maintain a constant power output the output voltage must also be varied by 33%. References Thus it 2. 5 and 2. 6 can accomodate a - 14% variation in in input voltage. would be desirable to employ a system that would decrease the variation in output voltage so that a not have to be designed. thermionic converter In The DC-DC converters described at a It more complex DC-DC converter does was therefore decided that the operation of a constant output voltage would be investigated. order to maintain a constant emitter temperature while operating at a constant output voltage, it is necessary to control both the cesium reservoir temperature and the voltage regulator shunt resistance. range of voltage outputs over which a variation temperature can cause a 33% variation decrease in the in the in In the cesium reservoir current output density a cesium reservoir temperature causes a decrease in output current density. Therefore the thermionic converter would be designed to provide the 20 desired power level with a low cesium reservoir temperature In life. order to cool the emitter end of at the beginning of at a faster rate at the life, the converter would be operated at a higher cesium reservoir temperature and consequently a high current density. power output constant, the will of design lifetime is reached. would have This means that the thermionic converter 2. 5) which would maintain a constant to the load. Figures 2. 2. 1. 2 and power density as functions The data performance held always be higher than required until the end (such as described in Reference ature. is be coupled to the load with a dissipative shunt regulator to power output Since the output voltage in of a 2. 2. I. 3 show the intrinsic efficiency and output cesium reservoir temper- of output voltage- and these figures was used to predict the beginning of thermionic converter designed to operate at a life constant output voltage and variable cesium reservoir temperature. Even though the emitter would be maintained ture its at a constant tempera - the exponentially decreasing heat flux to the collector w ould cause r , temperature to decrease because of the fixed heat transfer area collector radiation. Therefore Figures 2.2.1.4 and 2.2. 1.5, which show intrinsic efficiency and output power density as temperature and output voltage, were used performance It of the a function of collector to predict the end of life of the thermionic converter. was found that at output voltages higher than 0. 7 volts variation of the cesium reservoir temperature could not cause enough change in the output power density to provide the desired three year lifetime and maintain a reasonable efficiency. Thus 0. 7 volts was selected as the oper- ating output voltage for the individual thermionic converters. that seven thermionic converters still would have to be connected This means in series to 21 provide a life 4. 9 volt input to the DC-DC The beginning and end converter. of characteristics of the thermionic converter designed to operate at a constant output voltage and with variable cesium reservoir temperature are summarized Table 2. 3. 3 2. 3. 2. 1 at a Table 2. 3. 2. 1. The were calculated using the input power requirements listed in intrinsic efficiency. OPERATION AT A FIXED POWER POINT In point, in a order to allow the thermionic converter to operate at a fixed power system must be provided which maintains the emitter heat source constant temperature while the thermionic converter constant amount of heat. system which operates parameter of the heat The usual approach in parallel with the is to removes a provide a heat removal thermionic converters. Some removal system, such as heat transfer area, is varied such that the excess heat removed decreases with the same time constant as the exponential decay of the isotope fuel. an excellent review of some of the Reference more promising methods Unfortunately the only concept discussed that flattening. is of gives 2. 7 power neither beyond the present state of the art nor too complex to be simply automated is one which employs a variable radiator area. This method provides only approximate power flattening since the radiating surface finite steps by ejecting parts of the radiator. 33% variation in In is reduced order to provide for the the heat input to the emitter heat source and maintain a relatively constant temperature, the radiator would have to be of of these proposed power flattening schemes seem particularly well suited to this design's requirement of a three year lifetime. it made up many segments and would be very cumbersome. Thus none in Therefore, a power flattening mechanism was designed to at 22 CHARACTERISTICS OF CONVERTER WITH VARIABLE CESIUM RESERVOIR TEMPERATURE Beginning of Life End of Life Tungsten Emitter Material Emitter Temperature ( 2000 K) lybdenum Collector Material Collector Temperature (°K) 1000 Interelectrode Spacing 7 Output Voltage (Volts) Output Power Density (Watts/ cm ) Cesium Reservoir Temperature (°K) Total Emitter Area Total Power Output (cm 2 ) (Watts) Required Heat Input (Watts) Intrinsic Efficiency mils 10 630 608 56 5G 975 560 4820 3150 3. 2 TABLE 7 2.3.2.1 - 17.4 Design Lifetime (Years) Converters Required 750 0. 7 20. 2 of - 0. 7 (%) Number 2000 17. 8 - _ 23 This mechanism maintain a constant emitter temperature. in Chapter This power flattening mechanism 5. mionic converter operating at a made is described the design of a ther- constant power point feasible. converter would operate with the characteristics listed This Table in 2. 3. 3. 1. The converter was also designed using the performance characteristics presented in Figures 2. 2. 1. 2 and 2. 2. 1. 3. Again, the input power requirements were calculated using the intrinsic efficiency. A converter operating with this mode of power flattening has the following advantages over a converter using a variable cesium reservoir temperature (Table 2.3.2.1) for power flattening. thermal power input requirement results fuel costs 920 watt lower saving of $12, 900 on initial based on a cost of $14 per thermal watt (Reference five thermionic diodes are the in a Its DC-DC needed to provide the desired 5 1. 2). Only- volt input to converter instead of the seven required by the system using the variable cesium reservoir temperature mode of power flattening. Since the cesium reservoir temperature remains constant over the entire operating period, an internal adsorption type reservoir of the type described in Reference 2. 9 can be used. Since these advantages strongly favor a thermionic converter operating at a constant power point, a thermionic converter with the operating characteristics given this power supply design. in Table 2.3.3.1 was selected for use in 24 CHARACTERISTICS OF A CONVERTER OPERATING AT A CONSTANT POWER POINT Beginning of Life End of Life Tungsten Emitter Material Emitter Temperature ( 2000 K) Molybdenum Collector Material Collector Temperature ( K) 1000 Interelectrode Spacing 7 Output Voltage (volts) Output Power Density (watts/ cm Cesium Reservoir Temperature Total Emitter Area Power Output (cm ( K) 100( - 1.0 1.0 610 63. 5 ) - mils 8. 8 ) 2000 8.8 610 63. 5 (watts) 560 560 Required Heat Input (watts) 2540 2540 Excess Fuel Required 1360 Total Intrinsic Efficiency (watts) Design Lifetime (Years) Number of 22 22 3. 2 - (%) Converters Required 5 TABLE 2.3. 3. 1 _ 25 REFERENCES 2. 1 2. 2 "An Improved Theoretical Description of Thermionic Converter Performance Characteristics, " Procedings: 27th Annual Physical Electronics Conference, Cambridge, Mass.:, March, ___ Wilkins, D.R. , Wilkins, D.R. , "A Unified Theoretical Description of Thermionic " Journal of Applied 39, number 5, April, 1968, Converter Performance Characteristics, Physics, vol. 2. 3 2.4 Paquin, M. L. "High Te_mperature Multi-Foil Thermal Insulation, Thermo Electron Corp. Corliss, W. R. and Harvey, D. Englewood 2. 5 " , C. Prentice Hall, Cliffs: Radioisotopic , Inc. , Power Generation, 1964. Low Voltage Converter Regulator J. T. , "Thermionic " Conference Record of the Thermionic Conversion Systems, Lingle, Specialist Conference, November, 1966. 2. 6 Lingle, J. T. "Low Input Voltage Conversion, " Procedings of the 18th Annual Power Sources Conference, May, 1964. 2. 7 Lingle, 2.8 Rush, R. E. and Belofsky, H. "Power Flattening Studies for Radioisotope Thermoelectric Generators, " General Instruments Corp., NYO-9783 1963. , "Energy Source - Low Voltage Conversion System, T. Procedings of the 19th Annual Power Sources Conference. 1965. J. " , , , 2. 9 Harbaugh, W. E. and Basiulis, A. 'The Development of a HighTemperature Reservoir for Automatic Control of Cesium Pressure, Conference Record of the Thermionic Convers ion Specialist Conference, November, 1966. , " 26 CHAPTER •FUEL 3. 1 3 ELEMENT OPTIMIZATION GENERAL REMARKS This chapter explains. in detail the methods used to optimize the the fuel element design. Limitations placed on the fuel element geometry are discussed and two practical fuel element configurations, which were selected for study, are described. The heat losses which contribute to fuel element inefficiencies are defined and the methods used to calculate these heat losses are Heat losses and efficiencies, calculated for fuel explained in detail. elements of various lengths, diameters and strengths, are compared. Based on this for use in this 3. 2 comparison the optimum fuel element design is selected power supply design. FUEL ELEMENT CONFIGURATION The major supplier of cobalt- 60 is the Savannah River Laboratory. The cobalt is Atomic Energy Commission's obtainable in the form of i wafers which are 40 mils thick and up wafer is to 3.5 inches in diameter. Each plated with approximately one mil of nickel in order to prevent contamination of the equipment used to handle irradiated. (Reference 3.1) Due it once it to the size limitations has been placed on the cobalt wafers any fuel element large enough to be of interest will have to be composed of a large number of wafers. The two fuel element configurations which were considered for power supply design are shown element is composed cylinder; the other is in Figures 3.2.1 and of a stack of cobalt composed of 3. 2. 2. One this fuel wafers which form a solid washer like cobalt wafers and takes a 27 CROSS SECTION OF SOLID FUEL ELEMENT COPPER ROD OPPER HEAT REMOVAL PATH COBAL WAFERS MULTI-FOIL SULATION TUNGSTE EMITTER HEAT SO FIGURE 3. 2. 1 28 CROSS SECTION OF TUBULAR FUEL ELEMENT -COPPER ROD .COPPER HEAT REMOVAL PATH MULTI-FOIL INSULATION TUNGSTEN EMITTER HEATJSOUR( FIGURE 3. 2. 2 29 The tubular form. insulated from fuel at They are copper. low temperatures. order to insure that the fuel any heat generated in it any heat which reaches When removed. in the emitter heat source with multi-foil insulation and are designed to operate In elements are both clad due it to the self maintained at a absorption of low temperature gamma radiation or through the thermal insulation must be stacked to form a fuel element, the cobalt wafers offer a very poor heat transfer path due wafer interfaces. is Thus the fuel removing any heat generated to the low thermal conductance across the element design must provide a means of in the fuel element. In this case the stack which provides a path of high thermal of fuel wafers is clad in copper conductance for heat removal. For future reference the copper heat the fuel element is defined as the cobalt wafers, removal path (cladding) and the surrounding multi-foil The cobalt wafers and copper cladding insulation. will be referred to as the fuel rod. Since the fuel element source it is heat which is obvious that any energy which is is absorbed in the fuel or any transmitted through the insulation to the fuel canjiot be used by the thermionic converter. fuel thermally insulated from the emitter heat element so that the total It will therefore be benificial to design the energy which the system loses to it will be minimized. 3. 3 ENERGY LOSSES TO THE FUEL ELEMENTS In order necessary to to minimize the total energy loss know what the losses are and how to the fuel to calculate the energy loss rates are defined in this section. calculate them are then explained elements them. is Thus, The methods used in the following sections. it to 30 Eg energy loss due to absorption of beta particles copper per unit time. Er Ey^rr energy loss due to self absorption of per unit time. Ey = Ew= gamma radiation in the cobalt energy loss due to absorption of removal path per unit time. gamma radiation in the copper heat energy loss due per unit time. gamma radiation in the insulation absorption of to E„jr= energy loss due to the absorption of backscattered in the fuel element per unit time. Q H energy loss due to heat flux to the fuel element. T 3.4 gamma radiation through the insulation from the tungsten FUEL ELEMENT EFFICIENCY The efficiency (E % where E 1- = of the fuel element, f1p t.+ F E C + E T + E SQ + Q* T is defined as + E ft ) (3.4.1) g T is defined as the total energy released during radioactive decay of the fuel per unit time This definition power density 3. 5 and in the cobalt is minus any energy carried away by neutrinos. compatible with the convention used when calculating the of the fuel. CALCULATION OF Ep Eg resulting is the from the decay of the cobalt-60 are emitted with an energy spectrum which has an upper energy limit most energetic beta particle of cobalt. all of The beta particles simplest energy loss to calculate. is 81 Since this distance is mg/cm of 0. 31 which much shorter the beta energy is absorbed in the fuel. Mev. is The range equivalent to of this beta decay energy is 009 cm than any fuel chord length This means that 0. 31 are lost to the system for each disintegration of a cobalt-60 atom. 71% 0. of the Mev However, carried away by neutrinos (Reference 3. 2); 31 thus only 0. 09 Mev's per disintegration are deposited A sample in the fuel. of cobalt- 60 with an activity of 400 curies release a total of 58. 7 watts/ cm 3 ; 52. 4 watts/ cm per gram 3 is in form the will of gamma o radiation, 4.4 3 cm appears watts/cm V-,-, r carried away by the neutrinos and 1.9 watts/ as beta particle energy. E^ where is is the = volume 1.9 Thus Vp (3.5.1) of the fuel (cobalt-60) in cm o . valid only for cobalt with an activity of 400 curies per 3. 6 Equation 3. 5. is 1 gram. CALCULATION OF E v In order described finite E^p to calculate in detail in , Reference the results of calculations 3. 3 v/ere used. performed and This reference treats the source as a series of planes composed of point isotropic sources and integrates over the volume assuming scattering is straight ahead and This integral can be performed analytically attenuation is exponential. only if planes and cylinders of infinite length are considered. obtained are plotted in Figure is 3. The results 6.1 as a self absorption factor, equal to the fraction of emitted gamma f, which radiation absorbed in the fuel. Thus, E*F 3. 7 CALCULATION OF Ew-, Reference unit = f (E E. T" V (3.6.1) AND E^ and E^ T were computed using the following method developed 3. 3. I is in defined as the intensity of absorbed radiation per volume per second at a distance r from the axis a plane coincident with the end of the cylinder. of a cylinder and in 32 tf CO CO 1 55 Q s U — i E H X n x Q £ — pq < O H U < CO i I 4 2 H CD X CO* H O W CO O i— <J H CO LO O O 00 I> CD LO <# CO CM o o O o o o O 33 £-? where is if the macroscopic material surrounding the fuel radiation and D See Figure D is = z 7 related to 2 (3.7. 1) h '0 'o n + r 2 gamma at the 2 + - f> energy of the emitted and , absorption cross section of the gamma by z 2rp cos © (3.7.2) 3. 7. 1. obtained from equation 3. 7. 1 is one half the value of P the radial distribution in any normal plane of an infinite cylinder. There- The value fore, a of I new function is I defined where 2L (3.7.3) V I is the 1 - f normalized absorbed radiation intensity so that oo 2L' r d 5a» [UaR (r - 1 )] - (3.7.4) 1 ^ where R is the radius of the fuel and r The function r' V* The fraction shell between of the 1 f /Ja (r 2 - emerging energy is lXa t R(r' - 1) in Figure equal to R) P JWaR R)' r' d ff/aR U (r' 3. 7. 2. that is absorbed in an annular ^ 1 against 2 2I /*a (r egual to r/R. a^ and r r. is plotted is - 1)1 J This integration can be performed graphically on Figure (3. 7. 5) 3. 7. 2. 34 GEOMETRY USED IN THE CALCULATION OF h> FIGURE 3. 7. 1 35 O i— H Q W O en CM ffl < 00 O H >H H i— CO W H Q W N i—i O o CM a CM 36 E\/£ equal to is ,/'a(r (E c -R) -E VF )1 T -E^ 2^ r -d[|laR(r' - 1)] (3.7.6) 1)] (3.7.7) J where r c is the outer radius of the copper. ,Ua (E Ep - T - E^ F (r rj is the equivalent is equal to R) 21 f P ) J/^(r where - Ejj r d[/laR(r' - - c -R) outer radius of the multi-foil insulation. equivalent radius is defined such that rj - r Q is equal to the sum The of the thicknesses of the individual foils in the insulation. 3.8 CALCULATION OF E ou E was approximated S fr in the energy albedo for tungsten for are shown in Figure where Ej albedo at S , AN is the initial Ej and Once of the fuel A N /j. aF is E g E is o — the gamma number albedo is evaluated defined as (3.8.1) energy of the is the the value of of the backscaltered radiation A Ej x s radiation as a function of energy 3. 4. The average energy E gamma The number and These curves were found by interpolating 3. 8. 1. data found in Reference following mariner. radiation, A£ is the energy at E,. obtained the energy absorption cross section at this The backscattered radiation is average energy. assumed isotropic source at the surface of the fuel rod. to constitute a plannar The average distance that 37 1.0 1 —— — ——- O Q pq ^\ 0. ^L < V/ y . — / / // / ' / VA fs E / / 0.01 0. 10 1.0 1 GAMMA ENERGY ISOTROPIC SOURCE (Mev) GAMMA ALBEDO FOR TUNGSTEN FIGURE 3.8. 1 38 the backscattered radiation travels through the fuel rod is equal to the mean chord length of the fuel rod r 4 x fuel - __ _ . rod volume (3.8.2) area fuel rod surface Thus E 3. 9 = gy (E T E^ - - E^ F per layer exp(-UaF r) - 1 ) (3.8.3) Two terms design C. layers at performance (Reference latter arises watts per Figure 3. 9. Qt1 cm of the foil edges To is is the 3. 6 degrades the indicates that of edge is approximately twice the heat flux through the insulation. shows the thermal conductivity 1 2Lk -T F = N is the total layer, The average spacing the difficulty of matching the insulation as a function of source temperature. + Akj(T S (T s ) 1 N of tungsten 3. 5) Data from Reference of the insulation. cm 2 from The mismatching corners. the heat loss in watts per length, composed the heat lost through the insulationjQ contribute to The edge loss. where A is heat lost due to conduction through the insulation and the other is the is the in this Multi-foil of this composition has given satis- mils. is 4. d, factory performance at 1900 in c mils thick and separated by thorium oxide. foils 0. 5 foil E^ CALCULATION OF Qj The insulation selected for use One - TF - L is the total insulated edge of layers of foil, d is the average spacing per the temperature of the emitter heat source and rod temperature. The (3.9.1) ) d insulated surface area, number kj of the multi-foil foil thermal conductivity is evaluated Tp at is the fuel Tg 39 W-ThQ 2 MULTI-FOIL INSULATION THERMAL CONDUCTIVITY (k -4 10 1 1 1 r "" 1 i 1 l 1 l — O o £ o +-> 3 Eh i—i > — i -a 10 h O Q O O « W X h -6 10 !._. i . • 500 JL . .!.._. 1 1 1000 l 1500 SOURCE TEMPERATURE FIGURE 1 3. 9. 1 (°C) i i 2000 ) 40 3. EVALUATION OF SPECIFIC FUEL ELEMENTS 10 Once all the energy losses could be evaluated, the fuel elements were compared as follows. fuel The selected length were selected. its The element configuration, strength and element was then optimized and fuel The efficiencies were then compared efficiency calculated. in order to determine the optimum fuel element design. Each fuel element evaluated was optimized in the Values were selected for E T and fuel element length. E^j The number and Q, were calculated. selected so that the assumed sum of E ^ and Q SI sum that heat equal to the generated uniformly in the Ey , was of layers of insulation was minimum. a , E y.^ E^ f was then It and copper heat removal path. assumption since the copper This Q T was a good is very thin and has a high thermal conductivity. is The temperature rise along the length o 300 C and the outer radius, Then Eg I E^ of following way. of the fuel of the copper r, element was limited to was calculated using Equation 3. 10. 1. v2 where At = __ (Ep+E yF 300 C, + E yi + Ql R is the In Figure various values was then used 3. 10. 1, of ET monotonic increase fl Ev^ to calculate is (3 of copper, L radius of the cobalt fuel. thickness of the copper was determined, 3. 4. 1 +R 2 At 2TTk c kp is the thermal conductivity length of the fuel element and Equation )L fl and E^ _ 10>1) is the Once the were calculated. . plotted against fuel element length for and a solid cylinder fuel element geometry. in efficiency with to the decrease in self absorption. to the decrease in the decreasing E T The decrease diameter of the is due almost entirely in self fuel rods as Erp The absorption decreases. is due 41 COMPARISON OF SOLID FUEL ELEMENT EFFICIENCIES 80 f[ F (%) ^Eji = 250 - ET = 500 70 ** 60 1 1 I 1 1 1 1 10 5 FUEL ELEMENT LENGTH FIGURE 3. 10. 1 15 1 (CM) Erp = 1000 1 42 Figure In E T = 3. 10. 2, p rt plotted against fuel element length for is 1000 watts, but for the solid cylinder and tubular fuel element geometries. decrease The higher efficiency E^ F in and Ef c The gain . not for a significant increase in compared of the tubular fuel E^ in efficiency element is due to a would be higher were it and Qj for the tubular fuel element to the equivalent solid fuel element. See Table 3. 10. 2 for a tabulation of the various energy losses in these two fuel elements. Figure shows n 3. 10. 3 a tubular fuel element with diameter up p ET as a function of fuel element diameter for = cm, then remains relatively constant and then decreases to 4 as the diameter becomes very large. best be seen from Table since the cobalt The efficiency increases with 1000. 3. 10. 3. becomes thinner. The reasons E^ decreases with increasing diameter E^ decreases with increasing diamet- er since the copper heat removal path can be in Ey p E^ c and seen from Table increase in QJ made lead to an increase in efficiency. 3. 10. 3, for this behavior can thinner. The decrease However, as can be the increasing surface area leads to a which eventually overrides the decrease in marked E % F and E $ c and causes the efficiency to decrease. Table 3. 10. 1 shows the relative importance ents of the total heat loss and varied and E T how they vary as held constant at 1000 watts. along the fuel rod is held must be increased as at in E^ F ; compon- the fuel element length is Since the temperature drop 300°C, the thickness of the copper cladding the fuel element length is increased. copper thickness leads to an increase decrease of the various in E ^c The increased which practically offsets the thus there is little variation in fuel element efficiency with length. Based on the data presented in Figures 3. 10. 1 through 3. 10. 3 and 43 COMPONENTS OF HEAT LOSS LENGTH 5 IN cm SOLID CYLINDER FUEL ELEMENTS 10 cm 1 cm 5 Erp 1000 1000 1000 H 35 35 35 *F 222 174 145 E fc 27 E 18. 5 21. 2 26.4 E SS 17 14.1 14. 3 Ql 25. 3 26. 6 27.4 E Sl V 94.5 58. 5 65. 5 % 66.2 % 65.7 .__ (ALL HEAT LOSSES IN WATTS) TABLE 3. 10. 1 . — —~ ,— % 44 COMPONENTS OF HEAT LOSS FOR DIFFERENT FUEL ELEMENT CONFIGURATIONS FUEL ELEMENT CONFIGURATION SOLID CYLINDER LENGTH 10 cm TUBULAR cm 10 DIAMETER 4 cm ET 1000 1000 Ee 35 35 E &F 174 67. 5 E frC 58. 5 26. 2 E frl 21. 2 48 E sv 14. Q, 26. 6 66. 2 Of (ALL LOSSES IN 1 % WATTS) TABLE 3. 10. 2 5. 2 62. 75. 6 1 % 45 COMPONENTS OF HEAT LOSS -CJrp DIAMETER IN 1000 1000 1000 2 TUBULAR FUEL ELEMENTS cm 4 cm 6 cm - Ep 35 35 35 E ifF 125 67. 5 48.2 E SC 50. 5 26. 2 18.3 E 37.4 48 53.6 SI E Sfr Qj If 9.4 62. 34. 7 70. 7 % TABLE 3.4 5. 2 75. 6 3. 10. 3 % 1 86.6 75. 5 % 4G COMPARISON OF SOLID AND TUBULAR FUEL ELEMENT EFFICIENCIES (E T = 1000) 80 % <%) 4cm) 70 ;olid 1.J 60 I 10 5 FUEL ELEMENT LENGTH FIGURE 3. 10. 2 15 (CM) 47 TUBULAR FUEL ELEMENT EFFICIENCY (LENGTH = 10 CM) 80 Erpf) F (%> 70 u 1 / / / Rf> 2 4 6 TUBULAR FUEL ELEMENT DIAMETER FIGURE 3. 10. 3 8 (CM) 1000 48 the power requirements listed in Table 2. 3. 3. 1, tubular fuel elements would be used, each 4 and with an E of 1000 watts. cm it in was decided diameter, 10 that five cm long 49 REFERENCES 3. 1 3.2 Farace, J. P., "Experimental Cobalt-60 Heat Source Capsules," Savannah River Laboratory, DP-1 145. Corliss, W.R. and Harvey, Englewood 3.3 3.4 Cliffs: D. G. , Radioisotopic Prentice Hall, Inc., Hurwitz Jr. H. and Roe, G. M. 'Gamma Ray Storm, M. L. Absorption Distributions for Plane, Spherical and Cylindrical Geometries, " General Electric Company, Knolls Atomic Power Laboratory, KAPL-783. , , , , Berger, M.J. and Raso, D. J. "Monte Carlo Calculations of Backscattering, " Radiation Research 12 20-37, 1960. , Gamma Ray 3. 5 3. 6 Power Generation, 1964."" , "High Temperature Multi-Foil Thermal Insulation, Paquin, M. L. Thermo Electron Corp. " , Carvalho, J. and Dunlay, J. B. , "Quarterly Progress Report of Vacuum Foil-Type Insulation for Radioisotope Power Systems, " Thermo Electron Corp. TE Report Research and Development of , No. 4059-109-69, January 20, 1969. 50 CHAPTER 4 SHIELDING 4. 1 GENERAL REMARKS Radiosotope fueled generators intended for terrestrial use generally require considerable shielding since personnel in contact with them even though they may be may inadvertently installed in come remote locations. The Interstate Commerce Commission's shipping regulations for radioactive materials were therefore selected as the design criteria which the shielding for this power supply must satisfy. tions specify a and 10 maximum dose rate of 200 mr/hr mr/hr one meter from The members in shielding calculations. surface at the shield the shield surface. self- shielding of the fuel and the other structural These regula- element structure, the fuel itself of the generator is not usually included (Reference 4. 1) However in this design, these self shielding effects are significant and the self shielding of the fuel element and the tungsten emitter heat source are included in the shielding calculations. The shielding calculations are performed assuming gammas that two 1. are emitted for every disintegration of a cobalt-60 atom. 25 Mev The bremsstrahlung radiation resulting from the slowing down of the beta particles is mated as line 4. 2 neglected. The geometry sources located at the elements is approxi- center of each fuel element. METHOD FOR CALCULATION OF SHIELD THICKNESS The geometrical arrangement is of the fuel shown 4.2.1. in Figure 4. 2. 1. of the gamma The dose rate D source and the shielding at point P^ is given by equation 51 Ve- -£. I LINE SOURCE T ^P L / / /' / / / / / / / / / e-2 T . 7/e 1 GEOMETRY USED IN THE CALCULATION OF SHIELDING FIGURE 4. 2. 1 l 52 B (1-f) S D= L aR4Tf The dose rate D D at point P]_ is a is the emitted gamma , - F(0 2 , J 4. 2. 2, (4. 2. 2) b)J 4. 2), f is the radiation absorbed in the fuel (Figure 3.6.1), given in reference is it R photons/cm-sec. in The distance is the flux to 4. 3 a and the angles Q\ and b is defined in equation n b= (4.2.1) b) dose build up factor. (Reference conversion factor; energy. F(0 2 given by equation R 4Ty source strength line b) + [FO^b) - where B F(0 Xj l fraction of Sl the dose rate as a function of G2 is are shown gamma in figure 4.2.1. 4. 2. 3. /A* £>*, (4.2.3) 1 i=l tj is the P, and W thickness of the shielding material between the source and point i is the macroscopic cross section for gamma attenuation for the shield material. -9 e' | b sec 9" d0» (4. 2.4) '0 F(9b) is plotted as a function of b for various values of 9 in reference 4.3. All of the quantities in equation 4. 2. 1 and 4. 2. 2 are known with the exception of b and F(0b). The equations are thus solved for JFOjb) + F(9 2 b)l or from [F^b) - F(9 2 bJ] and the graphs in reference 4. 3. the value of b is determined 53 4. 3 SHIELD DESIGN The components Each fuel elements. has an E of the fuel of 1000 watts. system which must be shielded are the element cm is 10 The design long, 4 calls for cm them in diameter and be arranged to symetrically within the tungsten emitter heat source as shown 4. 3. 1. They are located exterior to the five vacuum housing it Figure and, with the exception of one end, are completely surrounded by the tungsten emitter heat source. It thus necessary to contain all components which are is located within the vacuum housing housing circular cylinder 23 is a right inside the shield. cm in The vacuum diameter and 20 cm in height. Using the line source approximation and the method of calculation described in section 4. 2, it was found that a value of b of 15. 5 on the sides of the cylinder and 15 on the ends was required to reduce the dose rate to the desired levels. The ends of the shield will which are intended to each be penetrated by five solid rods remove heat from the fuel rods on one end and the thermionic converter collector on the other end. 4. 3 from Data from Reference indicates that irregularities such as small ducts and iron stiffners in the shield cause the flux in the vicinity of the irregularity to increase by a factor of 5 to 10 over its value at other areas of the shield. of b for the ends of the shield was therefore increased decrease the flux by an additional factor an effect similar Table 4. 3. 1 to the It to 17. 5 in order to since the rods will have above mentioned irregularities. lists the values of b before and after they were modified to account for the self- shielding source. of 10, The value provided by the tungsten emitter heat also lists the thicknesses of lead and depleted uranium which would be needed to provide the modified value of b. 54 EMITTER HEAT SOURCE T CAVITY TUN FIGURE 4. 3. 1 55 - CO B CJ s CJ o CO OD CO to B B CJ m o I— co £o i 5^' tf H P M CO a o s o bjo Qw <j LO iH ^ J CJ LO Ci — I— i CO CO i II " SELF ' O •— O i CO C\l .—1 »— LDIN CO £> 1—1 CXI 02 CO CO* W i— T— . Q <# JD CO i— W CO PQ < E-f i Q SELF- LDING in LO LO in i— NO I— HIE H JQ co ti Q Q S Eh < O o 1 J W P W Q Fh CO _ « H H tf H > O U 56 The modified value of b for the converter end the fuel end because there is an additional 4 cm is less than that on of tungsten between the fuel and the shield on that end. Lead was selected as the uranium would have provided shielding" material a lighter and even though the depleted more compact shield. The relatively low cost and ease with which the lead shield could be fabricated were the basis for this decision. Due power to its low melting point, the lead was not compatible with the flattening concept incorporated in this design and described in Chapter Thus 5. of the shield. it was decided to use depleted uranium for the fuel end Since wrought depleted uranium has been successfully used as the shielding materia] for radioisotopic power generators SNAP - 7 series, no problem The low melting point 4. 1) tungsten bars lead. A is anticipated with its fabrication. (Reference of the lead also necessitated insulating the which penetrate the converter end of the shield, from the Aluminum oxide was selected as the insulating material. cross section of the shield configuration The shield is in the form is between an inner and outer casing of stainless made of shown of a right circular cylinder. and sides of the shield will be composed of lead. shield will be steel. The total shield 4. 3. 2. The converter end The will be cast fuel end of the The lead surface wrought depleted uranium. streaming between the surfaces. Figure in The lead the lead-uranium interface will be offset to prevent 1040 kg. in the gamma weight is radiation at from approximately 57 URANIUM TOP PLUG STAINLESS STEEL CASINGS 14. 5 cm 12. 5 CROSS SECTION OF SHIELDED ASSEMBLY FIGURE 4. 3. 2 cm 58 REFERENCES 4.1 Corliss, W.R. and Harvey, D.G., Radioisotopic Power Generation, Englewood Cliffs: Prentice Hall, 19M"! 4. 2 Nuclear Engineering Handbook, Etherington, H. McGraw Hill, 1958^ New 4. 3 Reactor Shielding Design Manual Rockwell, T. Van No strand Co., 1956. Princeton: , , , York: 59 CHAPTER 5 POWER CONDITIONING 5. 1 GENERAL REMARKS The term power conditioning includes power transformation and regulation. These topics have been mentioned power of flattening has been discussed in Chapter 2. mechanism flattening The necessity for was decided There it power input. power to in The design preceding chapters and are tied together the flattening, voltage is in this chapter. treated in detail. operate the thermionic converters with a constant This means that the emitter heat source must provide the thermionic emitters with from the decay a constant heat flux as the of the cobalt- 60 fuel characteristic half life of energy available decreases exponentially with a 25 years. 5. The thermionic converters can be supplied with a constant power input in two ways. The first method, mentioned in Chapter 2 and the only one to which reference was found in the literature, allows all the energy from the fuel to be deposited in the emitter heat source. variable heat transfer path is provided to emitter heat source to the surroundings. A shunt the excess heat from the As explained none of the systems which have been designed were practical for ' to in Chapter 2, accomplish this objective this design application. The second approach, the one used in this design, is to provide a constant energy input to the emitter heat source. the schematic design of a mechanism which is Figure 5. 1. 1 shows designed to provide the emitter heat source with a constant power input. 60 RADIATOR FINS DRIVE MOTOR GEAR TRAIN RELAY STAINLESS STEEL CASING POSITIONING /// PLATE DRIVE ROD in »— < K U H w H H <J ft o ER HEAT SOURCE ROD CAVITY O i— 61 OPERATING PRINCIPLE OF THE POWER FLATTENING MECHANISM 5. 2 vacuum housing, Since the fuel elements are located outside of the they can be partially withdrawn As heat source. will be from the fuel rod is from the fuel rod cavity in the emitter withdrawn from the surrounded by the uranium shield. Most fuel rod cavity of the gamma it radiation the portion of the fuel rod outside of the emitter heat source will be absorbed by the uranium shield. It is thus possible to vary the energy input to the emitter heat source by varying the position of the fuel rod. A maximum Most shield. It uranium of 1200 watts of heat will be deposited in the of the heat will be deposited in the vicinity of the fuel rods. will be conducted to the surface of the uranium with tempera- a small ture drop since the uranium provides a path of high thermal conductivity due cross section. to its large will allow it to The high melting point of the operate at a temperature high enough to allow uranium be to it cooled by natural convection. FUEL ROD POSITIONING MECHANISM 5. 3 The Each fuel rod positioning of the five mechanism is shown is Figure 5. 1. 1. copper rods used to conduct heat generated within the fuel rods to the cooling radiators penetrates the through and in uranium attached to a movable positioning plate. passes shield, The rod is then finned to provide sufficient heat transfer area to maintain the fuel rod at a low temperature. The movable positioning plate and It is is is circular in shape, 10 cm in radius, attached to each of the five fuel rods as shown in Figure positioned by a threaded drive rod located at drive rod is its center. turned the positioning plate travels up or down on 5. 1. 1. As it. the There 62 are two guide rods which prevent the positioning plate from exerting a This torque could cause the fuel rods torque on the fuel rods. to bind as they were being moved. Although the temperature of the fuel rod the emitter heat source, would The bellows seals shown air. fuel it rods can be maintained fuel rods to be which is is if exposed to are employed so that the These an inert atmosphere. vacuum system valves and allow moved without disturbing The drive rod 5. 1. 1 vacuum or seals are similar to those used on considerably lower than oxidize quite rapidly Figure in in a still is the the actual seal. driven through a gear train by an electric motor located on the centerline of the assembly as shown in Figure 5. 1. 1. 5. is 4 INITIAL FUEL ROD POSITION The rods are initially positioned so that the output of the system fuel 500 watts. position since gamma It would be very difficult it would be difficult radiation emitted from to to calculate the exact initial determine exactly how much of the the portion of the fuel located outside of the tungsten emitter heat source eventually reaches the heat source. However, Figure 3.7.2 indicates that most of the gamma energy is absorbed within the first three mean free paths of the material through which it is passing. Therefore a good approximation position can be obtained by assuming that none of the to the initial gamma radiation emitted from the fuel outside of the tungsten emitter heat source reaches it. The error caused by slight this approximation can be corrected by a adjustment of the fuel rod position once the power supply operating. is 63 From Table 2. 3. 3. 2 it is seen that each of the five thermionic The converters requires 510 watts of thermal power. an ET of 1000 watts, that each fuel cm element supplies Therefore, of length. 6% and are an n F of 75. 6. 75 10 cm cm of the fuel rod thermal energy per must be inserted The remaining the fuel rod cavity in the emitter heat source. of fuel rod will be initially positioned in the This means long. 75. 6 watts of useful elements have fuel 3. 25 uranium shield above into cm the emitter and will gradually be lowered into the fuel rod cavity as the fuel This procedure will allow the energy input decays. source 5. 5 to be maintained at a emitter heat to the constant level. OPERATION OF THE FUEL POSITIONING MECHANISM If the thermionic converter power output is allowed to vary 1% the power input can vary 4. 22%. This means that the energy input to each thermionic converter can vary by 23. With this 2 in watts which mind the When as follows. 5% since the is the thermionic converter efficiency is equivalent to fuel rod positioning 0. 3 cm of fuel rod length. mechanism power output drops below 500 watts circuit will close a relay and activate the drive will operate a sensing motor which will drive the gear train and in turn start lowering the fuel into the fuel rod cavity. One element of the gear train revolution during the time which time it it is geared so that it completes one takes to lower the fuel rod mechanically opens the relay and shuts 0. 3 cm, at off the drive motor. This action will be repeated anytime the power output drops below 500 watts. The frequency with which the determined. The fraction fuel will be repositioned can be easily of fuel which has decaved f^, is given by 64 equation 5. 5. 1, f where A F = - 1 e" At (5. 5. 1) = = 0. 132 yrs fuel half life and is the t For f F elapsed time in years. = 0. 0454, equation fuel will be repositioned time. If a fuel can be is gives t as once every 4 months smaller variation moved 5. 5. 1 in power output 0. if it is 35 years; is moved thus the 0. 3 cm each required or desired the a shorter distance at a shorter time interval. This accomplished simply by modifying the timing of the gear train element which opens the drive motor relay. VOLTAGE TRANSFORMATION AND REGULATION 5. 6 The series is 5 volt output of the five thermionic converters operating in transformed to 28 volts as explained in Chapter 2. by a current drive DC-DC The DC-DC converter output the load through a shunt type voltage regulator. will maintain a constant voltage output is converter coupled to The voltage regulator regardless of slight variations in the thermionic converter output caused by the non continuous form of power flattening. The voltage regulator with a constant load; point even though the vary. will also provide the this will allow them to thermionic converters operate at a constant power power required by the equipment they supply may 65 CHAPTER 6 ADDITIONAL DESIGN CONSIDERATIONS 6. 1 GENERAL REMARKS chapter heat loss through the insulation and structural sup- In this port members of the emitter heat the electrical leads are treated.. power is source are discussed. Due to The intrinsic efficiency. at to these heat losses a higher input required for the same power output. converter effectively operates Losses due Thus an efficiency which the thermionic is lower than the effect of these heat losses on the fuel design and the power flattening mechanism is element also discussed. Several additional problems related to the electrical insulation of the thermionic converters and radiator design, which are peculiar to this design are discussed. These problems are not treated as extensive- element optimization or the power flattening design. ly as the fuel ever, they were persued until it was determined How- that a practical solution did exist and that they would not prevent construction of a practical thermionic power supply based on this design. 6. 2 LEAD LOSSES Since the thermionic converters in this power supply are connected in series, the emitter of one converter must be connected to the collector of another converter. The heat conducted through the lead from the emit- ter to the collector is designated Q T . This heat loss by the emitter one of two contributing factors to the lead losses. buting factor losses which is to is is the Joulean heating in the lead, cause the thermionic converter lower than its intrinsic efficiency. to Qj. is The second contri- The operate at effect of these an efficiency 66 The optimum design to is not to minimize the sum of Or and Q T but have Qj where (6.2.1) ^.(Q L + Qj) = is the intrinsic efficiency. tl The lead losses will depend on the lead material, the lead length to lead area rates and the temperature difference between the emitter and collector. In this design T E 2000 °K and T = chosen for the lead material due found that equation was ratio means From was Figure cm 2.2. 1. 3 the watts/cm 9. 2 order in Joulean heating = to when 2 , was It the lead length to lead area 42. 5 watts and Q =12 watts, which J must be supplied emitter output power density to the emitter. at 1. volt is thus the area of each emitter must be increased provide the additional 12 watts disipated as in the lead. INSULATION AND SUPPORT OF THE EMITTER HEAT SOURCE The emitter heat source It E Tungsten was 1000 °K. temperature requirements. satisfied that an additional 54. 5 watts 1. 3 6. 3 1 The losses are Q 30. found to be by 6. 2. to = C is 21 cm in diameter, 14 cm is a right in height circular cylinder of tungsten. and weighs 85 kg. The thermal insulation for the emitter heat source consists of 80 layers of multi-foil insulation similar to that used in the fuel elements. The insulation source surface is 0. 9 cm thick and reduces the heat loss to 110 watts. This insulation is from the heat placed inside of the vacuum housing. If the weight of the emitter heat source foil insulation, was supported by the multi- the foils would be forced together and their insulating properties would be seriously degraded. Therefore pins of zirconium oxide are inserted in holes drilled through the insulation in order to 67 support the weight that would otherwise rest on the insulation. Con- duction by the pins constitutes only a fraction of the total thermal losses associated with the holes in the insulation. The remainder of the heat loss is associated with the thermal short circuiting of the in- sulation surrounding the pin. (Reference 6. 1) The exact value of the heat loss due to the pins would have to be determined experimentally, but Reference 6. indicates that for small pins the losses will be on 1 the order of 4 watts per pin. In this design 40 watts allowed for these is pin losses. Figure 6. 3. The pins on the 1 fuel end of the heat by disc springs. in which the pins will be mounted. source are held tightly in position This mounting technique allows for thermal expansion of the tungsten and By inserting shows the manner keeps the emitter end of the heat source the pins into recesses in the tungsten, it is in position. possible to prevent any sideways motion of the heat source. Another heat loss, that due to conduction through the structure of the thermionic converter, has not been calculated since sitive to the materials converter casing. A used in it is very sen- and the configuration of the thermionic value of 40 watts per converter is used as an estimate of this heat loss. 6.4 MODIFICATIONS REQUIRED TO FUEL ELEMENT DESIGN The additional heat loss from the emitter heat source due to lead losses and insulation losses totals 622 watts. Thus in order to produce 560 watts of electric power 3162 watts of thermal power must be supplied emitter heat source instead of the to the quired if 2 540 watts that would be re- the actual converter operated at the intrinsic efficiency. The initial fuel loading, F for the design life of t years is given by equation p- 6. 4. 1. FT where Pt = 3 is the years, F ET (6.4.1) required thermal power input. is found to be 6250 watts. of the five fuel rods ual = must be increased For P^ =3162 and Therefore the length of each to 12. 5 cm giving them an of 1250 watts. The increased input power requirement makes initially position the fuel rod necessary it cm so that an additional 1.65 of it contained within the fuel rod cavity in the emitter heat source. 8. 4 cm to are Thus of the fuel rod will be initially inserted into the fuel rod cavity. Other than a slight increase in the frequency with which the fuel rod repositioned, the increase in required input power will cant effect on the design or operation of the power flattening 6. 5 individ- have no is signifi- mechanism. ELECTRICAL INSULATION OF EMITTER AND COLLECTOR Since the five thermionic converters mounted on the emitter heat source are electrically connected in series, it is necessary to in- sure that the only electrical conduction paths between them are the leads connecting the emitters and collectors. cally insulated insulated The emitters must be from the emitter heat source and from the vacuum housing. Figure 6. 5. the collectors 1 electri- must be shows where the insulation will be placed in order to accomplish this. The material used for the electrical insulation ably good thermal conductivity. must have a reason- Beryllium oxide was selected as the insulating material because of its relatively high thermal conductivity and high electrical resistivity. vacuum atmosphere to Beryllium oxide temperatures of at least is stable in an air or 2000 °C. (Reference 6. 2) 69 URANIUM SHIELD •NGSTEN MITTER LEAD SHIELD MOLYBDENUM COLLECTOR TUNGSTEN HEAT TRANSFER ROD A1 2°3, INSULATION THERMIONIC CONVERTER CONFIGURATION FIGURE 6. 5. 1 70 6. 6 RADIATOR DESIGN The radiator used to dissipate the heat deposited converter at the The collector must be designed to maintain the collector at 1000°K. temperature drop rod conducting the heat from the collector in the minimized the radiator should be in order to allow the radiator to op- The higher the radiator erate at the highest possible temperature. temperature the smaller its The heat transfer rod end and copper of the rod as the operating 6. 5. 1. and the rod 270 C. is 4 If copper cm will be tion are the The copper will be used for as much order in is used once the temperature diameter the temperature drop in In this modes of tungsten at the collector temperature allows The collector radiator ature of 460 C. composed will therefore have a minimize to The composite heat transfer rod the temperature drop. Figure size for a given heat transfer rate. radiator end. at the to is in below 550°C is in shown it will be maximum temper- temperature range radiation and natural convec- of heat transfer temperature distribution in the which must be considered. radiator is difficult to Since the predict, the final radiator design must be determined experimentally. The design of the radiators associated with the fuel less critical since perature but only is not it to necessary to maintain them insure that they remain the temperature of the fuel. mechanism rods and fuel radiator are shown remove a maximum of 286 watts in Figure from each much at a specific to tem- conduct heat from same rods used by to position the fuel rods. is temperature well below The copper rods used the fuel rods to the fuel radiators are the flattening at a rods the power The heat conduction 5. 1. 1. These rods must fuel element. The rods 71 are 20 cm long and have an average diameter of ature drop along the rod will therefore be 150^. on the fuel rod is to 3. 5 If be maintained below 6009^, the radiator temperature will be 150 C. cm. The temper- the hottest point maximum fuel 72 REFERENCES 6. 1 Paquin, M.J-.., "High Temperature Multi-Foil Thermal Insulation," Thermo Electron Corp. Waltham, Mass. , 6. 2 Hove, J. E. and Riley, W. C. Ceramics for Advanced Technologies New York: John Wiley and Sons, Inc. 1965. , , , 73 CHAPTER 7 SUMMARY AND CONCLUSIONS 7. 1 DESIGN SUMMARY The final power supply design is summarized in Table The rational for this design has been given in the preceding chapters. final design uses five thermionic converters operating point and a power DC-DC decrease power Although the intrinsic efficiency of the thermionic is 22%, the overall system efficiency is only 9. 7%. This due to lead losses, heat lost from the emitter in efficiency is heat source, fuel rod and 7.2 at a fixed regulated converter to provide 500 watts of electric at 28 volts. converters used The 7. 1. 1. DC-DC converter inefficiencies. CONCLUSIONS This design shows that it is feasible to build a power supply fueled with cobalt- 60. system incorporated power supply The to fuel in the In addition, the practical thermionic power flattening design enables the operational lifetime of the be comparable to the half element design shows that life of it is cobalt-60. possible to obtain significant savings by using a tubular fuel element instead of a solid fuel rod. In this case there an Erp of 1000 watts. a 10% increase in the fuel element efficiency, for is Greater savings can be realized for larger values of Erp. The major advantage of the cobalt-60 At present strontium-90 is the most popular fuel is its relatively fuel low cost. used for terrestrial radioisotope power supplies with operating periods between one and five years. in this If it were used design and if in a fuel conjunction with the thermionic converters used element efficiency of 95% were realized, 4950 74 watts of thermal power would have to be provided by the strontium fuel. At a cost of $77 per thermal watt (Reference 7. 1) the total fuel cost would be $380, 000, as opposed to a cost of $37, 500 for the cobalt-60 fuel. price differential of $292, 500 is a This strong incentive to use cobalt-60 fuel. TABLE 7.1.1 FINAL DESIGN SUMMARY I THERMIONIC CONVERTERS High Pressure Cesium Diode Type Number of Converters Emitter Material Tungsten Emitter Temperature 2000° Collector Material Molybdenum Collector Temperature 1000° Interelectrode Spacing 7 Cesium Reservoir Internal Adsorption Cesium Reservoir Temp. 610 Output Voltage 1. volts Output Power Density 8. 8 watts/cm Intrinsic Efficiency 22% Total Power Generated Rea uired Thermal Power x Total Emitter Area II 5 K K mils o K 620 watts Input 2820 watts 70. 5 cm 2 FUEL ELEMENTS Fuel Cobalt- 60 Form Metal Wafers Specific Activity 400 curies/g Fuel Number Type of Fuel of Fuel Rods Element 5 Tubular Fuel Rod Lenght 12.5 Fuel Rod Diameter 4 cm cm 76 TABLE III 7. 1.1 (CONT. ) ADDITIONAL HEAT LOSSES From Emitter Heat Source Through Mult -Foil Insulation 110 watts Through ZK>2 Pins 40 watts From Thermionic Converters Lead Losses 272 watts Structural Support Losses 200 watts TOTAL IV V 622 watts BIOLOGICAL SHIELD Material Lead and Depleted Uranium Total Weight 1040 kg POWER CONDITIONING Power Flattening Movable Fuel Power - Constant Input Voltage Converter VI Type DC-DC Voltage Input 5 volts Voltage Output 28 volts Voltage Regulation Dissipative Shunt Efficiency 89% Current Drive POWER SUPPLY Power Output 500 watts Operational Lifetime 3 System Weight 1200 kg Overall Efficiency 9. years 7% 77 REFERENCES 7.1 W. R. and Harvey, D. G. Englewood Cliffs: Prentice Hall, Corliss, , Radioisotopic Inc., 1964. Power Generation, 78 BIBLIOGRAPHY Berger, M.J. and Raso, D.J. "Monte Carlo Calculations of Gamma Ray Backscattering. " Radiation Research 12 20-37. 1960. . Carvalho, J. and Dunlay, J. B. "Quarterly Progress Report of Research and Development of Vacuum Foil Type Insulation for Radioisotope Power Systems. " Thermo Electron Corp. Report No. 4059-109-69. January 1969. 20, D. G. Radioisotopic Power Generation. Prentice Hall, Inc. 1964. W.R. and Harvey, Corliss, Englewood Cliffs: J. B. "Description of a Cobalt-60 Fueled Thermionic Generator Experiment. " Conference Record of the Thermionic Conversion Specialist Conference. October, 1967. Dunlay, Etherington, H. Nuclear Engineerin g Handbook. Hill. New York: McGraw 1958. Farace, J. P. "Experimental Cobalt-60 Heat Source Capsules. River Laboratory. DP- 1145. " Savannah Harbaugh, W. E. and Basiulis, A. "The Development of a High-Temperature Reservoir for Automatic Control of Cesium Pressure. " Conferen ce Record of the Thermionic Conversion Specialist Conference November, 1966. . Hilbom, H. S. "Savannah River Laboratory Isotopic Power and Heat Sources, Part I Co-60. " Quarterly Progress Report July September, 1967. DP-1129-1. . Hove, J. E. and Riley, New W. C. Ceramics York: John Wiley and Sons, for Inc. Ad vanc ed Techn ologies . T965. "Energy Source - Low Voltage Conversion System. " Procedings of the 19th An nual Power Sources Conference. 1965. Lingle, J. T. Lingle, J. T. Annual "Low Input Voltage Conversion." Procedings Pow er Sources Conference. May, 1964. of the 18th "Thermionic Low Voltage Converter Regulator Systems. Conference Record of the Thermionic Conversion Specialist Conference. November, 1966. Lingle, J. T. Paquin, M. L. "High Temperature Multi-Foil Thermal Insulation. Thermo Electron Corp. " " Rockwell, T. Reactor Shielding Design Manual. Princeton: Van Nostrand Company! 1956. 79 BIBLIOGRAPHY (cent.) Rush, R. E. and Belofsky, H. "Power Flattening Studies for Radioisotope Thermoelectric Generators." General Instruments Corp. NYO-9783. " 1963. Hurwitz Jr. H. and Roe, G. M. "Gamma Ray Absorption Distributions for Plane, Spherical and Cylindrical Geometries. " General Electric Company, Knolls Atomic Power Laboratory. Storm, M. L. , KAPL-783 , . "A Unified Theoretical Description of Thermionic Converter Performance Characteristics. " Journal of Applied Physics, vol. 39. number 5. April, 1968. Wilkins, D.R. Wilkins, D.R. "An Improved Theoretical Description of Thermionic Converter Performance Characteristics. " Procedings: 27th Annual Physical Electronics Conference. Cambridge, Mass. March, 1967. ibk.