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EXCITATION AND IONIZATION OF GASES BY FISSION FRAGMENTS By ROY ALAN WALTERS A DI:.ERi'AT:ON PRESENTED TO THP GRADUATE COUNCIL OF THE 'UNVERSI't'l OF FIORIDA IN PARTIAL FULPILM[INT 01 TIhL : ;Cr 1 F'.L NTS FOR THE DEGREE OF DOCTOR OF PHBLOSOP, I INI'VL'PSITY OF FLORIDA 197 9 To my father, Harry Walters, who was, in my eyes, the greatest of engineers and the greatest of men. ACKNOWLEDGMENTS The author would like to express his deepest appreciation and gratitude to Dr. Richard T. Schneider, the chairman of his supervisory committee, for his guidance and support in this research, and for the faith and friendship he showed toward the author throughout this academic endeavor. Sincere thanks are extended to the other members of the supervisory committee, Drs. Hugh D. Campbell, Kwan Chen, George R. Dalton, and William H. Ellis. The author also wishes to thank Dr. Edward Carroll for his ideas and encouragement on the LMFBR detector studies. Special note should be made of the valuable contributions of Mr. Ernest Whitman, who aided the author with the design and construc tion of the vacuum chamber, and of Mr. Richard Paternoster, who developed the computer analysis and plotting programs. Thanks are also extended to Mr. George Wheeler for his valuable assistance in the construction of equipment and its operation. The author acknowledges the technical assistance provided by Mr. Henry Gogun and the other members of the UFTR crew. Special thanks are extended to the author's wife and son for their help in the production of this paper and for their patience and support through the years this endeavor has taken to complete. The author will be forever indebted to his father, the late Harry Walters, for his unfailing faith and encouragement, and most especially, for his aid in the actual production of this manuscript. Many of the diagrams that are a part of this dissertation are products of his highly skilled hands. Appreciation is expressed to Mrs. Edna Larrick for typing the final draft of this manuscript. This research was supported by NSA Grant NGL10005089. TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . LIST OF TABLES . . . LIST OF FIGURES . . . ABSTRACT . . . . CHAPTER 1 INTRODUCTION . . . 1.1 The NuclearPumped Laser . . 1.2 Previous Studies of Fission FragmentProduced Plasmas . . 1.3 Glow Discharge Irradiation and Fission Fragment Interaction Experiments . . 2 THEORETICAL CONSIDERATIONS . . 2.1 Energy Deposition by Fission Fragments and Other Particles . . 2.2 Energy Deposition by the Reaction He3(n,p)T in a Glow Discharge . . 2.3 Description of a Fission FragmentProduced Plasma 3 PLASMA RESEARCH APPARATUS . . 3.1 Introduction . . . 3.2 Primary System . . . 3.2.1 Plasma Region . . 3.2.2 Vacuum Chamber; Optical, Gas and Electrical Feeds .. 3.3 Uranium Coatings . . 3.3.1 Coating Requirements . 3.3.2 Coating Thickness . 3.3.3 Review of Methods and Chemistry . 3.3.4 Chemical Procedures . 3.3.5 Mechanical Coating Procedure . iii viii . ix . xiii . 1 . 1 S. 9 . 11 . 14 14 S 37 40 S 49 49 S 50 . 51 . 55 TABLE OF CONTENTS (Continued) CHAPTER Page 3 (Continued) 3.4 Support Systems . . 65 3.4.1 Reactor: Neutron Flux and Gamma Dose .. 65 3.4.2 Electrical Systems . ... 67 3.4.3 Gas Filling Systems . ... 68 3.4.4 Shielding . . 70 3.4.5 Safety . .... 71 3.5 Data Acquisition Systems . .. 75 4 ANALYSIS OF "INREACTOR" PLASMAS: FISSION FRAGMENT GENERATED AND GLOW DISCHARGE . .. 77 4.1 Experimental Procedure and Data Analysis: Fission Fragment Interactions . .. 78 4.2 Helium . . .. 86 4.2.1 Helium Kinetics and Spectral Analysis 88 4.2.2 Line Intensity and Excited State Density 92 4.2.3 Boltzmann Plot Analysis . ... .102 4.2.4 Field Amplification of Line Intensities 110 4.3 Argon Excitation by Fission Fragments ... 121 4.3.1 Argon Kinetics and Spectral Analysis .... .122 4.3.2 Line Intensity and Excited State Density 131 4.3.3 Boltzmann Plot Analysis .. .. 135 4.3.4 Field Amplification . ... 140 4.4 CF Fission Fragment Interactions .. .153 4.5 Glow Discharge Irradiations . .. 160 4.5.1 Experimental Procedures . .. 161 4.5.2 The Glow Discharge . .. 161 4.5.3 General Reactor Mixed Radiation Effects on the Glow Discharge ... .. 164 4.5.4 Volume Deposition . ... 171 4.5.5 Cathode Deposition . .... .174 5 APPLICATIONS OF FISSION FRAGMENTPRODUCED PLASMAS 178 5.1 The NuclearPumped Laser. . 179 5.2 A Neutron Detector for the Liquid Metal Fast Breeder Reactor .. . 187 5.2.1 Diagnostic and Power Supply Systems 190 5.2.2 Neutron Detector Experimental Results ..... 192 5.2.3 Data Projections and Realistic Chamber Design 198 TABLE OF CONTENTS (Continued) CONCLUSIONS . . . CHAPTER 6 APPENDIX I II III IV V BIBLIOGRAPHY . . . BIOGRAPHICAL SKETCH . . . Page 201 . 205 . 223 . 231 . 277 S. 295 302 308 PRESSURE DEPENDENCE OF RELATIVE LINE INTENSITIES AND EXCITED STATE DENSITIES HELIUM . BOLTZMANN TEMPERATURE PLOTS HELIUM . PRESSURE DEPENDENCE OF RELATIVE LINE INTENSITIES AND EXCITED STATE DENSITIES ARGON . BOLTZMANN TEMPERATURE PLOTS ARGON . FIELD AMPLIFICATION OF ARGON SPECTRAL EMISSION . LIST OF TABLES Table Page 41 HELIUM DATA .............. ... 116 42 IDENTIFIED CASCADES OF ARGON II . ... 134 43 ARGON DATA ............... .* .......... 145 44 CF FISSION FRAGMENT IRRADIATIONS: BAND PEAKS OBSERVED AT 760 TORR . .. 160 viii LIST OF FIGURES Geometry . . . Range of Fission Fragments in Helium and Argon . Deposition of Energy into Helium by Fission Fragments, 11 n = 3.8 10 . . cm sec 24 Deposition of Energy into Argon by Fission Fragments, = 3.8 X 10 2 2 . o cm sec 25 Energy Deposition by Fission Fragments in Argon and Helium A Fixed Cavity Reactor Mounting . . Chamber Experimental Sections . Chamber Detail Reactor Region . University of Florida Training Reactor . K as a Function of Density . The Kinetic Energy of Fission Fragments as a Function of Mass Number [38] ... . Chemical Procedures Coating Solution . Mechanical Procedures for Coating . Distribution of Thermal Neutron Flux along Experimental Chamber . General Gas Discharge IV Characteristic Chamber Mounting and Shielding Cave . Helium Spectrum . . . Helium Spectrum . . . Figure 21 22 23 Page 21 29 33 . . 36 . 52 . 53 . 54 . 56 . 58 31 32 33 34 35 36 37 38 39 310 311 41 '42 . 66 . 69 . 72 I I I 0 . LIST OF FIGURES (Continued) Figure 43 Helium Spectrum . . . 44 Helium Spectrum . . . 45 Helium Spectrum . . . 46 Helium Excited States and Transitions . 47 Optically Viewed Energy Deposition in Helium and Argon as a Function of Pressure . 48 Helium Intensity and Energy Deposition as a Function of Pressure . . 49 Relative Excited State Population Density as a Function of Pressure . . 410 Line Intensity versus Pressure Helium . 411 Boltzmann Plot Helium Glow Discharge . 412 Boltzmann Plot Fission Fragment Excited Helium . 413 Pressure Dependence of the Boltzmann Plot Correlation Coefficients Helium . . 414 Boltzmann Temperature as a Function of Pressure . 415 CurrentVoltage Characteristics of Fission Fragment Excited Helium . . 416 Line Amplification and Current as a Function of Applied Voltage 30.5 cm Long Helium Cavity . 417 Electron Energy Distribution Fission Fragment Excited Helium . . . 418 Argon Spectrum . . . 419 Argon Spectrum . . . 420 Argon Spectrum . . . 421 Argon Spectrum . . . 422 Argon Spectrum . . . 423 Argon Spectrum . . . Page . 81 . 82 . 83 . 87 . 95 . 97 . 98 . 99 . 104 . 105 . 107 . 108 . 112 . 114 . 120 S. 124 S. 125 S. 126 S. 127 S 128 129 LIST OF FIGURES (Continued) Figure Page 424 Intensity and Calculated Deposition (Viewed) as a Function of Pressure . ... 133 425 Boltzmann Temperature Plot 600 torr Argon I .. 137 426 Boltzmann Plot Argon II, 600 torr . ... 138 427 Argon Temperature and Correlation Coefficient versus Pressure . .... .. 139 428 Amplification and Current versus Applied Voltage  150 torr Argon . . .. .... 141 E 429 Amplification Coefficient versus , Argon ... 143 430 Electron Density and Temperature versus Pressure Argon 148 431 Ion Pair Generation Rate as a Function of Pressure Argon . . .. 149 432 Electron Energy Distribution Argon . .. 151 433 Electron Energy Distribution Argon . .. 152 o 0 434 Glow Discharge through 5.5 torr CF4 2000 A 5087 A 155 435 Band Peak Intensity of 100 torr CF4 as a Function of Time 156 436 Spectrum of Fission Fragment Excited CF4, o o 4 760 torr 2000 A 5087 A . .. 158 437 Spectrum of Fission Fragment Excited CF4, o 0 4 760 torr 2646 A 3280 A . ... 159 3 438 Glow Discharge IV Characteristics for He C02N2, 8:1:1, 10 torr . . .. 165 439 IV Characteristics for Hollow Cathode Glow Discharges 167 440 IV Characteristics, 3.3 torr Glow Discharge, Flat Cathode . . ... 168 441 Voltage Decay, Glow Discharge, for Reactor Shutdown  Constant I, 20 ma . .... 169 442 Voltage Decay, Glow Discharge, for Reactor Shutdown  Hollow Cathode . . ... .. 170 LIST OF FIGURES (Continued) Figure 51 52 53 54 55 56 57 58 Page . 181 . 184 . 186 . 191 . 194 . 195 . 196 . 197 Nuclear Pumped Laser . . NuclearPumped Laser Output . . Cavity Design . . LMFBR Neutron Detector Signal Flow . . Amplification of Argon Line Intensity versus Reactor Power . . . Ar I 6965 A Filtered Output Neutron Detector . Total Spectrum Signal Neutron Detector . PP Voltage versus Reactor Power Neutron Detector Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy EXCITATION AND IONIZATION OF GASES BY FISSION FRAGMENTS By Roy Alan Walters June, 1973 Chairman: Dr. Richard T. Schneider Major Department: Nuclear Engineering Sciences The excitation and ionization produced by fission fragments was investigated to identify basic mechanisms that could be applied to direct nuclear pumping or enhancement of gas lasers. A cylindrical U235 foil and its axial electrodes were placed in a vacuum chamber which was capable of transmission of fluorescence to o 0 its exterior from 2000 A to 8000 A. The chamber was filled with argon, helium or carbon tetrafluoride at various pressures and emersed in a thermal neutron flux of 3.8 1011 n/cm sec. The spectrum obtained from this excitation was qualitatively similar to a glow discharge for argon and helium except for the pres ence of excited ion species of He II and Ar III. The spectral output from irradiation of 760 torr carbon tetrafluoride provided a band system that is presently unidentified. Pressure dependent relative intensity and excited state density data provide information on state and species kinetics such as formation of molecular ions and their loss mechanisms. Four possible population inversions were identified in xiii Ar II. Boltzmann analysis of the excited states supplied a temperature for each species where the correlation coefficients of the fit lines indicate that the plasmas are typical nonequilibrium cascade systems. 10 3 Electron densities around 10 e /cm and Maxwellian temperature values for the collected electrons have been obtained from the recombina tion region IV characteristics. Electron energy distributions formu lated from the data compare favorably with referenced calculations. Ion pair generation rates were well within expected deviation compared to calculations using a tworegion energy deposition model. In the ion chamber region of the IV characteristics, line emission increased as an exponential function of field strength. A model for this amplification was developed for argon, utilizing an amplification coefficient applicable to all pressures. A neutron detector was developed for the liquid metal fast breeder reactor by using optical transmission from the reactor core of electric field modulated emission from fission fragment excitation. Measurement of the modulated field effect eliminates the majority of noise sources and gamma degradation signal loss associated with other detectors. Because of the excellent spectral output from Ar II, a nuclear pumped argon ion optical cavity was constructed. Data from reactor irradiation of the cavity indicate that it was lasing. The effect of mixed radiation from the reactor on a glow dis charge was studied. For thermal neutrbn fluxes less than 3.8 X 1011 n/cm2sec and gamma dose rates of 1.1 x 10 R/hr, irradiations of He3 4 He N and mixtures thereof show that there is no volume deposition effect on the glow discharge. A cathode photoemission effect was found that altered the balance of the discharge. Positive ion bombardment from the He3(n,p)T reaction products produced a considerable electron source that perturbed the cathode fall region. Enhancement of CO2 lasers was shown to be a mechanism of preionization for low voltage glow dis charge initiation and subsequent maintenance with lower power input. This lowers the temperature of the discharge and improves laser pumping efficiency. CHAPTER 1 INTRODUCTION During the last decade, fission fragments and other energetic heavy ions that are produced by neutron reactions have been examined as possible sources of energy for generation of high temperature plas mas. These high energyparticles can be produced in great numbers in a nuclear reactor where the reaction source (neutron flux) can range up to 1017 n/cm2sec in short pulses. The main thrust of research in this area has been toward the demonstration of a nuclearpumped laser. 1.1 The NuclearPumped Laser The term "NuclearPumped Laser" refers to a laser that is excited by products of nuclear reactions only and not by any electri cal or optical source. The link between the reactor and laser is natural when one considers that communications could be greatly aided with transmission of data to earth by laser beam in advanced extraterrestial equipment which will have to include a nuclear reactor for power generation. Direct coupling of a laser to a nuclear reactor is necessary in order to produce desired high input powers. One might envision a reactorlaser system where an optical cavity and the reactor fuel 235 are combined. A set of U235 internally coated tubes could be grouped together in a cylindrical shape where the optical cavity would be formed by mirrors reflecting through the tubes. A neutron moderator would surround the tubes and cooling could be accomplished by passing the laser gas through the tubes and then through a heat exchanger. 235 The fissioning of the U235 would supply both neutrons for sustaining the nuclear reaction and fission fragments for excitation of the gas. Each fission event supplies two fission fragments, a heavy fragment with an average energy of 67.5 MeV and a light fragment with an aver age energy of 98.7 MeV. These light and heavy fragments vary in weight according to the familiar fission product distribution, but both frag ments have the very important characteristic of being emitted with a charge of about 20 e. This results in a very large coulombic inter action rate and, thus, a very large deposition of energy in a small path length, producing the excited states utilized in the laser. Operating this reactor in a pulse mode will maximize the peak laser power output. Another nuclearpumped laser scheme involves a gas core reactor using UF6 as a fuel and.some fluoride molecular species derived from UF6 dissociation reactions as the lasing species. A similar homogen 235 eous concept involves insertion of U235 compounds into a liquid dye laser in order to produce a critical mass and thus a reactor. This system would derive its excitation from fission fragments rather than from chemical or optical sources. One disadvantage of the liquid dye laser concept is the apparent breakdown of long chain dye molecules by radiation interaction. R. Schneider [ 1] has inserted Rotemin b dis solved in ethyl alcohol into a reactor and observed fluorescence. When the dye was removed from the reactor, it was evident that it had been completely destroyed, since there was no color, or fluorescence, left in the liquid. Much experimental work has been done trying to show the feasibility of a nuclearpumped laser. To date, no proof has been presented that confirms the operation of such a laser. There are several alternatives when considering an energy source for direct excitation of a laser. The most widely available source is gamma radiation, but in order to effect efficient energy transfer, high density solids must be used. A desire to optimize the absorption led early workers [2,3] to concentrate on direct excitation of solid state lasers. However, gamma radiation was found to suppress, rather than aid, lasing action in all solids studied to date. This "cutoff" phenomenon is generally attributed to radiation damage in the solid. An obvious solution to the problem of radiation damage is to use a gas or liquid lasing medium. For gases, this implies the use of a high energy heavy particle that has a large dE/dx. Such a particle is exemplified by the fission fragment. Liquid lasers are still in their infancy and only one published report is available on an attempt at nuclear pumping [4]. Nuclear pumping of gas lasers has been studied extensively starting with a comprehensive study by L. Herwig [5] in 1964. He recognized the radiation damage problem associated with solids and decided to concentrate on gas laser nuclear pumping. His calculations showed that HeNe laser threshold requirements were theoretically within the reach of some reactor and accelerator radiation sources. Herwig also noted that a large diameter laser may be possible due to the inherently low electron temperature expected in the radia tion produced plasma. J. DeShong [6] carried out more detailed calculations and showed that a high pressure, large diameter nuclearpumped laser has theoretical efficiency two orders of magnitude greater than small diam eter devices. In 1967 he undertook a series of experiments to verify the feasibility of direct pumping. None of his devices showed proof of lasing. Eerkins [7,8] decided to study noble gases as a possible lasing medium because their high density allows a large dE/dx by the fission fragment and because their ionization energy is low (E. = 15.68 eV for 1 argon). Because recombination and dissociative recombination is ex tremely efficient in a cold plasma, it was felt that the argon ion tran sitions would exhibit a population inversion greater than that seen in conventional electrically pumped lasers. Eerkins's source of energy 17 2 was a TRIGA pulsed reactor with fluxes up to 101 n/cm sec. The 235 reactor neutrons interacted with a U coating on the laser tube wall and produced a fission fragmentgenerated plasma. Boroncoated walls 10 7 were also tried, using the reaction B (n,a)Li producing a plasma utilizing the reaction product energy of 2.3 MeV. Although Eerkins did not find any proof of lasing, he did generate a light output that was quite intense. Guyot [9], concentrating on Ar and CO2 lasers, also did not find lasing in his experiments. Nuclearpumped laser experiments previously mentioned concen trated on pumping with a highly energetic particle that was a result 10 of a neutron reaction with B or a fission event. These experiments also concentrated the reacting material on tube walls while inserting gas as a target for the particles. V. Andriakhin [10] attempted lasing in an entirely different manner. He utilized the large neutron cross section (5000b) of the He3 reaction [He (n,p)T + 760 keV] to provide 3 a source for excitation in a cavity filled with a gas mixture of He and mercury vapor. His device generated light output of 10 mW, but no proof of lasing was seen. Several researchers (T. Ganley [11], F. Allario [32], H. Rhoads [13]) noted the inability of others to generate a nuclearpumped laser and decided to look at the effects of several nuclear sources on an 3 operating laser. All of these studies involved the use of He as a replacement for He4 in a HeCO 2N2 laser gas mixture while operating the laser in a nuclear reactor. It was felt that the high efficiency of the CO2 laser would allow maximum conversion of the IHe(n,p)T reac tion energy, 760 keV, into laser output. All three authors noted an increase in the efficiency of the laser being irradiated in the reactor and, therefore, an increase in laser output. Rhoads recognized this increased laser efficiency as an increase of the glow discharge efficiency. He described this effect as primarily due to the bombardment of the cathode surface by gammas and He (n,p)T reaction products and thus an alteration in the cathode fall equilibrium. The output of a CO2 laser depends, among other things, on the electron temperature, Te, of the plasma. Bullis [14] has shown that the electron temperature for optimum pumping of a CO2 laser is far below that resulting from normal glow discharge pumping. The addition of the radiation source term to the cathode fall equilib rium allows the operation of a glow discharge at much lower currents and field strengths, allowing lower Te and much more efficient pumping. This irradiation effect also allows operation of glow discharges at much higher pressures than previously attainable. It would also be possible to increase the power output of present operating laser systems by the addition of a radiation source at the cathode. The glow discharge irradiation work described in this disserta tion was done simultaneously with the nuclearenhanced laser work de scribed above; the results shown in this paper basically agree with those described above. Upon termination of the nuclearpumped laser experiments, it became evident that the theoretical considerations used to calculate the neutron flux needed for lasing action may be inaccurate. The thermal flux level available in many reactors is well above the calcu lated lasing thresholds; therefore, some of the experimental devices should have lased. Most of the theoretical work has been based on the premise that one excited state is available for each 100 eV deposited in the gas [5,6]. This relation results from the assumption that once the energy is deposited in a gas by nuclear interactions, subsequent distribution of excited states, ionization, etc., is identical to that of electrically pumped lasers. G. R. Russell [15,16] has noted at least for the case of atomic argon direct nuclear excitation of gases is an entirely dif ferent kinetic process than that found in most CW electrically excited lasers. Generally, in electrically pumped gas lasers population inver sions are formed by metastable state collisions with ground state atoms (HeNe) or other energy transfer systems initiated by the electron swarm. The kinetics of the argon ion laser, where the population inversion is produced by electron collisional excitation of the upper state and electron recombination in the lower state, served as Russell's example. On the average, it takes two collisions with electrons to elevate the argon ground state to the ionized excited level required for population inversion. Such a ladderclimbing system is not evident in the low temperature plasma generated by nuclear sources. This low temperature system is more analogous to a recombining plasma at low thermal electron temperatures, where there is additional preferential excitation due to high energy particles superimposed on the thermal excitation. Therefore, it would not be expected that inversions formed in electrically excited CW lasers would necessarily be found in nuclear excited lasers. It is also very probable that the additional excita tion due to high energy heavy particles will create new inversions not previously observed in electrically excited lasers. Russell supports this last premise by calculating population inversions produced in argon by fission fragment interactions and not available in conventionally pumpedlasers. His calculations included formation of excited states due to recombination of thermal electrons and the associated radiative and collisional decay of these states. To complicate matters further, Miley [17] and others have indicated that there is a difference between how fission fragments and alpha particles lose their energy in a gas medium. This is because alpha particles remain essentially charge invariant over their path length, while fission fragments starting with an average charge of 20e lose their charge by recombination while losing energy by coulombic, rather than nuclear, elastic collisions. Recently several of the authors [ 1] mentioned above have revealed that they now feel that once the fission fragment deposits its energy into a gas, this excited gas may be regarded as identical to the electrically excited gas. From the above discussion it can be concluded that the exact nature of a gas excited by fission fragments is not known. Also, there is a distinct possibility of producing a nuclearpumped laser using some unusual (not normally available) population inversion; some gas now known to exhibit population inversions may become the standard for this type of laser. A less optimistic conclusion is that nuclear pumping is not presently feasible. No one has previously studied experimentally the excited states of a plasma produced by an extremely large source of heavy, highly charged particles such as fission fragments. Until detailed analysis of heavy particleproduced plasmas is complete, the nuclear pumped laser experiments are without foundation. 1.2 Previous Studies of Fission FragmentProduced Plasmas To study excited states of atomic and ionized species exper imentally, spectrographic analysis of the spontaneous photon emission from these states is necessary. Several researchers have studied experimentally alpha particle induced luminescence of gases with great success. S. Dondes et al. [18] have been able to supply very good spectrographic plates (long time 210 exposures) of many gases exposed to a Po 5 MeV, alpha source. Amplification of the gross light output was indicated upon placing a 350 V/cm field across the luminescing area. P. Thiess [19], using a similar but more powerful source and photon counting techniques, was able to obtain similar data. Other allied work has come from the French gas counter research program [20,21,22,233 and two very early studies [24,25]. These latter experimental works used sources of very low intensity and the data were decidedly biased toward use in the design of counting equipment. The source strengths used in all of the alpha particle interaction work are weak enough, and the electron density therefore small enough, that the gas should probably be described as a scintillating light source rather than a plasma. As mentioned previously, it is hard to draw comparisons between such low level a source luminescence and a plasma generated by a large fission frag ment source, but these studies do give basic knowledge of the kinetics of heavy particle interactions. In contrast to excited state measurements, fairly extensive measurements of electron densities in radiationproduced plasmas have been reported. Jamerson et al. [26,27] worked with "inreactor" fission fragmentproduced plasmas where, utilizing the IV curves produced by a field across the plasma, they were able to calculate values for electron temperature and density. For a flux of 1012 n/cm2sec a 600K electron temperature was found which compares favorably with the micro wave cavity measurements of Bhattacharya [28]. Ellis et al. [29,30,31], 3 have studied recombination coefficients in plasmas produced by He reac tion products, alpha particles, and fission fragments, and have added immensely to the knowledge of the kinetics of these plasmas. The above works indicate that the general kinetics studies of alpha and fission fragmentproduced plasmas are no longer in their infancy; therefore, one can draw on these data in explaining the source terms for generating atomic excited states. A very large library of cross sections for collisionproduced excited states is available in a book by E. W. Thomas [32]. These cross sections have been generated by bombarding various gases by heavy ions produced in accelerators. Unfortunately, none of the ions had energies above 1.5 MeV and few had energies above 0.5 MeV. The appli cability of these cross section data to fission fragment interactions is questionable, but certain techniques used to generate these data are of great interest in this study. Several researchers have attempted to study spectral emissions from fission fragment plasmas. F. Morse et al. [33] studied the luminescence of several gases under bombardment by fission fragments in a nuclear reactor. They did see some line structure, but concluded that it was too weak to study (96hour exposures!). They then returned to the use of alpha sources [18] where reactor associated problems were not present. R. Axtmann [34] studied the luminescent intensity of 252 nitrogen bombarded by fission fragments from Cf2, but he just assumed that the light was from the second positive system of molecular nitro gen emission and tried no spectroscopic analysis. The above studies led Pagano [35] to attempt spectroscopic analysis of various gases 252 bombarded by Cf252 fission fragments, but his source was not strong enough to allow recording of spectra. During the nuclearpumped laser studies of Eerkins [7,8], several spectroscopic plates of their pulsed plasma were taken, but at that time they were more interested in producing a laser than study ing the plasma that they assumed contained population inversions. Thus, the spectroscopic work was limited to a few plates in which the photon output was filtered by the mirrors of the laser system. The above spectroscopic studies gave great encouragement to this author in his studies of "incore" fission fragmentproduced plasmas. After careful analysis of the techniques used by these researchers, a set of experimental guidelines (see Chapter 3) were generated in order to avoid the known problems associated with such research. 1.3 Glow Discharge Irradiation and Fission Fragment Interaction Experiments The need for experimental data on fission fragmentproduced plasmas and on the radiationproduced changes in an already existing plasma has been established. The dual purpose of this dissertation is to fill some of this unknown area and to generate sound techniques for the study of "inreactor" particle produced plasmas. Fortunately, as will be shown in the following chapters, one basic experimental apparatus can be used for this dual purpose. The first probe into this area involves the study of a known plasma, the glow discharge, and what happens to its operation under bombardment by gamma and reaction products of the He (n,p)T reaction. Several cathode configurations and several gases are studied for their response to the reactor sources. Conclusions are drawn as to the extent of changes and how they occur. The most difficult area, the investigation of fission fragment produced excitation, is presented utilizing the assumption that the plasma is an interacting Maxwellian system. The analysis of the data emphasizes the deviations from equilibrium of this system. This approach was taken due to the availability of large numbers (45 Ar II spectral lines) of easily measurable spectral lines emitted by atomic as well as 4 ion species of several gases. He Ar, and CF4 were studied for pos sible population inversions by using Boltzmann plot techniques and analysis of deviations of excited state populations as a function of pressure. Data are supplied on the effect of pressure and a DC field on the intensity of line emission. A unique neutron detector for the liquid metal fast breeder reactor was suggested by Dr. Edward E. Carroll [36]. Drawing from the above data, a detection system was developed and tested using electric field amplified light variations as a basis for its operation. Also, an argon ion laser was tested utilizing pumping by fission fragment 13 interactions only. Results from this device, although not proof of las ing, show promise for future investigators. In summary, this chapter has outlined the great need for experimental data on the nature of effects of mixed radiation sources on a glow discharge and has shown why the study of fission fragment produced plasmas is necessary. CHAPTER 2 THEORETICAL CONSIDERATIONS To assess adequately the effects observed in the experimental procedure, certain theoretical considerations must be made. The two basic considerations that will be reviewed in this chapter are, first, the way a particle deposits its energy, and, second, how this energy might be distributed in a plasma. Basic calculational techniques will also be reviewed for use in analysis of the data described later in this study. 2.1 Energy Deposition by Fission Fragments and Other Particles The passage of charged particles through matter has been studied for at least half a century. It is not surprising that the theoretical and experimental description of alphaparticle and proton penetration phenomena is well advanced as these are the charged particles with which most experiments were performed before the discovery of nu clear fission. Presently there is emphasis on the study of the inter action of ions with larger mass and charge than these elemental par ticles. It is common practice to label ions such as fission fragments as "heavy ions" in order to distinguish them from light ions such as protons and alpha particles. This distinction is strictly arbitrary since most of the phenomena involved in energy deposition by these particles are identical. Fission fragments distinguish themselves as heavy ions because they are very massive and have, immediately after formation, about twenty electrons stripped from their atoms. Thus, the effective charge of these fragments is considerably higher than those of the light ion group. This is an important distinction, since heavy ions suffer coulombic interactions, as well as the nuclear elastic scattering found in light ion interactions. A light ion is essentially charge invariant over its path length, while the fission fragment is charge variable over part of its path. The life of a fission fragment or other heavy particle is summarized by Northcliffe [37]. If an atom is given a velocity greatly in excess of the orbital velocities of its electrons and allowed to enter a material medium, these electrons will be stripped from the atom and the bare nucleus will proceed through the medium, gradually losing energy because of coulombic interactions with the electrons of the medium. At this point, where the heavy particle velocity is high, elastic or inelastic collisions with the nuclei of the medium will be relatively rare and will add little to the energy loss process. At first there is a small, but finite, probability that the ion will cap ture an electron in one of these collisions and a large probability that the electron will be lost in the next collision; but as the ion slows down and approaches velocities comparable with the orbital veloc ity of a captured electron, the capture probability increases and the loss probability decreases. As the ion slows to velocities smaller than the orbital velocity of the first captured electron, the capture probability becomes very large and the loss probability approaches zero. Meanwhile the probability of capturing a second electron grows and the corresponding loss probability decreases, so that with increasing prob ability the second electron is retained. As the velocity decrease con tinues, a third electron is captured in the same gradual way, and then a fourth, and so on. The major difference in the description of the capture process for successive electrons is the change in velocity scale necessary to match the progressive decrease of orbital velocity of these electrons within the ion. Eventually the ion reaches velocities smaller than the orbital velocity of the least tightly bound electron and spends most of its time as a neutral atom. By this time its kinetic energy is being dissipated predominately by the energy transfer arising from elastic collisions between the screened nuclear fields of the ion and atom, and a diminishing amount of energy is being transferred to the atomic electrons. The neutralized ion is said to be stopped when it either reaches thermal velocities or combines chemically with the atoms of the stopping material. With respect to the medium into which the heavy particle or fission fragment is penetrating, most of the ionization and excita tion is caused by secondary electrons (delta rays) produced during the initial coulombic stripping and recombination interactions. This does not hold true, though, for a fission fragment near the end of its track, where it is essentially neutral. To calculate the space dependent deposition of energy in a medium, it is usual to start with a stopping power relation. Using appropriate geometry, one first calculates the available energy per unit volume, and then using ion or excited state generating terms, the kinetics of the system. The Bohr stopping equation for fission frag ments is [38] 4 4 dE 2 e 22 e 2 = NZ L, + 2NZ L (1) dz eff 2 e 12 2 v( my M2v where Sa /3 1/3 1 1 L =L L (x1/3 + x ee e 4 "x Lv = ( (Z23z/3 2/3 m(M1+M2) 2 )2 22 RM 2 1 2 M1M2 N = atom density of the density stopping material M1,Z1 = mass and nuclear charge of the moving fragment MZ2 = mass and nuclear charge of the stopping material e,m = electronic charge and mass v = velocity of the moving fragment Zeff= effective charge of the fission fragment example: eff 1/3 Z = Z1/3 v/v eff o v = velocity of a Bohrorbit electron (2.2 x 10 cm/sec) o V o x= 2Z  eff v L = term for electronic stopping power e Le = the electronic stopping power for particles of comparable velocities (about 6.33 10 v). velocities (about 6.33 x 10 v). The first term in the righthand side of equation (1) describes the electronic stopping power derived from coulombic interactions. The second term describes energy transfer by nuclear elastic inter actions. It is standard practice to ignore the second term since the amount of energy deposited by nuclear interactions is small compared to the total energy deposited. Thus, using the first term only of equation (1), the range of a fission fragment can be determined. 1 2 Assuming for the particle that E = M v and that the ThomasFermi 2 1 1/3 effective charge, Zef = Z v/v is valid, the fragment velocity eff o follows from equation (1) as dv d K(N,Z1,M1) (2) where F 2/9 4 8 6Z K(N ) 2N e 6.33 x 10 1/3 1 (3) K(N,Z1,M1) = 2N  8M + 1 (3) 2 8M 1 1 1/3 my 1 2 o  K is therefore a function of the mass and charge of the moving fragment and the density of the medium, but is velocity and space inde pendent. Solving this equation shows that v(x) = v. Kx (4) Solving this velocitydistance relationship for x when v(x) = 0 or v(x) x=R = O, where R equals the range of a particle with initial velocity v., the result is V. R(v.) = (5) 1 K 1 2 Assuming the initial energy E. = M Vi and substituting into equation (4) produces the wellknown square law energy deposition rela tionship of a fission fragment, x 2 E(x) = E(l1 ) (6) x R This relationship is therefore equivalent to the Bohr stopping power equation using the ThomasFermi approximation for Zeff with the nuclear stopping term neglected. Several authors'using the general equation, x n E = E(l ) (7) have disagreed with the n=2 value derived above. Axtmann [34], using the luminescence of nitrogen under fission fragment bombardment, found n equal to 1.7. Long [39] used n= 1 for his calculations where the n value was obtained from collated rangeenergy data for a variety of stopping materials. Steele [40] used n= 1.5 to compute energy deposi tion by fission fragments in water. To generalize the square law equation (6) for a point source in an infinite homogeneous medium, an energy transfer function can be stated as 2 G(x,p) = E.(1 ) (8) 1R I where cos 1 is the angle between the xaxis and the direction of particle movement. To calculate the deposition in a gas by a fission fragment, one must remember that a fission fragment source such as a coating of U308 has a finite thickness. The foil is a dense medium and thus absorbs a large amount of the fission energy available. Calculations should therefore include this second medium unless the fuel is in a gaseous form, such as UF6. It is very tempting to assume that only perhaps onehalf of the energy available will get through the foil into the gas. This assumption would be hard to prove because of the difficulty of relating a measurement of this energy in one particular experiment to a calculation where either the thickness or the density of the uranium compound is different. To calculate energy deposition at any point z of Figure 2.1, one first assumes that scattering of the fission fragment by the medium is negligible and that only straight line paths need be considered. The origin of the geometry is at the left face of the source slab which has a thickness R1, the range of a fission fragment in the source medium. When x is larger than R1, the substitution z= xR1 is made so that z=0 at the interface. The source is assumed isotropic in emission with azimuthal symmetry about x. The angle between the path and the xaxis is 8. The slowing down of the particle in both media is described by equation (4). While the fragment is in medium I moving along the abscissa, the residual velocity at x v1(x ;x), of a particle borne at x with initial velocity vi is v1(x';x) = vi KIx' xI x x' < R1 (9) while for medium II v2(z;x) = C(x) K2z , (10) MEDIUM I (fuel) MEDIUM II (gas) X =0 \ I X=R1  R  Z=0 r / MEDIUM II ORIGIN Figure 21 Geometry where C(x) is the residual velocity at z=0 or the interface of a particle born at x in medium I. Assuming continuity at the interface, v (x';x) R v (z;x) ; then C(x) = v. K (R x) (11) and thus, the residual velocity in medium II is v2(z;x) = v. K1(R1 x) K2z (12) Since the thickness of medium I is equal to the range of a fragment in medium I, equation (11) is valid for any 0 : x R1. For a fission fragment not moving along the abscissa, but in the 1 direction 9 = cos ,equation (12) becomes (R x) (R1X) z v (z;p,x) =v K K (13) 2 v 1 p 2 p provided that (R x) (RIX) z K + K < v for all p > 0 1 p 2 p o or, in other words, provided that the particle arrives in medium II. Since it was previously shown in equation (5) that vK v K 2 ' 2R R2 1 2 one can state that .r RlX z ] 14 v2(z;LP,x) = v 1 (14) The Energy Transfer Function of equation (8) can now be stated as the twomedium function 1 2 F(z;p,x) = 2 M1v2(z;p,x) r (R x) 2 = E 1 (15) In order to eliminate the dependence on R2, a conversion factor "a" is derived from the BraggKleeman rule which converts the range of a charged particle in one medium to its range in another medium. R P (A /A)1/2 R1 (16) R2 = p 2 Therefore, R2 = aR1 and a (A2/A1/2 (17) P2 where p = density, and A = atomic weight. ,t ,t a" may also be derived from the theoretical stopping equation or from experimental measurements. Equation (14) thus becomes G(z;p,x) = E 1 (R1 (18) o 1 p.R1 PCaR From the general geometry of Figure 21, a total energy current is derived for a point r in medium II due to the source S(r ,Eo, ) in medium I. J (r)= drJ Ero 4 r o 4 r O E o S(r ,E ,X?)dr dE dc 0 0 0 0 dJ dE S(r ,E ,fQ) G(r;r ,E ,0) , S0 o 0 0 E 0 (19) = a spacial point in medium I, = a spacial point in medium II, = a solid angle characterizing the direc tional distribution of the source, = initial energy of the fission fragment. = the distribution of the fission fragment source at r in dr at n in dQ and o o at E in dE (usually a constant). o o G(r;ro,Eo,) = o0 0 4 the energy at r, carried by a fragment originated at ro, moving in direction 0 with initial energy Eo, assuming no scattering. If it is assumed that C(x) is the fission density, C(x) = f (x)$(x), and that f(E ) is the normalized fission fragment spectrum, then with isotropic emission, the differential source within a thin layer dx at x, emitted in the solid angle width dpdc with initial energy E in dE is ,cp)dx dE S(x,E ,pcp)dx dE dpqp = Cf (E )dx dE ddp (20) o o 4r o o where Using the energy transfer function of equation (18) and equation (20) in (19), one obtains the total energy current at z in medium II, JE(z), resulting from a distributed source of fission fragments in medium I 2n co R1 1 S(z) d dE f(E )E dx d pC(x) E 4TJ o /a aR1ax+2 aR1 X ( (R x) R1 a 1 (21) R aR1 ) Nguyen [38] discusses the limits of integration and how one would analytically integrate this function. With a constant fission density of C SCE pR 1 1 22 21 33 3 22 ] ( energy JE(z) 2 bz+ b z + bz (bz) cm sec (22) where 1 1 b =  1 2 R1 and R2 being the ranges of fission fragments in mediurmsI and II, respectively, of a fragment having the initial energy Ep. The required boundary condition JE(z)l =0 (or at bz = 1) is satisfied. 2 Equation (22) represents the total residual energy at point z. The instantaneous energy loss per volume as a function of z is obtained by taking the derivative of JE(z) with respect to z. JE(Z) CE 1 3 2 2 energy (23) d z [b z 2b2z On (bz) b(23) dz 2 3 cm sec An almost identical empirical energy deposition relationship can be derived, as previously noted, based upon the relationship E(x) = E (1 1 5 n 3 (24) Both equations give similar results for small z, but vary considerably for z approaching the range R2 in medium II. This energy deposition function ignores any nuclear elastic collisions; but if one calculates an ion production source, a socalled "ionization defect" takes into account this nuclear deposition, which is less effective in ionization than coulombic interactions. At this point researchers split to several different techniques for generating source terms for a kinetic system. Most studies have constructed an ion source term and used the standard w values for fission fragment interaction with various gases. These values include the "ionization defect" and are experimental in origin. Using the square law point deposition form of equation (23), one can derive, simply by dividing by w, the volumetric ion production rate. dJ (z) CE. R. r22 a I dE(z CEp i 2 z22bz ion pairs Sw* dz 2w. Li x J 13 1 cm sec (25) where the distinction is made between the light and heavy groups of fission fragments. Therefore, I1 1 (26) IT(Z) = IL(z) + 2 I(z)(26) eV The assumption that w V is a constant value over the ion pair entire path of the fragment is false, but if one includes the "ioniza tion defect" and views the target as a whole, such as a plasma system, this approximation should be close to the actual generation rate. P. Thiess [17] approached the problem in an unusual manner. Using the semiempirical energy deposition approach, a suggested alternative shown above, he avoids the use of w values by calculating excited states and inoization directly. This approach requires knowledge of a complete set of cross sections for generating the source terms for excited levels. Thiess used modified BetheBorn cross section data based upon proton impact. Russell [16] used another approximation, the Gryzinski electron interaction cross section, for his excited state calculations. Both authors clearly state that the use of these cross sections may be entirely invalid, but must be used because there are no experimentally measured cross section data available for such interactions. One factor that may make the Gryzinski electron interaction approximation more applicable than the others is the fact that about twothirds of the ionization and excitation is distributed to the gas by secondary delta rays or fast electrons, rather than by the primary fission fragment particle. The range of a fission fragment in a gas is a function of the density of that gas and its molecular weight. Range relations are strictly empirical and are derived from measured data independent of straggling or other statistical phenomena. Range as a function of pressure can be calculated using the following equation [411 KE2/3 R(cm) = where K = 1.4 for most gases (Figure 35). Figure 22 shows a plot of range vs. pressure for both the light group (Eo = 98.7 MeV) and heavy group (Eo = 67.5 MeV) fission fragments in argon and helium. Experimental procedures such as those used in this dissertation are based on cylindrical geometry. The average chord length (s w 4 volume/area) best represents the distance that a particleif born on the surface or in the volume of the cylinderwould travel in a straight line before it would collide with the surface. For a cylinder 30.5 cm in length and 3.7 cm in diameter, the average chord length is 3.4 cm. These lengths are identical to those found in the experi mental apparatus used here. It is interesting to note in Figure 22 that at all pressures below 1 atmosphere (760 torr), the range of fission fragments in helium is greater than the average chord length. The situation for argon is different since it is ten times as dense for equal pressures; therefore, the average chord length is equal to the range of the light fragment at 360 torr and equal to the range of the heavy fragment at 280 torr. A quick conclusion could be that for most of the experimental data that one would observe, only a small fraction of the fission fragment energy would be deposited in the gas. This is not necessarily true, because the energy deposition from the foil is ht FragmEnts I Heavy Fra t HELIU  \ \  __ Siht Fragmnts Heavy Fra t meit ARGON i ARGO 10 PRESSURE (torr) Figure 22 Range of Fission Fragments in Helium and Argon in0 skewed towards the foil surface due to the finite thickness of the source and the fact that the great majority of the fission fragments do not leave the source surface with the typical 67.5 MeV or 98.7 MeV average energies that they are born with. A much better view of the energy deposition can be gained by calculating the deposition profile at each pressure. A calculation of the energy deposition utilizes the square law deposition function and geometry used for equation (23). First, several assumptions must be made in order to equate the slab geometry calculation to the cylin drical geometry that is presented in most experimental situations. 1. The slab and cylindrical tworegion energy current functions are essentially identical. This is a good approximation since the range of a fission frag ment in the U308 source foil used in these calculations is only 4 7.5 x 104 cm; therefore, the great majority of the energetic fission fragments that have a considerable range are emitted perpendicularly from the surface. 2. Little energy is emitted to the gas when a fission fragment collides with a surface. This assumption is not adequate for exact analysis but should be valid for the accuracy required here. 3. Energy deposition by other sources is a very small fraction of the fission fragment deposition. This assumption has been proved experimentally to be valid by Leffert [263, where he has shown that other sources, such as gamma radiation, deposit less than 1 per cent of the total energy to a volume in normal reactor situations. In order to proceed further, the fission rate must be calcu lated as follows: C = R = Nt O = E (27) Nt = number density of target nuclei a = fission cross section = average neutron flux along the foil S= macroscopic cross section. For these conditions, Thickness = 6.2 mg/cm2 (the range of a fission fragment in U30 ) 11 n Average thermal flux = 3.8 x 10 2 cm sec Fission cross section = 505 barns 93% enriched uranium, 2 11 missions the generating function per cm surface area is 8.06 x 10 fiss cm sec From equation (23) dJE(z) dJEi (Z) dz X dz i=1,2 Cf EpiRi b3z2 2b2z n (bz) b energy (28) L= 2 cm sec i=1,2 where C = fission rate E = most probable energy at birth (each group) 1 1 b R2i aRli i = fission fragment group. This generating formula is calculated by splitting the depend ence on light and heavy particles, then adding the results, giving the energy deposition profile shown in Figure 23 for helium and Figure 24 for argon. The gas pressure, or atom number density, is the most important factor in the deposition of energy in a fixed cavity. For pressures below 760 torr in helium, the energy deposition across a 3.4 cm average chord length cavity is approximately uniform. But, in argon, only below 75 torr is the energy deposition somewhat uniform across the cavity. Since this calculation takes into account only coulombic inter actions and ignores the nuclear elastic and inelastic scattering of the particles when they reach the neutral status, the energy deposition curves fall off extremely fast. If the nuclear scattering terms were included, the range would be extended slightly, but only a small addi tion would be made to the deposition of energy at the end point of the fission fragment path. The effect on the total deposition would also be small [37]. One of the unknowns, as previously described, involves how the energy is utilized, what excited states or ions are produced, and what 109 10 U DJ 7 LU I DISTANCE FROM U308 FOIL, Z (cm) Figure 23 Deposition of Energy into Helium by Fission Fragments, D = 3.8x1011 n cmnsec 760 trr 1 00 torr 50 torr      ~~ : : 100 102 70 or S0 t r 150 tor" 75 tor   1 0 1 10 100 101 DISTANCE FROM U308 FOIL, Z (cm) Figure 24 Deposition of Energy into Argon by Fission Fragments, D = 3.8x10 cm2sec u m E u > 08 LL 10 LU I L C, 'a 107 photon emissions are coming from the "plasma." These items are a function of cross section for the various species that are present in the gas. Measurements of the photon emission of the gas are based on total emission from the optical cavity; thus, this photon output can be compared to the total energy deposited into the gas in this cavity. A description of the total energy input can be obtained by integrating the energy deposition function over all source areas and over the average chord length. From equation (23), dJ (z) E = dA (Ez )dz (29) JA f dz f z z SA CE R E = 1 b3z2 2b2z m (bz) b] dz (30) o where z = average chord length, or z = R2, if R2 < z 1 = R2 = range of fission fragments in gas and is a function of pressure. Integrating, A CE R 3 3 z f p z 22 n b b1 MeV E= bz (2bz)bz (31) 2 L3 2 sec o Again, as in equation (28), the calculation is split for each group of fission fragments. Figure 25 shows the solution of equa tion (31), where E is calculated as a function of the gas pressure for 1011 1010 PRESSURE (torr) Figure 25 Energy Deposition by Fission Fragments in Argon and Helium A Fixed Cavity  the representative cylinder with an average chord length of 3.4 cm. The deposition in the cavity filled with helium is almost a linear function of pressure. In argon, the effect of the range being less than the cavity dimensions is evident by the leveling off of the curve above 200 torr. Depending on the recombination and diffusion of elec trons at pressures above 200 torr, the fission fragmentproduced excitation may generate a torroidal luminescent output in the cylin drical cavity. This would alter the uniformity of the photon output into the fixed solid angle view of the diagnostic equipment and may provide erroneous data, especially if some of the surface region were optically shielded from the detector system. It is estimated that such a shading effect exists in the experimental equipment associated with this work. Further review of this problem can be found in Chapter 4. 2.2 Energy Deposition by the Reaction He (n,p)T in a Glow Discharge High energy products of the reaction He (n,p)T are of interest here because of the use of He3 in the glow discharge experiments to be described later. The proton and triton share the reaction energy of 760 keV with the heavier triton taking 190 keV and the proton 570 keV. The initiat ing neutron energy is in the range of less than a few eV; therefore, little momentum is transferred and the reaction particles travel randomly in opposite directions. Thus, the interactions with the gas are independent of one another. Fortunately, the linear stopping power formulation for protons and heavyheavy protons (tritons) has been established as satisfactory for calculating energy loss phenomena. Interesting calculations for this reaction include total energy deposited in the cylindrical glow discharge and total ionization produced by this deposition. These calculations are done assuming that the gas is He3 at a pressure of dE 15 torr for an 8:1:1 mixture of HeCO N is 2.6 times that of dx 2 2 helium [13]; therefore, the calculation of total energy deposited should be multiplied by this amount for experiments involving CO2 gas mixtures. Reference 8 gives the stopping power of helium as dE P = 105 eV for 570 keV protons, dx cmtorr dET eV E = 270 for 190 keV tritons. dx cmtorr For a cylindrical cavity 3.7 cm in diameter and 12.7 cm long (identical to the dimensions of the experimental apparatus) the average chord length is 2.87 cm. The total energy deposition is calculated using the following equations: 1. Reaction rate 3 R = N to cm3 (32) 3 where N = number density of He atoms S= thermal neutron cross section = 5400 b = thermal neutron flux 3.8 x 101 n/cm sec. 2. Total energy deposition E E (dE s PRV V (33) dx/ +dx)J sec p T where s = average chord = 2.87 cm P = pressure = 15 torr 3 V = volume = 136 cm . 3. Total energy available keV E = (760 keV) RV ke. (34) sec Upon application of the data to these equations, it is found 13 eV that only 1.75 x 10 1 is being deposited into the cavity. This is sec 14 eV only onetenth of the total available energy, 1.12 x 10 generated in the cylindrical volume. 6 This energy input is equal to only 2.8 x 10 watts, so the total energy both available and deposited at this neutron flux level is but a small fraction of the energy deposited by electrical excitation. In fact, measurements that will be detailed in Chapter 4 for glow dis charges show that the minimum electrical power input needed to generate a glow discharge in such a cavity is 0.5 watt. The one conclusion that can be drawn from the calculations is that volume ionization or excita 3 tion by He reaction products probably does not account for any signif icant changes in the operation of typical low power glow discharges, especially for neutron fluxes below 1012 n/cm 2sec. Butler and Buckingham [42] state that for high energy ions whose velocity is much greater than the thermal ion or electron velocity, the loss rate of energy to the electrons is larger than to 2 3 ions by the factor (m./m )(p /zi p.). For He this ratio is approx 1 e e 1 1 imately 20. This could account for some volume enhancement of energy, especially in the case of fission fragment deposition. But, pe and Pi are extremely small in both cases and most of the energy transfer is to neutral particles. This effect then, is not significant in the tenuous plasmas described here. Since it has been established [11,13] that the nuclear reactor does affect the operation of a glow discharge and thus laser operation, the changes occurring must be a function of either changes in glow discharge structure or irradiation of the elec trodes. Data describing these effects are presented in Chapter 4. 2.3 Description of a Fission Fragment Produced Plasma At present much effort is being expended in the area of char acterization of the tenuous "plasma" produced by fission fragment sources [ 1 ]. The assembly of a set of kinetic rate equations is the ideal approach to the characterization of this gas. But, because of this method's detailed description of the number density of all species and their important excited states, all reaction cross sections must be known. Considering the number of species of a gas (atoms, ions, and molecular combinations) and the excited states possibly present in these species, this becomes an arduous task. In most experimental processes, a small amount of impurity gases are always present. These impurities enter into the kinetics of the system and complicate the rate equation approach even more. An example of this is the presence of a small amount of nitrogen. Even in amounts of less than one part per million, spectroscopic anal ysis of an alpha particle or fission fragment excited gas show the presence of the first negative system of N2 with very intense band peaks. This indicates the presence of an additional ion generating term of significant magnitude to alter the population of many species. N is formed in several ways. The two most important transfer reac N2 tions are + Hemett + N He + N + e + AE (35) metastable 2 2 and He ++ N2 2He + N + AE. (36) 2 2 2 Thenormally considered te predominant reaction speified in reaction (35) ison of normally considered the predominant reaction for the formulation of the N ions. Thus the population of N2 is predominately a function 2 2 of the population of the metastable He(23s)'state and the recombina tion rate of N. N + will then increase as a function of increased 2 2 helium gas pressure, since the collision rate, as well as the meta stable population, also increases as a function of pressure. The reac tion described in equation (36) also produces the N2 ion, but at a rate about five times slower than the Penning type ionization rate [43]. This is still significant, but the effect is diminished even more because the population density of the molecular ion is far less than the metastable state density. The molecular helium ions are formed in many ways. The follow ing reactions generate the majority of the ions. He + 2He He + He (37) 2 He(23s) + He(23s) He (38) More information on formation and decay of these molecules is given in References 43, 44, 45 and 46. If the excited states are neglected and only number densities of ion, atomic, and molecular species are included in the rate equa tions, the set of equations is reasonable and easily solved with the inclusion of only a few unknown reaction cross sections. Examples of this technique, which include the effects of wall losses from the excited gas, are given in References 26 and 47. In order to study fission fragmentproduced excitation without using rate equations, it is advantageous to assume some model. Such models, although probably invalid for exact representations, should use an equilibrium distribution of excited states based on Maxwell Boltzmann statistics or some combination of equilibrium distribution, plus a calculation of individual excited states by approximate cross section. The latter approach was used by Russell [16] in his calculations of population inversions in argon. This model is presented here since it is reasonably complete and takes into account most of the processes for forming excited states in an individual manner, rather than by empirical statistical distribution methods. It does ignore all excited states other than those of atomic argon, and it would require extensive modification to include analysis of ion excited states which are experimentally available for study in fission fragmentgenerated plasmas. Also, no provisions are made for inclusion of impurity species in the equation set, but they could be added without great difficulty, since most impurity interactions are loss terms for the primary gas. This semiequilibrium model is similar in many ways to that used by Leffert [47], except that in the latter case no attempt was made to calculate excited states densities. Using the theory of Bates, Kingston, and McWhirter [48], the production terms for argon excitation have been reduced to five principal processes: 1. Recombination of thermal electrons with atomic ions 2. Inelastic collisions between excited atoms and thermal electrons 3. Radiative transitions 4. Direct excitation due to fission fragments and high energy secondary electrons 5. Formation of excited states in the products of dissocia + * tive recombination of diatomic ions (He + e He + He ). Combining the above processes, an infinite set of excited state density functions are obtained. n(p)= () [ne (K(p,c)+ K p,q)) + (pq) (pq) qjp q
