Isentrope Parameter Effect in the Compression Process of the Fusion Advanced Fuel

In inertial confinement fusion, Fermi degeneracy plays an important role in reducing the cost of driver energy. In this research, based on recent progresses in the laser electron accelerators research, we have physically designed a D/³ He target and examine the isentropic parameter of a D/³ He fuel to achieve the goal of gains of order 500. The design target significantly depends on the isentrope parameter and the pressure of the D/³ He fuel. In during the compression, If the D/³ He fuel stays in the degeneracy state, the compression energy is smaller than the ignition energy for the same amount of fuel. The energy requirement to compress a D/³ He fuel with density 2.9 × 10⁴ g/cm³ is 4.2 × 10⁷ J/g. Also, the driver energy needed to achieve these gains is estimated to be 1000 MJ when the coupling efficiency is 10 % and isentropic parameter is 1.5.     

Study of the Ignition Requirements and Burn Characteristics of Aneutronic Fusion in Degenerate Plasma

The reactions such as; D?+?³ He and p?+?¹¹B are aneutronic fusion reactions that, in characteristic conditions create degenerate plasma. The electronic stopping power of degenerate plasma is smaller than the classical plasma, because some transitions between the electron states are forbidden. The equations that predict the behavior of these plasmas are different from the classical ones, and this is the main factor in decreasing the ignition temperature of the plasma. In this research, the nuclear fusion in deuterium–helium with a small seeding born, D/³ He/¹¹B, is considered using a time dependent model based on nuclear reactions, including ion-electron collisions, Bremsstrahlung losses and mechanical expansion. The effect of the initial born concentration on ignition temperature and energy gain is analyzed with calculating the effect of radiation loss in ignition temperature.     

Estimate of fusion through bose degeneracy

An estimate is made of the fusion probability for an aggregate of D₂ molecules that have suffered bose degeneracy. A WKB analysis for the tunneling of deuterons through the electron intermolecular barrier gives the penetration rate $$R = (2E/h)\exp \left[ { - \frac{8}{3}\sqrt {\frac{{2mV_0 x_0^2 }}{\hbar }} \left( {1 - \frac{E}{{V_0 }}} \right)^{3/2} } \right]$$ In this expression,V ₀ andx ₀ are the potential barrier height and width, respectively, andE is the zero point energy of a deuteron in its ground molecular state. With molecules assumed effectively to be adjacent in the bose condensate, the number of fusion events per mole is found to be vanishingly small.     

The Essential Requirements of Transition to Non-equilibrium Burn Stage of DD Fuel in Simple Spherical Targets

In this research, the transition from equilibrium ignition to non-equilibrium burn is evaluated by calculating the energy balance equations analytically for targets which consist of inner DD fuel and surrounded by a high-Z pusher. It is expected that these targets can trap much of the produced charged particles, radiation or even fast neutrons because of their high-Z pusher. Accordingly, DD fuel can be ignited in volume ignition regime with low ignition temperatures of 35 keV compared to central ignition. Thus, to get a non-equilibrium burning stage, we have examined all the important gain and loss processes for these targets as the energy deposition of fusion products, thermal conduction, radiation flux, mechanical work, bremsstrahlung radiation and inverse Compton scattering as well as competition among them. These conditions have investigated for different areal densities of DD fuel in ρR?~?1–100 g/cm² and it is shown that as areal density rises, transition temperature decreases. But at high areal densities, the transition temperature does not vary significantly and the limiting temperature of ~?20 keV will be obtained. Also, transition into non-equilibrium burn is studied for such cases that thermonuclear burn occurs at stagnation moment, before and after that. It is observed that the positive and negative role of mechanical work on the transition conditions is very important and varies transition temperature remarkably. In all cases, transition temperature to non-equilibrium burn phase is always much lower than ideal ignition temperature in specific areal density.     

The Effect of Plasma Profiles on the Critical Value of $$n\uptau_{E}$$ for Ignition

The effect of plasma profiles for ignition condition in a stationary D–T plasma is investigated using the energy conservation equations for ions and electrons, assuming that steady state fusion power is produced with no external power. The alpha power heating is sufficiently large to sustain the plasma and to balance the combined Bremsstarhlung and thermal conduction losses. The space dependent Lawson criteria is derived and critical condition is identified. As a result of this analysis we have shown that the optimum temperature might be \(\bar{T} \approx 26\,{\text{keV}}\) and that the peaked profiles with \(n\sim\left( {1 - \frac{{r^{2} }}{{a^{2} }}} \right)^{{v_{n} }}\), ν _n  = 1, and \(T\sim\left( {1 - \frac{{r^{2} }}{{a^{2} }}} \right)^{{v_{T} }} ,\,v_{T} = 2\) are good to minimizing \(\bar{n}\uptau_{E}\) for ignition. The results for these profiles show the critical value of \((\bar{n}\uptau_{E} )_{min} = 0.08 \times 10^{20 } \,{\text{m}}^{ - 3} \,{\text{s}}\) showing the reduction by 1/3 from the reference value limit ν _n  = ν _T  = 0. For a 26 keV plasma with an energy confinement time of 1 s, a pressure of about 6.24 atm is required for the plasma to be ignited; that is, it is sustained purely by the self-heating of the fusion alpha particles.     

Grain growth kinetics in uranium-plutonium mixed oxides

Grain growth rates were investigated in uranium-plutonium mixed oxide specimens with oxygen-to-metal ratios 1.97 and 2.0. The specimens in the form of cylindrical pellets were heated in a temperature gradient similar to that existing in a fast reactor. The results are in agreement with the cubic rate law. The mean grain size D(μm) after annealing for time t (min) is represented by D³ − D₀³ = 1.11 × 10¹²·exp(−445870/RT)·t and D³ − D₀³ = 2.55 × 10⁹·exp (−319240/RT)·t for specimens with overall oxygen-to-metal ratios 1.97 and 2.0, respectively (activation energies expressed in J/mol). An example for the influence of the oxygen-to-metal ratio on the grain growth in mixed oxide fuel during operation in a fast reactor is also given.     

Surface bombardment rates for mirror fusion reactor designs

Arrival rates of D⁰, T⁰, D⁺, T⁺, He⁺⁺, neutrons, and photons are given for FERF (Fusion Engineering Research Facility, a mirror confinement reactor dedicated to materials research and to component testing), a hybrid fusion-fission reactor designed primarily to produce fissile fuel, and a D-T power reactor design. For comparison a next-generation confinement-mirror experiment called MX is included. The surfaces of interest are the first wall, the end wall, the direct converter and the injector.     

High dose He+ bombardment of niobium at 800° tO 1400°C

In proposed fusion reactors, the first wall will be bombarded by low energy D⁺, T⁺ and He⁺ ions to very high doses. Room temperature irradiations with 9 keV He⁺ (Roth et al. 1975) showed an initial phase of blistering between 0.05 and 0.25 C/ cm², and a final state of considerable surface roughness at 8 to 112 C/cm²(7 × 10²⁰He⁺/cm²). The present irradiation experiments with 6 keV He⁺ are carried out with polycrystalline Nb foils at temperatures between 800 and 1400°C in order to study the influence of He mobility and of Nb surface diffusion during irradiation. The applied doses range from 2.5 × 10¹⁷He⁺/cm² (blistering) to 5 × 10²⁰He⁺/cm² which corresponds to at least several weeks of reactor operation. The resulting changes of the niobium surface structures are observed by scanning electron microscopy and are pictorially presented in this paper. Mainly, sponge-like open structures are seen to develop at high doses, with increasing physical dimensions at higher temperatures.     

Magnetohydrodynamic Free Convective Flow Past an Infinite Vertical Porous Plate with Magnetic Induction

The steady two-dimensional magnetohydrodynamic free convective laminar flow of an electrically conducting, viscous and incompressible fluid with finite electrical conductivity past an infinite heated vertical porous plate has been investigated. The coupled ordinary differential equations governing the velocity, the temperature and induced magnetic field distributions are solved analytically. The effects of Prandtl number (P _r ), Grashof number (Gr), magnetic field parameter (M), and suction parameter ( $ \overline{V}_{0} $ ) on the flow field are analysed using graphs. The study reveals that the increase of the Prandtl number (Pr) and the suction velocity ( $ \overline{V}_{0} $ ) lead to a decrease in the temperature, velocity and the induced magnetic field in the boundary layer region whereas increase in Grashof number and magnetic field parameter lead to increased induced magnetic field.     

Investigation of Fuel Energy Gain for Tritium-Poor Fuels in Fast Ignition Fusion Approach

One of the most fascinating ignition schemes for the inertial fusion energy that might be feasible is fast ignition.Its targets are ignited on the outside surface so there is no need to low density and high temperature center is required by central hot spot ignition.Fast ignition concept is noteworthy for a simple but fundamental reason:In principle it requires less total energy input to achieve ignition.In this paper,fuel energy and fuel energy gain of nearly pure deuterium capsule are calculated.This capsule is ignited by a deuterium-tritium seed,which would reduce the tritium inventory to a few percentages.The variations of fuel energy gain versus fuel density have been studied and submitted.On the basis of different physical parameters the following results of the investigation are presented and discussed.The energy gain curves for different tritium concentrations are found and limiting gain curves are derived.Finally,tritium-poor fast ignitor is compared to equimolar deuterium-tritium fast ignitor.     

The effects of gas transport properties on blister formation in He+-implanted glass

Blister formation in He⁺-implanted glasses is correlated with the measured helium gas diffusivity. A scries of glasses with diffusivities from ～3 × 10^?7 to ～5 × 10^?12cm²sec^?1 was implanted under nearly identical conditions with 150 keV He⁺ ions at a flux of 15 μA cm^?2 and a nominal sample temperature of 110°C. Glasses with D less than ～1 × 10^?9cm²sec^?1 were fully blistered, whereas those with D greater than ～3 × 10^?8cm²sec^?1 showed no surface deformation. Glasses with diffusivities between ～3 × 10^?8 and ～1 × 10^?9cm²sec^?1 had local regions with low density coverage of relatively large blisters. The critical concentration of implanted helium, estimated by comparing experimental data with results from a simple theoretical model, is ^{～1 × 1019 cm?3}, consistent with high pressure solubility measurements. Reemission data at low fluence are qualitatively in agreement with analytical calculations. Implications for CTR technology are discussed.     

Online integrated visual inspection and sorting system for fast reactor fuels

Mixed oxide (MOX) fuel for prototype fast breeder reactor (PFBR) is designed to have initial burn up of 100,000 MWD/T. The major differences from thermal reactor fuel are relatively smaller dimension with central hole and higher plutonium concentration (21% and 28% of PuO₂) MOX pellets which are loaded into 2.5 m long clad tubes with depleted UO₂ blanket pellets at either end of the MOX stack. The relatively smaller dimension of fuel pellets for PFBR results in large volume at fabrication and inspection. To ensure fast and accurate inspection and sorting of as sintered pellets with less radiation exposure to personnel an integrated on line pellet inspection system for remote visual inspection and sorting of pellets based on diameter has been developed. Details of the integrated pellet inspection system developed at Advanced Fuel Fabrication Facility, Bhabha Atomic Research Centre, Tarapur along with the results of the performance trials has been described in this paper.     

Calcuiational Method for Neutron Heating in Dense Plasma Systems, (II)

Abstract

The effect of neutron heating on the burn characteristics of inertial confinement fusion pellets is investigated by applying the calcuiational method developed in an earlier paper (Part I). The basic equations are time-dependent transport equations for fusion neutrons and recoil ions, being written in terms of the modified Eulerian coordinates originally proposed by Wienke (1974). After incorporating these equations into the one-dimensional hydrodynamics code MEDUSA, burn simulations are made for isobaric D-T pellets models compressed to 1,000 times the liquid density. It is found that in reactor-grade pellets, the inclusion of neutron heating decreases the fuel gain from the values obtained by neglecting the neutron heating. Calculations neglecting the energy transport by recoil ions overestimate the neutron energy deposition to plasma ions. The energy spectrum of neutrons emitted out of a typical D-T burning pellet is also shown. These neutrons contain fast components whose energies reach more than 20MeV.     

The Potential of Fast Ignition and Related Experiments with a Petawatt Laser Facility

A model of energy gain induced by fast ignition of thermonuclear burn in compressed deuterium-tritium fuel, is used to show the potential for 300× gain with a driver energy of 1 MJ, if the National Ignition Facility (NIF) were to be adapted for fast ignition. The physics of fast ignition has been studied using a petawatt laser facility at the Lawrence Livermore National Laboratory. Laser plasma interaction in a preformed plasma on a solid target leads to relativistic self-focusing evidenced by x-ray images. Absorption of the laser radiation transfers energy to an intense source of relativistic electrons. Good conversion efficiency into a wide angular distribution is reported. Heating by the electrons in solid density CD₂ produces 0.5 to 1 keV temperature, inferred from the D-D thermo-nuclear neutron yield.     

Sputtering of materials by H+, D+, T+ and He+ Ions

The sputtering yields of various materials by H⁺, D⁺, T⁺, He⁺ ions were calculated using the theoretical dependence of sputtering yields on energy and ion mass and taking into account experimental sputtering yield values, whenever available, as measured for H⁺, D⁺, T⁺, He⁺ ions.     

Thermodynamics and Kinetics of Deuterium Absorption in Scandium System

Thermodynamic and kinetic characteristics of the Sc-D system are investigated as a complement to the earlier studies of the Sc-H system. A Sieverts apparatus is employed to conduct the measurements. The Sc-D system is characterized by two phase regions: the metal-rich and the deuteride phases. The equilibrium plateau relationships in the two-phase regions are determined from the Van’t Hoff plots and found to be: $ \ln P({\text{Pa)}} = {{\left( {-{\text{ 16374}}{\text{.48}} \pm{\text{188}}{\text{.88}}} \right)} \mathord{\left/ {\vphantom{{\left( {{\text{ - 16374}}{\text{.48}} \pm{\text{188}}{\text{.88}}} \right)} T}} \right.\kern-0em} T} + ({\text{23}}{\text{.56}} \pm{\text{0}}{\text{.18)}}$ _. The enthalpy and entropy of reaction are calculated to be (?136.14 ± 1.57) kJ mol^?1 D₂ and (?100.06 ± 1.50) J mol^?1 K^?1 D₂, respectively. From the relationship of ln[(P₀?P_f)/(P?P_f)] and time t, the reaction of the Sc-D system is confirmed to be a first-order reaction in the temperature range of 923–1,073 K. The temperature has a negative effect on the reaction rate (k_a), which decreases from 0.0717 to 0.0130 s^?1 with the temperature increasing from 923 to 1,073 K. In addition, a minus activation energy of (?93.87 ± 6.22) kJ.mol^?1 is acquired. However, once increasing temperature up to 1,123 K, the relationship of ln[(P₀?P_f)/(P?P_f)] and time t firstly satisfies an exponential equation of y = ?0.5471exp(?x/9.1879) + 0.00272. After 50 s, it begins fitting a linear equation again, indicating the various reaction mechanisms.     

The 11B(p,α)8Be?→?α?+?α and the 11B(α,α)11B Reactions at Energies Below 5.4?MeV

Measurements of the absolute cross section and angular distributions for the $^{11} \hbox{B}(p,\alpha)^{8}{\text{Be}}\rightarrow\alpha+\alpha$ and the ¹¹B(α,α)¹¹B reactions have been performed from 0.15 to 3.8?MeV for the ¹¹B(p,α) study and from 2 to 5.4?MeV for the ¹¹B(α,α) reaction. The absolute cross sections are presented in terms of the total number of α-particles detected in order to avoid uncertainties due to ambiguities in the number of alpha particles emitted in the reaction at a particular energy. The angular distributions of the ¹¹B(p,α)⁸Be(2⁺) reaction were fit to a Legendre polynomial expansion and the coefficients are presented. Finally, the ¹¹B(α,α)¹¹B data were fit in terms of phase shifts (ignoring the spin of the target), providing a convenient representation of the elastic cross section data between 2 and 5.4?MeV.     

Rydberg and autoionizing triplet states in Helium up to the N = 5 threshold

Energy levels of highly excited bound Rydberg states, the position and widths of autoionizing states, and oscillator strengths are calculated for He ³S, ³P^e, ³P^o, ³D^e and ³D^o symmetries up to the N = 5 He⁺ excitation threshold. The calculations are performed with the K-matrix B-spline method with maximum orbital angular momentum ?_max = 8. Reliable doubly excited-state parameters up to the n = 20 multiplet below each ionization threshold are presented. One thousand and six hundred newly identified bound and metastable states, seven times those available in literature, fill many gaps, reveal a dozen intruder states, and allow new speculations on propensity rules and radiative decays of triplet Rydberg states.     

Calculation of Internal Inductance and Poloidal Beta Using Solovev’s Assumption in a Circular Cross Section Tokamak

We calculated the internal inductance and the poloidal beta in a circular cross section Tokamak using Solov’ev assumption in the solution of Grad–Shafranov equation (GSE). GSE is solved by considering linear source functions and fixed boundary conditions. This solution has the three quantities (plasma current I _p , plasma minor radius r _p and $ \beta_{p} + l_{i} /2 $ ) that they are as input data. In two different discharges on IR-T1 Tokamak with this solution, we have shown that the internal inductance at a low value is required to extend the duration of Tokamak plasma discharge that it is consistence with other method.