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.     

Nuclear multiplets in light odd-odd nuclei and their manifestation in γ-transitions occuring after thermal neutron capture

We consider those states of odd-odd nuclei with A < 60 which differ in their total angular momentum J, but whose configurations contain an odd proton and an odd neutron with given angular momenta j_p and j_n. We review the experimental data on the basis of which one may assume the existence of such nuclear multiplets lying close to the ground states. We compare the γ-decay schemes of those states of even-odd (odd neutron) and odd-odd nuclei with A < 60 which arise as a result of the capture of thermal neutrons. The characteristics of γ-transitions in odd-odd nuclei are explained on the basis of multiplet concepts.     

Accelerators with similar orbits

We obtain the conditions that must be satisfied by a magnetic system in order that the frequencies of radial and vertical betatron oscillations be independent of the particle momenta (in this case the orbits are called dynamically similar). In such systems mere should in principle be no excitation of betatron oscillations associated with synchrotron oscillations and other phenomena. A magnetic field with n₀ = const produces both geometric and dynamic similarity of the orbit. In weak-focusing accelerators with segments (race tracks) and in strong-focusing proton synchrotrons, the orbits are not dynamically similar. In order to obtain this kind of similarity in the first case, in addition to n₀ = const it is necessary that the magnet sectors have a common center. Different types of annular synchrocyclotrons are considered. In the first type the centers of neighboring magnet sectors are located on different sides of the doughnut and in the second type at the same point (at the center of the accelerator). In the second type the orbits are dynamically similar, unlike those of the first. It is shown mat it is possible to design an annular synchrocyclotron in which the particles can move with stability simultaneously in both directions within the doughnut.     

Chemical potential of oxygen of UO2 close to stoichiometry

Conclusions A closed solid electrolyte cell, permitting reliable values of to be obtained up to –775 kJ/mole, using a ceramic oxygen pump of stabilized ZrO₂, was developed. The temperature dependence of of uranium dioxide was determined for O/U=2.0039; 2.0021; 2.0018; 2.0012; 2.0009, and 2.0006. Coulometric titration of uranium dioxide was performed in the range of O/U from 2.0039 to 1.9991, and the influence of the degree of nonstoichiometry on was studied at 1273°K. A very strong dependence of at 1273°K was demonstrated in the range of O/U from 2.0001 to 1.9999. A change in O/U by 0.01% causes a 70% decrease in .Translated from Atomnaya Énergiya, Vol. 51, No. 4, pp. 228–230, October, 1981.     

Dosimetry method for β radiation based on investigations of the electron spectra in the fields of β emitters

A method has been developed for -ray dosimetry based on the investigation of the effective electron spectra in the fields of emitters. The spectra was investigated with the help of a scintillation spectrometer. It was shown, that the value of the dose , where N is the number of particles penetrating an infinitesimal volume around the point being considered; is the value of the ionization loss averaged over the spectrum. It was established that the quantity is determined by the maximum energy of the spectrum of the isotope and may be considered to be independent of the depth of the medium and of the source diameter. Curves of depth doses for S³⁵, Tl²⁰⁴, Y⁹¹, and Ce¹⁴⁴ + Pr¹⁴⁴ are given and criteria for selecting isotopes to provide optimal conditions of irradiation are established.     

Pulsational characteristics of two-cassette model of boiling-water reactor

Conclusions On a large-scale two-cassette model of the natural-circulation loop of a reactor with vertical dimensions and reduced hydraulic-drag coefficients of the basic loop elements that are close to the full-scale values, an experimental investigation has been conducted, with the following conclusions:With design parameters of the heat carrier, the specific thermal stress of the fuel elements, and the discrepancy coefficients of the pile power, the zone of hydrodynamic instability is characterized by the values ; liquidation of total-loop pulsations of the heat-carrier flow rate entails vapor condensation under the water level in the reactor; total liquidation of the pulsations requires, in addition, the introduction of disks at the input to each pile; the reduced hydraulic-drag coefficient _re of the disk must be no less than 0.8 of the sum of _re for the pile and the ITS.Translated from Atomnaya Énergiya, Vol. 69, No. 2, pp. 87–92, August, 1990.     

Nuclear information obtainable from low energy neutron spectroscopy

The results of measurements of thermal-neutron cross sections, level distributions in the resonance region, ratios, and determinations of the effective nuclear radius from potential:.scattering of slow neutrons are considered.A discrepancy in the results of measurements of the thermal-neutron fission cross secticn in U²³⁵ is noted. The distribution of levels exhibits a deficiency in small spacings as compared with a random distribution, i. e., there seems to be a repulsion of levels. The dependence of on atomic number A is nonmonotonic, in accordance with the complex-potential model of the nucleus; however there is a considerable discrepancy between the experimental data and theory for atomic numbers in the neighborhood of 100. The effective radius determined from potential scattering of slow neutrons indicates a nonmonotonic dependence on A, in agreement with the model of a semi-transparent nucleus with smeared-out edges.     

Effect of Various Parameters on Edge Plasma Stability in IR-T1 Tokamak

Edge plasma turbulence was investigated over a wide range of plasma and field parameters in the IR-T1 tokamak for the first time. Fluctuation levels and spectra were measured using two arrays of Langmuir probe in the region r/a = 0.75–1.2. Under almost all conditions the edge plasma was turbulently unstable, with a broadband fluctuation spectrum in the drift wave range of frequencies f = 10–1000 kHz. A stable state was observed only in the very cold, low-current discharge formed at unusually high neutral filling pressure. Otherwise, the relative fluctuation level as monitored by the ion saturation current was very high, in the range $ {{\tilde{\rm J}^{ + } } \mathord{\left/ {\vphantom {{\tilde{\rm J}^{ + } } {\bar{\rm J}^{ + } }}} \right. \kern-0pt} {\bar{\rm J}^{ + } }} \cong 0.2{-}0.8 $ , while the fluctuation power spectra were roughly invariant in shape. The relative fluctuation level was always highest near the wall and decreased monotonically toward the plasma centre.     

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.     

Use of perturbation theory in investigating the engineering and physical characteristics of nuclear power plants

Conclusions and recommendations Thus, the use of perturbation theory allows an economical, searchless, computation procedure to be constructed for the problem of parametric identification. The method may be extended to the case of a multidimensional model with nonlinear and nonsteady operators.At high noise levels of the experimental signal, a functional that is more conservative with respect to noise is preferable, in the form , for which perturbation theory is constructed analogously, under the condition P_j=1. Here also, z^e and y^e may be taken in the form of the results of statistical measurements R_zz and R_zy, i.e., the self- and mutual correlations of the noise functions of these signals, respectively.The perturbation formulas in Eqs. (6) and (9) are useful for the engineering diagnostics of NPP elements performed on the basis of an analysis of slow variations over time in the parametersa _i . In this case, identification by the given algorithm must be repeated periodically in the course of NPP running tests or use.Translated from Atomnaya Énergiya, Vol. 48, No. 4, pp. 238–242, April, 1980.     

Scaling Laws of Nitrogen Soft X-ray Yields from 1 to 200 kJ Plasma Focus

Numerical experiments are carried out systematically to determine the nitrogen soft X-ray yield for optimized nitrogen plasma focus with storage energy E₀ from 1 to 200 kJ. Scaling laws on nitrogen soft X-ray yield, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found. It was found that the nitrogen X-ray yields scales on average with $ {\text{Y}}_{\text{sxr,N}} = 1.93 \times {\text{E}}_{0}^{1.21} {\text{J}} $ (E₀ in kJ) with the scaling showing gradual deterioration as E₀ rises over the range. A more robust scaling is $ {\text{Y}}_{\text{sxr}} = 8 \times 10^{ - 8} {\text{I}}_{\text{pinch}}^{3.38} $ . The optimum nitrogen soft X-ray yield emitted from plasma focus is found to be about 1 kJ for storage energy of 200 kJ. This indicates that nitrogen plasma focus is a good water-window soft X-ray source when properly designed.     

Simulation of nuclear-fuel solvent-extraction reprocessing 7. Separation of macroscopic amounts of plutonium and uranium by displacement reextraction of plutonium in reprocessing fast-reactor fuel (section 1)

Conclusions These data have been obtained from simulating displacement reextraction in a system with two inputs (system for reprocessing a fast-reactor fuel), and they show that it is possible to obtain a uranium extract with not more than 100 g Pu/kg U in a counter current system with 18 stages to provide partial separation of the uranium and plutonium by reprocessing of an organic solution containing U⁺ Pu (10 1) with 64% saturation in the sum of the metals to produce reextract containing plutonium with U : Pu3 and over 99.99% extraction of the uranium; this requires 90 g/liter of uranium in the reextractant and the parameters n=2.06–2.00 ( =0.3 M); n=1.82–1.87 ( =0.5 M); n=1.61–1.78 ( =1.0 M).Full data obtained from the simulation are to be found in [5], from which one can extract the parameters of the working state of the extractor and other data on the separation of uranium and plutonium, e.g., for other specifications for the plutonium level in the uranium. The next part of the present study will be concerned with engineering solutions that can extend the range of conditions that provide the appropriate output parameters within specified ranges and thereby improve the reliability in operating the process in the optimal region.Translated from Atomnaya Énergiya, Vol. 47, No. 6, pp. 377–381, December, 1979.     

Polarographic investigation of complex plutonium oxalates

The composition and stability of complex ions of tri- and tetravalent plutonium in oxalate solutions were investigated polarographically. The complexes Pu(C₂O₄)₄ ^?4 (preponderant amount) and Pu (C₂O₄)₄ ^?5 were formed in solutions of potassium oxalate with pH 3.5–6. Under these conditions, Pu⁺⁴ gave a well expressed reverse reaction wave, suitable for the quantitative polarographic determination of plutonium. The oxidation-reduction potential of this reaction in 1 M potassium oxalate was equal to 0.205 v (relative to a saturated calomel electrode at a temperature of 25 ° C). Two Pu⁺⁴ complexes were simultaneously present in solutions at pH 6–8. From data on the solubility of Pu(C₂O₄)₃, we determined the instability constants of the complex oxalate ions Pu(C₂O₄)₃ ^?3 and Pu(C₂O₄)₄ ^?5, and from the polarographic data those forPu(C₂O₄)₄ ^?4 ions:

$$K_{Pu(C_2 O_4 )_4 ^{ - 3} } = 2.4 \cdot 10^{ - 12} .K_{Pu(C_2 O_4 )_3 ^{ - 3} } = 2.2 \cdot 10^{ - 11} .K_{Pu(C_2 O_4 )_4 ^{ - 4} } = 33 \cdot 10^{ - 23} $$     

Density Profiles in the Levitated Dipole Experiment

A multi-chord interferometer (center frequency 60 GHz) has been constructed to measure the electron density profiles of plasmas in the Levitated Dipole Experiment (LDX). Theoretical considerations suggest that the density of a dipole-confined plasma will vary with radius as 1/r ⁴. Measurements have been made for LDX plasmas, where the dipole-field was produced by a coil that was not levitating but rather suspended from a central column by thin supports. A ray-tracing code has been written to fit the chord data, which are line-integrated densities, to azimuthally-symmetric electron density profiles n _e (r, t). Initial analysis has focused on the model , where A(t) and α(t) are free parameters; α(t) is referred to as the “steepness exponent.” The density profiles are observed to exhibit dynamics due to ECR heating and neutral-gas fueling. The model-fit, meant only to serve as a rough approximation, suggests that LDX plasmas have steepness exponents in the range of 1.5–4. The density at the location of the 2.45 GHz ECRH resonance is reconstructed and found to be of the same order of magnitude as the heating cut-off .     

Deformation systems of α-zirconium

The deformation systems of -zirconium iodide have been studied in coarse-grained polycrystalline specimens deformed by upsetting. The orientation of the grains was determined from Laue patterns obtained in a special back-reflection camera using a small-diameter beam. The indices of the deformation systems were determined by the two-surface method and by the pole locus method.It was found that -zirconium is deformed by slip along the plane in the direction and along the plane. A number of twinning systems have been discovered In -zirconium: a) K₁ , 1 , K₁ , ₂ and s=0.173; b) K₁ , ₂ [1126], K₂ (0001), ₂ [1120] and s=0.629; c) K₁ (1122), ₁ [1123] and in one case, d) K₁ , ₁ .     

Accelerators with similar orbits

We obtain the conditions that must be satisfied by a magnetic system in order that the frequencies of radial and vertical betatron oscillations be independent of the particle momenta (in this case the orbits are called dynamically similar). In such systems mere should in principle be no excitation of betatron oscillations associated with synchrotron oscillations and other phenomena. A magnetic field\(H_0 \left( {\theta } \right)\left( {{{r_0 } \mathord{\left/ {\vphantom {{r_0 } r}} \right. \kern-\nulldelimiterspace} r}} \right)^{\Pi _0 } \) with n₀ = const produces both geometric and dynamic similarity of the orbit. In weak-focusing accelerators with segments (race tracks) and in strong-focusing proton synchrotrons, the orbits are not dynamically similar. In order to obtain this kind of similarity in the first case, in addition to n₀ = const it is necessary that the magnet sectors have a common center. Different types of annular synchrocyclotrons are considered. In the first type the centers of neighboring magnet sectors are located on different sides of the doughnut and in the second type at the same point (at the center of the accelerator). In the second type the orbits are dynamically similar, unlike those of the first. It is shown mat it is possible to design an annular synchrocyclotron in which the particles can move with stability simultaneously in both directions within the doughnut.     

Dependence of Plasma Focus Argon Soft X-Ray Yield on Storage Energy, Total and Pinch Currents

Numerical experiments are carried out systematically to determine the argon soft X-Ray yield Y_sxr for optimized argon plasma focus with storage energy E₀ from 1 kJ to 1 MJ. The ratio c = b/a, of outer to inner radii; and the operating voltage V₀ are kept constant. E₀ is varied by changing the capacitance C₀. These numerical experiments were investigated on argon plasma focus at different operational gas pressures (0.41, 0.75, 1, 1.5, 2.5 and 3 Torr) for two different values of static inductance L₀ (270 and 10 nH). Scaling laws on argon soft X-Ray yield, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found. It was found that the argon X-ray yields scale well with \textY_\textsxr = 8 ×10 ^{- 11} \textI_\textpinch^4.12 {\text{Y}}_{\text{sxr}} = 8 \times 10^{ - 11} {\text{I}}_{\text{pinch}}^{4.12} for the high inductance (270 nH) and \textY_\textsxr = 7 ×10 ^{- 13} \textI_\textpinch^4.94 {\text{Y}}_{\text{sxr}} = 7 \times 10^{ - 13} {\text{I}}_{\text{pinch}}^{4.94} for the low inductance (10 nH), (where yields are in joules and current in kilo amperes). While the soft X-ray yield scaling laws in terms of storage energies were found to be as \textY_\textsxr = 0.05 ×\textE₀^0.94 {\text{Y}}_{\text{sxr}} = 0.05 \times {\text{E}}_{0}^{0.94} at energies in the 1–100 kJ region. The scaling ‘drops’ as E₀ is increased, and Y_sxr scales as \textY_\textsxr = 1.01 ×\textE₀^0.33 {\text{Y}}_{\text{sxr}} = 1.01 \times {\text{E}}_{0}^{0.33} at high energies towards 1 MJ for 10 nH at argon gas pressure of 1 Torr. The optimum efficiencies for SXR yield were found to be 0.00077% with a capacitor bank energy of 112.5 kJ for high inductance (270 nH) and 0.005% with a capacitor bank energy of 4.5 kJ for low inductance (10 nH). Therefore for larger devices, it may be necessary to operate at a higher voltage and use higher driver impedance to ensure increasing X-ray yield efficiency beyond the optimum values. As storage energy is changed the required electrode geometry for optimum yield is obtained and the resultant plasma pinch parameters are found. Required values of axial speed for argon soft X-ray emission were found to be in the range 11–14 cm/μs.