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.     

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.     

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.     

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.     

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.     

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.     

On M1-transitions from highly excited states

This article is concerned with the probabilities of Mi-transitions from states created by the capture of thermal neutrons for even-odd and odd-odd emitting nuclei with A from 20 to 60. In the single-particle model, such transitions are forbidden with respect tol. A comparison with the probabilities of E1-transistions shows that in even-odd nuclei, the probabilities of forbidden Mi-transitions which we observed, did not differ much from the probabilities ofl-allowed M1-transitions for lighter nuclei.In the case of odd-odd nuclei, certain M1-transitions are characterized by a large number of quanta per single neutron capture and a large value of      

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.     

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.     

Numerical Experiments on Oxygen Plasma Focus: Scaling Laws of Soft X-Ray Yields

Numerical experiments have been investigated on UNU/ICTP PFF low energy plasma focus device with oxygen filling gas. In these numerical experiments, the temperature window of 119–260 eV has been used as a suitable temperature range for generating oxygen soft X-rays. The Lee model was applied to characterize the UNU/ICTP PFF plasma focus. The optimum soft X-ray yield (Y_sxr) was found to be 0.75 J, with the corresponding efficiency of about 0.03 % at pressure of 2.36 Torr and the end axial speed was v_a = 5 cm/μs. The practical optimum combination of p₀, z₀ and ‘a’ for oxygen Y_sxr was found to be 0.69 Torr, 4.8 cm and 2.366 cm respectively, with the outer radius b = 3.2 cm. This combination gives Y_sxr ~ 5 J, with the corresponding efficiency of about 0.16 %. Thus we expect to increase the oxygen Y_sxr of UNU/ICTP PFF, without changing the capacitor bank, merely by changing the electrode configuration and operating pressure. Scaling laws on oxygen soft X-ray yield, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found over the range from 1 kJ to 1 MJ. It was found that the oxygen soft X-ray yields scale well with $ {\text{Y}}_{\text{sxr}} = 2 \times 10^{ - 7} {\text{I}}_{\text{pinch}}^{3.45} $ and $ {\text{Y}}_{\text{sxr}} = 6 \times 10^{ - 7} {\text{I}}_{\text{peak}}^{ 2. 9 2} $ for the low inductance (L₀ = 30 nH) (where yields are in J and currents in kA). While the soft X-ray yield scaling laws in terms of storage energies were found to be as $ {\text{Y}}_{\text{sxr,O}} = 5.354 \times {\text{E}}_{0}^{1.12} $ (E₀ in kJ and Y_sxr in J) with the scaling showing gradual deterioration as E₀ rises over the range. The oxygen soft X-ray yield emitted from plasma focus is found to be about 8.7 kJ for storage energy of 1 MJ. The optimum efficiency for soft X-ray yield (1.1 %) is with capacitor bank energy of 120 kJ. This indicates that oxygen plasma focus is a good soft X-ray source when properly designed.     

Zero Flux Eigenvalues of Relaxed Axisymmetric Compact Tokamaks (CT’s)

Compact toroidal configuration is of simpler construction than the conventional tokamak and has important advantages due to the novel physics properties of low aspect ratio. In this paper we are developing a numerical program to study the magnetic dynamo or relaxation of CT’s characterized by arbitrary tight aspect ratio. It is shown that the numerical method (Collocation Method), used here, works quite well to calculate numerically the lowest zero flux eigenvalues μ of Taylor’s relaxed plasma state equation [(?)\vec] ×[(B)\vec] = m[(B)\vec] \vec{\nabla } \times \vec{B} = \mu \vec{B} for an axisymmetric tokamaks of circular cross section. An excellent fulfillment of the toroidal flux vanishing boundary condition \iint B_? \textdr\textdz = 0 \iint {B_{\emptyset } {\text{d}}r{\text{d}}z = 0} along the whole boundary for such tokamaks are achieved. Dependence of μ on the aspect ratio is also obtained. Several runs of the program for various wave numbers k showed that μ is very insensitive to the choice of k. Besides, the poloidal magnetic field topologies inside the tokamak are well represented.     

Spheromak Formation and Current Sustainment Using a Repetitively Pulsed Source

By repeated injection of magnetic helicity (K = 2φψ) on time-scales short compared with the dissipation time (τ_inj << τ _K ), it is possible to produce toroidal currents relevant to POP-level experiments. Here we discuss an effective injection rate, due to the expansion of a series of current sheets and their subsequent reconnection to form spheromaks and compression into a copper flux-conserving chamber. The benefits of repeated injection are that the usual limits to current amplification can be exceeded, and an efficient quasi-steady sustainment scenario is possible (within minimum impact on confinement). A new experiment designed to address the physics of pulsed formation and sustainment is described.     

Soft X-ray Emission Optimization Studies with Krypton and Xenon Gases in Plasma Focus Using Lee Model

The X-ray emission properties of krypton and xenon plasmas are numerically investigated using corona plasma equilibrium model. Numerical experiments have been investigated on various low energy plasma focus devices with Kr and Xe filling gases using Lee model. The Lee model was applied to characterize and to find the optimum combination of soft X-ray yields (Y_sxr) for krypton (~4 Å) and xenon (~3 Å) plasma focus. These combinations give Y_sxr = 0.018 J for krypton, and Y_sxr = 0.5 J for xenon. Scaling laws on Kr and Xe soft X-ray yields, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found over the range from 2.8 to 900 kJ. Soft X-ray yields scaling laws in terms of storage energies were found to be as $ {\text{Y}}_{{{\text{sxr}},{\text{Kr}}}} = 0.0003 \times {\text{E}}_{0}^{1.43} $ Y sxr , Kr = 0.0003 × E 0 1.43 and $ {\text{Y}}_{{{\text{sxr}},{\text{Xe}}}} = 0.0064 \times {\text{E}}_{0}^{1.41} $ Y sxr , Xe = 0.0064 × E 0 1.41 for Kr and Xe, respectively, (E₀ in kJ and Y_sxr in J) with the scaling showing gradual deterioration as E₀ rises over the range. The maximum soft X-ray yields are found to be about 0.5 and 27 J from krypton and xenon, respectively, for storage energy of 900 kJ. The optimum efficiencies for soft X-ray yields (0.0002 % for Kr) and (0.0047 % for Xe) are with capacitor bank energies of 67.5 and 225 kJ, respectively.     

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.     

Suppression of betatron oscillations in strong-focusing electron synchrotrons

Different methods are considered for obtaining radiation damping of synchrotron and betatron oscillations in a strong-focusing accelerator. Formulas are given for the calculation of the damping decrements. It is noted that the curvature of the orbits in the damping magnets must be different from the curvature in the main sectors. It is shown that the sum of damping decrements is the same in all cases and is independent of the type of damping system which is employed.     

Mode structure symmetry breaking of reversed shear Alfvén eigenmodes and its impact on the generation of parallel velocity asymmetries in energetic particle distribution

In this work, the gyrokinetic eigenvalue code LIGKA, the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of reversed shear Alfvén eigenmodes (RSAEs). Using the parameters from an ASDEX-Upgrade plasma, a benchmark with the three different physical models for RSAE without and with energetic particles (EPs) is carried out. Reasonable agreement has been found for the mode frequency and the growth rate. Mode structure symmetry breaking (MSSB) is observed when EPs are included, due to the EPs' non-perturbative effects. It is found that the MSSB properties are featured by a finite radial wave phase velocity, and the linear mode structure can be well described by an analytical complex Gaussian expression ${\rm{\Phi }}(s)={{\rm{e}}}^{-\sigma {\left(s-{s}_{0}\right)}^{2}}$ with complex parameters σ and s0, where s is the normalized radial coordinate. The mode structure is distorted in opposite manners when the EP drive shifted from one side of ${q}_{\min }$ to the other side, and specifically, a non-zero average radial wave number 〈ks〉 with opposite signs is generated. The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport. The parallel velocity of EPs is generated in opposite directions, due to different values of the average radial wave number 〈ks〉, corresponding to different initial EP density profiles with EP drive shifted away from the ${q}_{\min }$.     

Impact of Solid Breeder Materials on Tritium Breeding in a Hybrid Reactor

Tritium breeding ratio (TBR) is one of the important parameters in design of a Deuterium–Tritium (DT) driven hybrid reactor. Therefore, selection of tritium breeder materials to be used in the blanket is very crucial. In this study, tritium breeding potential of the solid breeders, namely, or in a (DT) fusion driven hybrid reactor fuelled with or was investigated. For this purpose in addition to these solid breeders, different types of liquid breeders, namely natural lithium, Flibe, Flinabe and were used to examine the tritium breeding behavior of liquid–solid breeder couple combinations. Numerical calculations were carried out by using Scale 4.3. According to numerical results, the blanket with fuel using natural lithium as coolant and as solid breeder had the highest TBR value.     

Measurement of the effective number of secondary neutrons from Pu239 in the incident neutron energy region from 7 to 30 ev

Measurements have been made of the energy dependence of the quantity (wherer is the average number of fast neutrons per fission event, _f is the fission cross section and _a is the absorption cross section) in Pu²³⁹ for the energy region ranging from 7 to 30 ev. A knowledge of this quantity is of interest both for practical reactor calculations and in the theory of nuclear fission. The measurements consist of counting the number of fast fission neutrons emitted from a sample of Pu²³⁹ with slow neutrons incident upon it. A higher resolving power in the neutron collector has made it possible to measure the ratio for the separate resonances. In this connection it is assumed thatv remains constant over the entire measurement region. From the data of the present work it is found that the fission widths of ten levels in Pu²³⁹ vary strongly from one to another and that they may be grouped.The authors are indebted to S. Ya. Nikitin for advice and continued interest in the present work.