Advantages of high-field tokamaks for fusion reactor development

High-field designs could reduce the cost and complexity of tokamak reactors. Moreover, the certainty of achieving required plasma performance could be increased. Strong Ohmic heating could eliminate or significantly decrease auxiliary heating power requirements and high values of n_E could be obtained in modest-size plasmas. Other potential advantages are reactor operation at modest values of , capability of higher power density and wall loading, and possibility of operation with advanced fuel mixtures. Present experimental results and basic scaling relations imply that the parameterB ²a, where B is the magnetic field and a is the minor radius, may be of special importance. A superhigh-field compact ignition experiment with very high values ofB ²a (e.g.,B ²a=150 T² m) has the potential of Ohmically heating to ignition. This short-pulse device would use inertially cooled copper plate magnets. Compact engineering test reactor and/or experimental hybrid reactor designs would use steady-state, water-cooled copper magnets and provide long-pulse operation. Design concepts are also described for demonstration/commercial reactors. These devices could use high-field superconducting magnets with 7–10 T at the plasma axis.     

Recent progress on the Tokamak Fusion Test Reactor

The deuterium-tritium (D-T) experiments on the Tokamak Fusion Test Reactor (TFTR) have yielded unique information on the confinement, heating and alpha particle physics of reactor scale D-T plasmas as well as the first experience with tritium handling and D-T neutron activation in an experimental environment. The D-T plasmas produced and studied in TFTR have peak fusion power of 10.7 MW with central fusion power densities of 2.8 MWm^–3 which is similar to the 1.7 MWm^–3 fusion power densities projected for 1,500 MW operation of the International Thermonuclear Experimental Reactor (ITER). Detailed alpha particle measurements have confirmed alpha confinement and heating of the D-T plasma by alpha particles as expected. Reversed shear, highl _i and internal barrier advanced tokamak operating modes have been produced in TFTR which have the potential to double the fusion power to 20 MW which would also allow the study of alpha particle effects under conditions very similar to those projected for ITER. TFTR is also investigating two new innovations, alpha channeling and controlled transport barriers, which have the potential to significantly improve the standard advanced tokamak.     

Lawson concepts and criticality in DT fusion reactors

The original Lawson concepts (amplification factorR and parametern as well as their applications in DT reactors are discussed in two cases: the ignition regime and the subignition regime in a self-sufficient plant. The modified Lawson factor or internal amplification factorR (a function of alpha power) is proposed as a means to measure the ignition level reached by the plasma, in a more precise way than that given by the collective parameter (nkT). The self-sufficiency factor () is proposed as a means to measure the plant self-sufficiency, being more significant than the traditionalQ factor. It is stated that the ignition regime (R =1) is equivalent to a critical state (energy equilibrium); then, the corresponding critical mass concept is proposed. The analysis of theR relationship with temperature (kT), (n), and recirculating factor () gives the conditions for the reactor to reach ignition or for the plant to reach self-sufficiency; it also shows that an approach to ignition is not improved by heating from 50 to 100 KeV.     

The impact of ripple on the design of advanced fuel tokamaks

Enhanced ion transport due to toroidal field ripple is a concern in the design of tokamak power reactors. This concern is quantified for advanced fuel cycle applications where the simultaneous requirement of highn and highT makes the constraint on deviation from axisymmetry especially severe.     

Calculating the transient temperature field in a reactor tube and the thermoelastic stresses in the fuel element cladding

Approximate analytic methods are given for calculating the transient temperature field in the fuel elements and the coolant temperatures at any point along the reactor tube, as well as the transient thermoelastic stresses in the cladding of a cylindrical fuel element. The coolant temperature at the input to the tube is constant, and the coolant undergoes no changes in state of aggregation. The approximate methods are illustrated by examples.Results are given, for comparison, of accurate calculations of the same examples made with a rapid calculating machine.List of symbols time - r; z coordinates (radius, distance along tube) - r₁; r₂ internal and external radii of fuel element cladding respectively - H total active length of fuel element - a₁; ₁;c _{1 1} coefficients of temperature conductivity, heat conductivity, specific heat capacity and specific gravity of fissionable material respectively - a₂; ₂; C_p2; ₂ cladding parameters - a; ; c_p; coolant parameters - mean cladding radius - f:f₂ cross-sectional area of tube for coolant and cladding respectively - w coolant velocity - coefficient of heat release to coolant - t (r, ); (); () fuel temperature, mean temperature over cross section of cladding, and coolant temperature at pointz. along tube respectively - qv() specific volume of coolant at pointz - values averaged overz - quantities at the initial instant of time - ₃ delay time - _n time required for coolant to go from z=0 to the point in question     

D-T experiments on TFTR

Temperatures, densities and confinement of deuterium plasmas confined in tokamaks have been achieved within the last decade that are approaching those required for a D-T reactor. As a result, the unique phenomena present in a D-T reactor plasma (D-T plasma confinement, alpha confinement, alpha heating and possible alpha driven instabilities) can now be studied in the laboratory. Recent experiments on the Tokamak Fusion Test Reactor (TFTR) have been the first magnetic fusion experiments to study plasmas with reactor fuel concentrations of tritium. The injection of 20 MW of tritium and 14 MW of deuterium neutral beams into the TFTR produced a plasma with a T/D density ratio of 1 and yielded a maximum fusion power of 9.2 MW. The fusion power density in the core of the plasma was 1.8 MW m^–3 approximating that expected in a D-T fusion reactor. In other experiments TFTR has produced 6.4 MJ of fusion energy in one pulse satisfying the original 1976 goal of producing 1 to 10 MJ of fusion energy per pulse. A TFTR plasma with T/D density ratio of 1 was found to have 20% higher energy confinement time than a comparable D plasma, indicating a confinement scaling with average ion mass, A, of _E. The core ion temperature increased from 30 keV to 37 keV due to a 35% improvement of ion thermal conductivity. Using the electron thermal conductivity from a comparable deuterium plasma, about 50% of the electron temperature increase from 9 keV to 10.6 keV can be attributed to electron heating by the alpha particles. At fusion power levels of 7.5 MW, fluctuations at the Toroidal Alfvén Eigenmode frequency were observed by the fluctuation diagnostics. However, no additional alpha loss due to the fluctuations was observed. These D-T experiments will continue over a broader range of parameters and higher power levels.Work supported by U.S. Department of Energy Contract No. DE-AC02-76-CHO-3073.     

Measuring the mean lifetime of thermal neutrons from a small specimen

The author describes a method of measuring the mean lifetime of thermal neutrons for specimens whose dimensions a r e commensurate with the thermal transport length. The method makes use of a pulsed neutron generator and is intended for determining for rocks by means of measurements on core samples. It can also be used to estimate the concentrations in rocks of elements with large thermal-neutron absorption cross sections.Translated from Atomnaya Énergiya, Vol. 22, No. 1, pp. 33–38, January, 1967.     

The dynamics of nuclear power stations

This paper makes a comparison of the results of eXperimental and theoretical studies that have been carried out on the properties of the engineering model of the Beloyarskii atomic electric station under construction in the USSR, which uses nuclear superheating of the steam. It is shown that a number of the simplifying assumptions are correct which are often used in discussing the dynamics of nuclear power stations.The results of the studies may be used to make a theoretical analysis of the dynamic properties of several types of nuclear power installations, as well as in analyzing and synthesizing the optimum control system.Notation q() specific heat load, referred to length of segment, kcal/hour · m - f(x) distribution function of specific heat load along the length of segment - () heat transfer coefficient, including the thermal resistence of the fuel element, kcal/m² · hour · degree - t_f.e. (x, ) the current value of fuel element temperature, averaged over the corss section, degrees C - t(x, t) current value of coolant temperature, degrees C - p perimeter of fuel element, bathed by coolant, m - m weight of metal per unit length of fuel element kg/m - C_M heat capacity of metal and fuel element, kcal/kg · degree - i(x, ) current value of heat content of coolant, kcal/kg - specific gravity of coolant, kg/m³ - S live cross section of fuel element, m² - D(x, ) current value of flow of steam phase, kg/hour - G(x, ) current value of the flow of water phase, kg/hour - (x, ) current value of the fraction of the cross section occupied by steam - , specific gravity of water and steam at saturation temperature, kg/m² - i, i heat content of water and steam at saturation temperature, kcal/kg - t_S() saturation temperature, degrees C - P_i() pressure in i-th segment, kg/m² - l height, determining the level pressure between segments, m - g acceleration of gravity, m/hour² - w_i() coolant velocity at the i-th segment, m/hour - D_i() steam flow at the i-th segment of the superheating circuit, kg/hour - V_i volume of i-th segment of the superheating circuit, m³ - mean steam temperature at the i-th segment for the superheating circuit, degrees C - k₁,k₂,k₃,k₄ constant coefficients - N/N₀ relative power change in the evaporating channels, % - P_I, P_II pressure change in the first and second loops, atm - t_sps, t_fw change in temperature of superheated steam and feed water, respectively, degrees C Translated from Atomnaya Énergiya, Vol. 15, No. 2, pp. 115–120, August, 1963     

Pulse method of measuring neutron age in graphite

Using a pulse source located within a prism, the age of thermal neutrons from the reactions D-D and D-T in graphite was measured. From the time dependence of the thermal neutron density the author calculated the effective age of D-D neutrons _eff = 355 ± 9 cm², recalculated for a graphite density equal to 1.6 g/cm³.The slowing down of D-T neutrons in graphite can be approximately expressed with the aid of two neutron groups: neutrons suffering but one inelastic collision when slowed down (_eff =600 cm²), and neutrons suffering several inelastic collisions (_eff = 240 cm²). In determining the age the relative contributions of both groups were assumed equal to 0.65 and 0.25, respectively. A third group is composed of neutrons slowed down only by means of elastic collisions. These neutrons may be neglected in the first approximation, since their contribution is small (about 0.1), while the increase is large.This work was carried out at the P. N. Lebedev Physics Institute of the Academy of Sciences of the USSR.In conclusion, the author expresses his gratitude to Corresponding Member of the Acad. of Sei. of the USSR I. M. Frank for suggesting the research topic, for his steadfast interest in the work, and for valuable remarks during the course of discussion.     

Slowing down of fission neutrons by water

In this articie we describe the method and results of measurement offor U²³⁵ fission neutrons slowed down by water to energies of 1.46 ev. The value obtained for _{1.46 ev} = 294 ± 1.5 cm² In conclusion, the authors express their sincere gratitude to I. I. Gurevich and D. V. Timoshuk for reviewing the results, to A. P. Venediktov for help in the work, and to G. R. Golbek for lending the -apparatus with low background.     

Dose characteristics of a mixture of uranium fission fragments

Results are presented for calculations for the different dose characteristics of fragment elements: the percentage composition of the mixture for a uranium exposure time t₀=100 days and a cooling off period =15–540 days, the time variation of the activity of the mixture for t₀, equal to 60, 100 and 150 days. The calculated data are in satisfactory agreement with the results of radiochemical analyses.The gamma constant of the mixture is essentially independent of t₀ (within the limits 60–150 days) and also remains approximately constant for values of ranging from 15–180 days.     

Techniques for measuring the alpha-particle distribution in magnetically confined plasmas

Methods are proposed for measuring the alpha-particle distribution in magnetically confined fusion plasmas using neutral-atom doping beams, ultraviolet spectroscopy, and neutral particle detectors. In the first method, single charge exchange reactions, A⁰+He²⁺A⁺ +(He⁺)^*, are used to populate then=2 andn=3 levels of He⁺. The ultraviolet photons from the decaying excited states are Doppler shifted by 5–10 Å from those produced by the thermalized alpha-particle ash. In the second method, double charge exchange reactions, A⁰+He²⁺A²⁺+He⁰, enable fast neutralized alpha particles to escape from the plasma and be detected by neutral particle analyzers. These methods are distinguished from similar techniques of observing plasma impurities in that, in principle, they allow a determination of the dependence of the distribution function on energy and pitch angle, as well as on spatial position. Detector configurations are analyzed, count rates are estimated, and the detector feasibility is discussed. A preliminary analysis of the feasibility of the required neutral beams is presented, and exploratory experiments on existing devices are suggested.     

A Review of Confinement Requirements for Advanced Fuels

The energy confinement requirements for burning D-³He, D-D, or P-¹¹B are reviewed, with particular attention to the effects of helium ash accumulation. It is concluded that the DT cycle will lead to the more compact and economic fusion power reactor. The substantially less demanding requirements for ignition in DT (the n_{e E} T required for ignition in DT is smaller than that of the nearest advanced fuel, D-³He, by a factor of 50) will allow ignition, or significant fusion gain, in a smaller device; while the higher fusion power density (the fusion power density in DT is higher than that of D-³He by a factor of 100 at the same plasma pressure) allows for a more compact and economic device at fixed fusion power.     

Start of the Experiment on the Absolute Calibration of Particle Energy in VÉPP-4M near the τ-Lepton Production Threshold

An experiment, using the new detector Kedr, on the precise measurement of the -lepton mass is being readied on the VÉPP-4M. The resonance depolarization method is used for absolute calibration of the particle energy. The main difficulty in using a polarized beam at the -lepton production threshold (1777 MeV) is the closeness of an integral spin resonance (1763 MeV). Experiments observing the polarization of particles in VÉPP-4M after injection of the polarized beam from the VÉPP-3 storage booster with different detunings from resonance have been performed. For comparison, the depolarization time of a beam due to quantum fluctuations in the presence of characteristic disturbances of the guiding field is calculated. The temporal stability of the energy indications is studied.     

Effecting the condition of quasistationary thermonuclear burning in tokamaks with a high plasma density

Conclusion The zero-dimensional analysis and the numerical calculations have shown that stable conditions of the thermonuclear burning in a tokamak with a high plasma density are achieved only when _E depends strongly upon the plasma temperature (_E – ^m, where m<–2). Since in the experiments the retention laws have a significantly weaker temperature dependence, special measures are required for obtaining stable burning. Such conditions are reached by introducing feedbacks over, say, the plasma temperature and the rate of plasma-temperature change. It was shown in the present work that the corresponding regulation parameters are on the 0.3–0.5 level. Feedback can be obtained by, say, relaying operation of the source of additional heating.Translated from Atomnaya Énergiya, Vol. 63, No. 2, pp. 147–148, August, 1987.     

Compact ignition test reactor (CITR)

Design considerations have been developed for a compact ignition test reactor (CITR). The objectives of this tokamak device are to achieve ignition, to study the characteristics of plasmas that are self-heated by alpha particles, and to investigate burn control. To achieve a compact design, the toroidal field magnet consists of copper-stainless steel plates to accommodate relatively high stresses; it is inertially cooled by liquid nitrogen. No neutron shielding is provided between the plasma and the toroidal field magnet. The flat-top of the toroidal field magnet is 10 s. Strong auxiliary heating is employed. In one design option, adiabatic compression in major radius is employed to reduce the neutral beam energy required for adequate penetration; thiscompression boosted design option has a horizontally elongated vacuum chamber; illustrative parameters are a compressed plasma witha=0.50 m, R=1.35 m,B _T =9.1 T, and a neutral beam power of 15 MW of 160 keVD ⁰ beams. A design option has also been developed for alarge bore device, which utilizes a circular vacuum chamber. Thelarge bore design provides increased margin and flexibility; both direct heating with RF or neutral beam injection and compression boosted startup are possible. The large bore design also facilitates the investigation of high-Q driven operation. Illustrative plasma parameters for full use of the large bore area=0.85 m,R=1.90 m, andB _T =7.5 T.     

Requirements for ohmic ignition

An analysis of ohmic ignition criteria is presented, giving the requirements onT, n, andn/j in a form easily applicable to various confinement assumptions. For circular cross-section NeoAlcator tokamaks with Spitzer resistivity, a value ofB ₂ a approximately equal to 250 T²m is required. The outstanding uncertainties in schemes to lower this value are how much increase in current density is achievable by plasma shaping and what the exact NeoAlcator coefficient is.     

3D Wave Propagation and an Ultra–Low-Frequency Instability in Magnetopause

A model set of equations for the low-frequency electromagnetic perturbations in a magnetized nonuniform plasma is presented. A more convenient and systematic procedure is suggested to treat the fluid equations in order to deduce electrostatic and electromagnetic limits. A general dispersion relation is derived for the waves propagating in 3D under local approximation in nonuniform plasmas, which includes almost all the known modes of cold ion magnetized plasmas in the limit < _i (where _i is the ion cyclotron frequency). Both the limits 1 and O(1) have been discussed briefly. The shear Alfvén waves and electromagnetic ion acoustic waves near ultra low frequency (ULF) range are found unstable in the high plasma of magnetopause. The results are in complete agreement with the satellite observations.     

Methods for preparing ions of short-lived isotopes

Conclusions A source with thermal ionization in a cavity is extremely convenient for obtaining ion beams with an ultralow quantity of the starting material. Its efficiency with ionization potentials of the starting atoms V_i<6 eV is equal to 100% and drops to 1% for V_i=8 eV [7]. This makes it possible to use it in the study or more than two-thirds of the periodic system of elements, including the actinides. Thus for 10¹² uranium and plutonium atoms ^*9% and 50%, respectively; for 10⁶ curium atoms ^*70%; and, for 10⁵ californium atoms ^*37% [13]. It was shown in [14] that this source can be successfully used in mass spectroscopy to analyze trace quantities of different elements in the solid phase. With its help yttrium isotopes with _1/2=0.4 sec were detected in [16].This source is now widely used in our country, where with its help tens of new isotopes have been discovered [15, 17], and abroad (for example, [16]). The source is effective for short-lived isotopes with _i/_1/2<10 and V_i<7 eV. To study isotopes with _i/_1/2<10 and V_i>7 eV but with _i/_1/2>10 it is desirable to develop sources with thermal and photoionization in the cavity. For elements whose atoms have a long residence time on the surface, these sources, just as the gas-discharge sources, are inefficient. Means must be developed for raising the rate of desorption of the indicated atoms from the surface within the framework of the techniques examined here.Translated from Atomnaya Énergiya, Vol. 60, No. 2, pp. 114–119, February, 1986.     

Lessons learned from recent D-3He tokamak power reactor studies

Conclusions In conclusion, the advantages of the D-³He fuel cycle are compelling but the challenges are great. The economics of a fusion power plant with a permanent first wall, especially in terms of availability and reliability, should translate into an attractive future option for society. The safety and environmental features of this type of power could make this energy source irresistible for a world choked by pollution and racked with wars over the remaining scraps of fossil fuel energy. These advantages will not come free; the physics in terms of highernT, larger plasma currents, ash removal requirements, and the need to use fuel from settlements on the Moon (which should be in place long before we need³He for power reactors) are all problems that need to be solve in the next 20 years. The benefits to mankind surely will overweigh these latter problems and the nation, or nations who develop this energy source will have an important strategic advantage in the twenty-first century.