Showing papers in "Nuclear Fusion in 1979"
TL;DR: A summary of the present status of research on plasma-surface interactions in tokamaks is given in this paper, where three groups of important interactions are considered: recycling of the principal ion species, usually hydrogen or deuterium; the release and effect of low-Z contaminants; and the release/effect of high Z contaminants.
Abstract: A summary is given of the present status of research on plasma-surface interactions in tokamaks. Three groups of important interactions are considered: recycling of the principal ion species, usually hydrogen or deuterium; the release and effect of low-Z contaminants; and the release and effect of high-Z contaminants. In each case the basic physical processes are reviewed and the relevant data from particlebeam measurements are summarized. Emphasis is given to discussing the effect of the various surface interactions in present-day tokamak discharges and in future fusion reactors. Surface studies in tokamaks are reviewed and methods of controlling the surface interactions and their effects are considered.
455 citations
TL;DR: In this article, an optimal force-free spherical plasma configuration was analyzed for its MHD stability properties, and it was shown that the spherical ellipse with = k (k independent of ) should be stable against all magnetically driven MHD and resistive tearing modes if surrounded by a conducting wall at about rw/r0 = 1.15.
Abstract: The 'Spheromak', an optimal force-free spherical plasma configuration, is analysed for its MHD stability properties. It is shown that flattened ellipse (oblimak) with = k (k independent of ) should be stable against all magnetically driven MHD and resistive tearing modes if surrounded by a conducting wall at about rw/r0 = 1.15. β's of at least 2% can be stably confined, equivalent to 20% in tokamaks.
326 citations
TL;DR: Experimental and theoretical studies of runaway electrons in toroidal devices are reviewed in this article, with particular reference to tokamaks, and the complex phenomenology of runaway effects, which have been the subject of research for the past twenty years, is organized within the framework of a number of physical models.
Abstract: Experimental and theoretical studies of runaway electrons in toroidal devices are reviewed here, with particular reference to tokamaks. The complex phenomenology of runaway effects, which have been the subject of research for the past twenty years, is organized within the framework of a number of physical models. The mechanisms and rates for runaway production are discussed first, followed by sections on runaway-driven kinetic relaxation processes and runaway orbit confinement. Next, the equilibrium and stability of runaway-dominated discharges are reviewed. Models for runaway production at early times in the discharge and the scaling of runaway phenomena to larger devices are also discussed. Finally, detection techniques and possible applications of runaways are mentioned.
305 citations
TL;DR: In this paper, an analytical theory of ideal-MHD ballooning modes that can be excited in finite-β equilibria is carried out on model configurations which include the effects of the increase of the poloidal field toward the outer edge of the plasma column and the dependence of the rate of magnetic shear on the polar angle.
Abstract: An analytical theory of ideal-MHD ballooning modes that can be excited in finite-β equilibria is carried out on model configurations which include the effects of the increase of the poloidal field toward the outer edge of the plasma column and the dependence of the rate of magnetic shear on the poloidal angle. The relevant growth rates and eigensolutions are, in fact, significantly different from those derived on the basis of 'low-β' model configurations that omit one or both of the effects mentioned above, and provide different indications for the expected interaction between ideal-MHD and kinetic modes. For each value of the shear parameter , the normalized growth rate Γ becomes real at a critical value of the dimensionless pressure gradient parameter G. When the latter is increased at constant , Γ is found to increase only up to a saturation point, after which it decreases and tends to vanish at a second critical value of G.
120 citations
TL;DR: In this article, a model for the rate of density rise observed when neutral gas is fed into a plasma-containing chamber is presented for regimes where known collisional transport processes do not provide an adequate explanation.
Abstract: A model for the rate of density rise observed when neutral gas is fed into a plasma-containing chamber is presented for regimes where known collisional transport processes do not provide an adequate explanation. A dense layer of cold plasma produced at the edge of the plasma column and the resulting relatively sharp ion temperature gradient, as compared with the local density gradient, can lead to the excitation of electron temperature fluctuations driven by ion drift modes. The net inflow of electrons and ions that is produced by these modes has been included in a one-dimensional transport code used to simulate experiments performed by the Alcator device. The linear and quasi-linear theories of these modes are given for the regimes of interest. The cold-plasma-layer model is also consistent with the presence of an outflow of impurity ions, due to impurity driven modes, that balance the inflow produced by discrete collisions.
107 citations
TL;DR: Guiding-centre trajectories in non-circular axisymmetric tokamak plasmas are studied in this article, where it is shown that the existence of an absolute minimum B in the higher- (7.7%) equilibrium results in an orbit topology dramatically different from that of the lower case.
Abstract: Guiding-centre orbits in non-circular axisymmetric tokamak plasmas are studied in the constants of motion (COM) space of (v, ζ, ψm. Here, v is the particle speed, ζ is the pitch angle with respect to the parallel equilibrium current, J||, at the point in the orbit where ψ = ψm, and ψm is the maximum value of the poloidal flux function (increasing from the magnetic axis) along the guiding-centre orbit. Two D-shaped equilibria in a flux-conserving tokamak having values of 1.3% and 7.7% are used as examples. In this space, each confined orbit corresponds to one and only one point, and different types of orbit (e.g. circulating, trapped, stagnation and pinch orbits) are represented by separate regions or surfaces in the space. It is also shown that the existence of an absolute minimum B in the higher- (7.7%) equilibrium results in an orbit topology dramatically different from that of the lower- case. The differences indicate the confinement of additional high-energy (v → c, within the guiding-centre approximation), trapped, co- and counter-circulating particles, with an orbit ψm falling within the absolute B-well.
99 citations
TL;DR: In this paper, the scaling with geometrical quantities including aspect ratio, elongation, and triangularity in the parameter regimes appropriate to both current and reactor-sized plasmas was investigated.
Abstract: Extensive numerical studies of ideal-MHD instabilities have been carried out to gain insight into the parametric dependence of critical β's in tokamaks. The large number of interrelated equilibrium quantities involved in establishing a critical β has demanded a careful, systematic survey in order to isolate this dependence. The results of this survey establish the scaling with geometrical quantities including aspect ratio, elongation, and triangularity in the parameter regimes appropriate to both current and reactor-sized plasmas. A moderate dependence on the pressure profile and a strong variation with the current profile is found. The principal result is that, for aspect ratio R/a ≈ 3, critical β's are of the order of 2% for circular cross-sections and 5% for plasmas with elongation K ≈2; somewhat higher values could be achieved with more optimal shaping. Finally, sequences of equilibria have been analysed to compare critical β as a function of toroidal mode number n. It is concluded that the infinite-n analytic ballooning theory provides a sufficient condition for ideal-MHD internal-mode stability. Low-n free-boundary modes appear to set a lower limit.
90 citations
TL;DR: In this paper, it was shown that a relatively weak initial shock introduced into an otherwise isentropic hollowshell implosion can cause central fuel ignition, the bulk of the fuel undergoing little increase in entropy.
Abstract: It is shown that a relatively weak initial shock introduced into an otherwise isentropic hollowshell implosion can cause central fuel ignition, the bulk of the fuel undergoing little increase in entropy. The imploded-state fuel configuration is analysed at the threshold of ignition, and it is found that electron heat conduction is the predominant cooling mechanism opposing fuel ignition. Approximate temperature-dependent ρR requirements are presented for the conduction-limited ignition of thin DT shells, and for the equality of electron heat conduction and α-particle transport in thermonuclear burn propagation.
89 citations
TL;DR: In this article, a number of new methods are discussed for determining the electron heat conduction coefficient χe in a tokamak from the experimental observation of the space-time evolution of the temperature perturbations induced by internal disruptions.
Abstract: A number of new methods are discussed for determining the electron heat conduction coefficient χe in a tokamak from the experimental observation of the space-time evolution of the temperature perturbations induced by internal disruptions. In the Oak Ridge Tokamak (ORMAK) the various average values of χe and the radial dependence of χe are found to be consistent with and more precise than the χe(r) determined by conventionally analysing the electron power balance equation. The net result of these measurements is to conclusively prove that the dominant radial electron heat transport mechanism in tokamaks is a microscopic, diffusive process.
85 citations
TL;DR: In this paper, a low-Z impurity transport in tokamaks was simulated with a one-dimensional impure transport model including both neoclassical and anomalous transports.
Abstract: Low-Z impurity transport in tokamaks was simulated with a one-dimensional impurity transport model including both neoclassical and anomalous transports. The neoclassical fluxes are due to collisions between the background plasma and impurity ions as well as to collisions between the various ionization states. The evaluation of the neoclassical fluxes takes into account the different collisionality regimes of the background plasma and the impurity ions. A limiter scrape-off model is used to define the boundary condition for the impurity ions in the plasma periphery. To account for the spectroscopic measurements of power radiated by the lower ionization states, fluxes due to anomalous transport are included. The sensitivities of the results to uncertainties in rate coefficients and plasma parameters in the periphery are investigated. The implications of the transport model for spectroscopic evaluation of impurity concentrations, impurity fluxes, and radiated power from line emission measurements are discussed.
80 citations
TL;DR: In this article, the effect of toroidal modulation of shear or magnetic field on drift wave propagation was investigated by using a two-dimensional model representing long-wavelength drift waves in a large-aspect-ratio tokamak.
Abstract: In a uniform plane slab, with shear in the magnetic field, damping of drift waves is due to the outward convection of energy by the wave. It is known, however, that the inclusion of two-dimensional effects, such as toroidal modulation of shear or magnetic field, can inhibit propagation of the wave and so reduce shear damping. This effect is investigated by using a two-dimensional model representing long-wavelength drift waves in a large-aspect-ratio tokamak. It is shown that this two-dimensional problem can be reduced to a one-dimensional eigenvalue equation from which the shear damping can readily be computed. It is confirmed that toroidal effects can annul the shear damping, and some examples are given.
TL;DR: In this paper, an upper bound on the density of the plasma boundary in tokamaks was derived from a condition for thermal stability of the boundary in a tokaman.
Abstract: From a condition for thermal stability of the plasma boundary in tokamaks, an upper limit on the density which is consistent with the experimental observations has been derived.
TL;DR: In this paper, the results of a study on the non-linear stability of tearing modes for hollow current profiles in cylindrical geometry are presented, which leads either to saturation of the tearing mode (a new non-axisymmetric equilibrium is reached) or to a re-distribution of the flux and field line reconnection in Kadomtsev's sense.
Abstract: The results of a study on the non-linear stability of tearing modes for hollow current profiles in cylindrical geometry are presented. Their non-linear evolution which, through magnetic island formation, leads either to saturation of the tearing mode (a new non-axisymmetric equilibrium is reached) or to a re-distribution of the flux and field line reconnection in Kadomtsev's sense (a new axisymmetric equilibrium is obtained) has been studied. An empirical prediction for the accessibility of the reconnected state is given. In particular, tearing modes with low poloidal mode number (m = 2, 3) are considered in order to interpret some minor disruptions observed in tokamaks, i.e. m = 3 minor disruptions in the Princeton Large Torus. Tearing modes with higher poloidal mode number have also been examined
TL;DR: In this paper, the saturation amplitude of the m = 2 tearing mode is calculated from the safety factor profile using a non-linear Δ' analysis, which gives an absolute result (no arbitrary factors) for the amplitude of perturbation in the poloidal magnetic field everywhere and in particular at the limiter.
Abstract: Elementary non-linear tearing-mode theory in a two-dimensional cylindrical geometry is used to predict accurately the amplitude of the m = 2 poloidal-magnetic-field fluctuations (Mirnov oscillations) at the limiter of a tokamak. The input required is the electron temperature radial profile from which the safety factor profile can be inferred. The saturation amplitude of the m = 2 tearing mode is calculated from the safety factor profile using a non-linear Δ' analysis. This gives an absolute result (no arbitrary factors) for the amplitude of the perturbation in the poloidal magnetic field everywhere and, in particular, at the limiter. An analysis of ORMAK and T-4 safety factor profiles (inferred from electron temperature profiles) gives results that are in agreement with the experimental data. – A study of a general profile shows that, as a function of the safety factor at the limiter, a maximum occurs in the amplitude of the Mirnov oscillation. The magnitude of the maximum increases with a decrease in temperature near the limiter.
TL;DR: The theory of launching lower hybrid waves in fusion-oriented plasmas using waveguide arrays (the "grill") is generalized to allow for the excitation of the fast wave in the outer layers of the plasma as mentioned in this paper.
Abstract: The theory of launching lower hybrid waves in fusion-oriented plasmas using waveguide arrays (the 'grill') is generalized to allow for the excitation of the fast wave in the outer layers of the plasma. It is found that the reflection coefficient of the antenna and the fraction of power radiated in the 'inaccessible' portion of the parallel-wavenumber spectrum remain essentially the same as those predicted by the simplified theory considering only the slow plasma wave. The most important new feature is that the power radiated in this part of the spectrum is mainly coupled to discrete waveguide-like eigenmodes confined to the outer layers of the plasma, which guide the power away from the antenna in the direction parallel to the wall of the chamber. This fraction of the power is likely to be lost from the point of view of the heating efficiency; therefore, one should make it as small as possible by using arrays of four guides or more.
TL;DR: In this paper, a control of the current density profile in the resistive shell tokamak has been studied, and the results of kink and tearing modes analysis agree well with the experimental observations.
Abstract: In the resistive-shell tokamak, JIPP T-II , a control of the current density profile has been attempted by programming both gas puffing and plasma current waveform. A stable high-density plasma has been obtained with the following parameters: the maximum line-average electron density is e = 8.5 × 1013cm−3, the minimum q(a)-value is 2.2, and the relative amplitude of the m/n = 2/l mode is suppressed to an extent less than 10−3. A derivation of the current density profile by solving the magnetic-diffusion equation on the basis of the experimental data shows that the current density profile favourable to the stability of low-m kink and tearing modes is realized by combining the effects of cooling through an increase in density and of heating by a current rise in the outer plasma region. The results of kink and tearing modes analysis agree well with the experimental observations. The criterion that the current density profile is successfully controlled by this method is derived as a function of the ratio of plasma current to electron density in the current-rise phase, i.e. 20 × 10−13 Ip/e 30 × 10−13 kA·cm3. The major disruption due to the density increase is completely suppressed by the method proposed in this paper. The major disruption due to a reduction of q(a) to less than 2.2 has, however, not yet been suppressed. In future, the current density profile should be maintained more precisely at its optimum shape by using a feedback-control technique and a control of the plasma boundary with titanium gettering, etc.
TL;DR: In this article, the stability of electrostatic drift wave eigenmodes in a resistive plasma with finite magnetic shear was investigated. And the authors found that resistivity contributes to an enhancement of this damping and the enhancement factor increases with the electron-ion collision frequency.
Abstract: Several different techniques are used to study the stability of electrostatic drift wave eigenmodes in a resistive plasma with finite magnetic shear. It is found that in the slab approximation, where usual shear damping is operative, resistivity contributes to an enhancement of this damping and the enhancement factor increases with the electron-ion collision frequency νei. Thus no unstable eigenmodes result. If the shear damping is nullified, either by introducing a strong spatial variation of the density gradient or by working in toroidal geometry with strong toroidal coupling effects, then unstable eigenmodes with growth rates increasing with νei are recovered. A perturbation calculation shows that retention of electron temperature fluctuations associated with the mode and inclusion of temperature gradients do not alter these conclusions. Extensive numerical calculations are also presented.
TL;DR: In this paper, field-reversal experiments in the neutral-beam-injected 2XIIB mirror machine are reported, and the best result is an estimated field-residual parameter ζ = ΔB/Bvac = 0.9 ± 0.2 with vacuum field strength Bvac=4.35 kG.
Abstract: Data on field-reversal experiments in the neutral-beam-injected 2XIIB mirror machine are reported. The best result is an estimated field-reversal parameter ζ = ΔB/Bvac = 0.9 ± 0.2 with vacuum field strength Bvac = 4.35 kG. Experiments at higher field strength Bvac = 6.7 kG achieved ζ = 0.6 ± 0.1. Ion energy confinement nτEi for the Bvac = 6.7 kG experiment is less than that predicted by classical Spitzer electron drag. Ion-cyclotron oscillations increasing with injected neutral-beam current suggest that ion-cyclotron losses are present and that ΔB/Bvac could be increased by improving stabilization of the ion-cyclotron oscillations.
TL;DR: In this paper, the resonant plateau diffusion coefficients for ions in a tandem mirror solenoid were derived by assuming that the ∇B azimuthal drift is small compared to × contribution, and that the radial drift per bounce is determined by properties of the vacuum magnetic field.
Abstract: Analytic approximations to resonant plateau diffusion coefficients for ions in a tandem mirror solenoid are developed. These are obtained by assuming that the ∇B azimuthal drift is small compared to × contribution, and that the radial drift per bounce is determined by properties of the vacuum magnetic field. The resulting expressions are used to estimate radial transport life-times for the Lawrence Livermore Laboratory Tandem Mirror Experiment (TMX) and for a proposed future experiment, MFTF-B. These estimates indicate radial loss comparable to axial for TMX, but smaller than axial for most operating modes considered for MFTF-B.
TL;DR: In this paper, the Doppler shift of lines emitted by ionized oxygen impurities was used to measure the rotation of the LT-3 plasma in stable discharges and unstable discharges.
Abstract: Rotation of the plasma in LT-3 has been measured from the Doppler shift of lines emitted by ionized oxygen impurities. In stable discharges, toroidal rotation of the ions in the direction of the discharge current was measured at velocities of up to 5 km ? s?1, while poloidal rotation was observed in the electron diamagnetic drift direction, reaching linear velocities of 1.6 km ? s?1 at a minor radius of 5 cm. In unstable discharges, the plasma rotation collapses at the disruptions, and then re-appears as the magnetic surfaces are reformed.
TL;DR: In this article, a modified energy principle is used, and the stability problem is reduced to determination of the eigenvalues of an ordinary differential equation along each field line, and a threshold hot electron current is required for stability; its value agrees with experimental measurements.
Abstract: Magnetohydrodynamic stability limits are determined for the ELMO Bumpy Torus. The relativistic hot electron annuli are considered to be rigid, modifying the magnetic field, but not interacting with the instability. A modified energy principle is used, and the stability problem is reduced to determination of the eigenvalues of an ordinary differential equation along each field line. A threshold hot electron current is required for stability; its value agrees with experimental measurements. The calculations show that stable high-beta equilibria can be created. Experiments are being planned to test these predictions.
TL;DR: In this paper, it was shown that current diffusion with the experimental Te profiles typically leads to hollow current profiles and that the disruptions appear to be related to the local minimum of q inside the plasma attaining near-integral values.
Abstract: During the current rise phase of the Alcator A discharge a series of disruptions occurs, related to MHD activity of poloidal periodicity m, at limiter q-values approximately 1.6 m (m integral). The electron temperature profile is peaked at the centre throughout. It is shown, however, that current diffusion with the experimental Te profiles typically leads to hollow current profiles and that the disruptions appear to be related to the local minimum of q inside the plasma attaining near-integral values. Disruptions may be avoided by decreasing the rate of current rise. This leads to improved plasma conditions throughout the discharge.
TL;DR: In this paper, the use of the resonance fluorescence method with laser pumping of optical transitions of excited hydrogen atoms for high-temperature plasma diagnostics was discussed for the Balmer Hα line, λ = 6563 A.
Abstract: The authors discuss the use of the resonance fluorescence method with laser pumping of optical transitions of excited hydrogen atoms for high-temperature plasma diagnostics. The calculations were performed for the Balmer Hα line, λ = 6563 A. The conclusions reached may also be generalized to other hydrogen lines. Experimental results obtained on the FT-1 tokamak are presented and discussed.
TL;DR: In this paper, it was shown that by suitably controlling the gas influx, it is possible to contract the current channel, decrease impurity radiation from the core of the discharge, and increase the gross energy confinement time, whether the aperture limiters are of tungsten, stainless steel or carbon.
Abstract: Experiments conducted on the PLT tokamak have shown that both plasma-limiter interaction and the gross energy confinement time are functions of the gas influx during the discharge. By suitably controlling the gas influx, it is possible to contract the current channel, decrease impurity radiation from the core of the discharge, and increase the gross energy confinement time, whether the aperture limiters are of tungsten, stainless steel or carbon.
TL;DR: In this paper, the neutral-ablation model describing ablation of solid hydrogen fuel pellets in thermo-nuclear plasmas has been extended to determine the species composition of the ablatant consistent with the fluid profiles, and has been used to assess pellet shielding mechanisms.
Abstract: The neutral-ablation model describing ablation of solid hydrogen fuel pellets in thermo-nuclear plasmas has been extended to determine the species composition of the ablatant consistent with the fluid profiles, and has been used to assess pellet shielding mechanisms. Aside from neutral-ablation shielding, none of the shielding mechanisms studied is very effective. Dissociation of hydrogen molecules extends pellet lifetimes by 10-20%. Ionization reduces the temperatures in the ablation by about a factor of three, but extends pellet lifetimes by only a few per cent. Excitation of atoms is not important because the fraction of excited atoms does not exceed a few per cent anywhere in the ablation. Bremsstrahlung and recombination radiation are negligible energy losses. Where emitted abundantly, line radiation is trapped within the optically thick ablatant. Incident electron heat is reduced by less than 10% in overcoming the electric potential of the pellet. Magnetic shielding is treated elsewhere.
TL;DR: In this paper, a Fokker-Planck treatment of the current induced by a beam of fast ions circulating in a toroidal plasma is developed, and the resulting net plasma current has a very different functional dependence upon electron temperature than that given by the conventional theoretical treatment in which the electrons are assumed to be Maxwellian.
Abstract: A Fokker-Planck treatment of the current induced by a beam of fast ions circulating in a toroidal plasma is developed. The electron Fokker-Planck equation is first reduced to an integro-differential equation which is then solved analytically in the limiting cases of: (a) a large plasma Z and (b) a large ratio of the electron thermal velocity ve to the fast ion velocity vb. In addition, a numerical solution was obtained for the complete range of values of ve/vb and for several values of Z. It is found that the resulting net plasma current has a very different functional dependence upon electron temperature than that given by the conventional theoretical treatment in which the electrons are assumed to be Maxwellian. In particular, for ve > vb and Z = 1, which is the limit appropriate to many present tokamak experiments, the net current is found to be in the opposite direction to the fast-ion current. The theory is compared with recent measurements of this current which were made by using the Culham Levitron, and agreement is found between theory and experiment.
TL;DR: In this article, a scaling law for the repetition time of small tokamak TOSCA with a period of 100?200?s was shown to be compatible with Ohmic heating and a resistive instability whose growth rate is dependent upon the decrease in q below unity.
Abstract: Sawtooth oscillations are observed in the small tokamak TOSCA with a period of 100?200 ?s. The q = 1 singular surface occurs at a radius of 1?1.5 cm. The sawtooth oscillations are not suppressed by shaping the plasma into a triangle. By comparing the results with those of larger tokamaks an empirical scaling law for the repetition time is obtained. It is demonstrated that this scaling law is compatible with Ohmic heating and a resistive instability whose growth rate is dependent upon the decrease in q below unity.
TL;DR: In this article, the complete linear hot-plasma dispersion relation derived from kinetic theory is numerically solved for the ion cyclotron range of frequencies, which is an accurate approximation for both fast and ion Bernstein waves.
Abstract: The complete linear hot-plasma dispersion relation, derived from kinetic theory, is numerically solved for the ion cyclotron range of frequencies. A compact dispersion relation is obtained which is an accurate approximation for both fast and ion Bernstein waves. With the help of this dispersion relation, the three-dimensional ray equations for a tokamak geometry are solved, parabolic density and temperature profiles, the 1/R variation in the toroidal magnetic field, and the resulting poloidal magnetic field due to a rotational transform being incorporated. The ray-tracing analysis is applied to a conceptual design tokamak reactor. The results indicate the nature of the scaling of fast-wave heating to large tokamaks.
TL;DR: In this paper, the suprathermal drag force and motion of electrons in momentum space are analyzed for a multi-component plasma. And the acceleration and slowing-down of runaways are also briefly discussed.
Abstract: The suprathermal drag force and the motion of suprathermal electrons in momentum space are analysed for a multi-component plasma. The calculations of the particle motion are based on the suprathermal Fokker-Planck equation and include relativistic effects. It is found that, owing to pitch angle scattering, the flow patterns in momentum space are more complicated than previously assumed. Simple expressions for the runaway threshold and the perpendicular momentum of relativistic runaways are derived. The acceleration and slowing-down of runaways are also briefly discussed.
TL;DR: In this article, the effect of the longer mean free path of highenergy ions, preferentially lost from small pellets containing thermonuclear reactants, was calculated and, in the most extreme case calculated, a factor of about four reduction of reaction rate in DT from the Maxwell average rate at the same mean ion kinetic energy was found.
Abstract: Because of the longer mean free path of highenergy ions, they will be preferentially lost from small pellets containing thermonuclear reactants. This effect has been calculated and, in the most extreme case calculated, a factor-of about-four reduction of the reaction rate in DT from the Maxwell average rate at the same mean ion kinetic energy is found.