One-dimensional Transport Code Research Articles

Transmutation of the actinide neptunium-237 with a hybrid reactor

Calculations and analyses on the transmutation of long-lived actinide 237Np radioactive waste with a fusion-fission hybrid reactor are reported. A new waste management concept of burning HLW (high-level waste), utilizing the released energy and converting 237Np into 239Pu fissile fuel through transmutation has been adopted. Time-dependent depletion calculations were performed using a modified version of the BISON 1.5 one-dimensional neutron transport and burn-up calculation code system. The transmutation rate of 237Np and its relationship to neutron wall loading and Pu and Np concentrations in the transmutation zone were explored; relevant results are given.

Estimation of the tritium production and inventory in beryllium

Abstract Beryllium has been proposed as a candidate material for the neutron multiplier in fusion blanket designs. Tritium will be produced and will accumulate in beryllium under neutron irradiation. The tritium production and inventories under 1.5 and 3.0 GW fusion power operation were calculated for a layered pebble bed blanket with lithium oxide (Li 2 O) breeder and beryllium (Be) multiplier. Neutronics calculations were carried out using the one-dimensional transport code ANISN, and the tritium production due to direct reaction of 9 Be ( n , T ) 7 Li and the two-step reactions 9 Be ( n , α ) 6 Li ( n , α ) T was taken into account. The tritium production due to the two-step reaction was calculated to be 50% of the total tritium production after 1 year full power operation (FPY). The tritium inventory was estimated by considering three kinetic parameters, the permeability from the breeder region, diffusivity in a beryllium matrix, and solubility. Tritium permeation from the breeder region to the beryllium region through a 316SS wall was as much as 3 g h −1 , which is 30% of the tritium production (9.6 g h −1 ) in the breeder region. Using the diffusion coefficient of beryllium with no oxide layer on its surface, the total tritium inventory was calculated to be 7 g FPY −1 , mainly owing to solubility. The content of beryllium oxide significantly affects the effective diffusion coefficient. Using a diffusion coefficient for beryllium with beryllium oxide layer on its surface, the tritium inventory was found to be equal to the amount produced.

Galactic cosmic ray transport methods: Past, present, and future

The development of the theory of high charge and energy (HZE) ion transport is reviewed. The basic solution behavior and approximation techniques will be described. An overview of the HZE transport codes currently available at the Langley Research Center will be given. The near term goal of the Langley program is to produce a complete set of one-dimensional transport codes. The ultimate goal is to produce a set of complete three-dimensional codes which have been validated in the laboratory and can be applied in the engineering design environment. Recent progress toward completing these goals is discussed.

Transport modelling including radial electric field and plasma rotation

In order to study the role of the radial electric field in the tokamak transport, a one-dimensional transport code which describes the toroidal and poloidal plasma rotation as well as the radial electric field has been developed. The neoclassical transport, turbulent transport and ion orbit loss are included. Using a simple turbulent transport model with a constant diffusion coefficient and a fixed temperature profile, the density profile in a steady state and the transient behavior during the co and counter neutral beam injection are studied. More consistent analysis has been initiated with a turbulent transport model based on the current diffusive high-n ballooning mode. The enhancement of the radial electric field due to ion orbit losses and the reduction of the transport due to the poloidal rotation shear are demonstrated. The preliminary calculation indicates a sensitive temperature dependence of the density profile.

Ion temperature profile deconvolution and corrections to confinement parameters in spheromaks

The purpose of this work is to determine ion temperature profiles in spheromaks [Nucl. Fusion 19, 489 (1979)] for the first time. Knowledge of the ion temperature profile is necessary in the correct calculation of plasma confinement parameters. The work herein details the calculation of ion temperature profiles for the Compact Torus Experiment (CTX) [Nucl. Fusion 28, 1555 (1988)] and S-1 [Phys. Rev. Lett. 46, 188 (1981)] spheromaks. Data from single chord Doppler ion temperature measurements in these devices have been analyzed with the aid of a one-dimensional equilibrium charge state transport code. Using electron temperature and density profiles from Thomson scattering, and estimates for transport rates, a most probable position for the emission of line radiation can be determined and correlated with the measured Doppler ion temperature, thus generating an ion temperature profile. From this ion temperature profile determination, plasma confinement parameters for the small solid flux conserver CTX [Phys. Fluids B 2, 1342 (1990)] spheromak can be determined, and confinement parameters for S-1 can be reevaluated, eliminating the previous confinement calculations assumption Ti(r)=Te(r). The CTX device has a calculated volume averaged beta 〈β〉 ranging from 3% to 8% and a volume averaged energy confinement time 〈τE〉 between 14 and 35 μsec; while the S-1 spheromak has 〈β〉 between 15% and 40% and 〈τE〉 ranging from 30 to 70 μsec.

Lower Hybrid Heating in a High-Field Deuterium-Tritium Ignition Experiment

This paper reports that high-magnetic-field, toroidal deuterium-tritium plasmas can have a window of accessibility to lower hybrid radio-frequency at moderate frequency. As an example, lower hybrid waves at 8 GHz are shown to penetrate most of the way into subignited and ignited Ignitor plasmas at full density and magnetic field, using a one-dimensional transport and ray-tracing code. Better heating of the plasma interior is obtained by launching from a negative poloidal angle relative to the horizontal midplane.

Accelerated physical modelling of hazardous-waste transport

This Paper presents the results of a research programme conducted on the Cambridge University balanced-arm centrifuge, to study the long term transport of contaminants in the soil surrounding an engineered landfill site. The phenomena which govern the transport of hazardous waste through porous media are discussed, the principles of geo-technical centrifuge modelling are outlined, and relevant scaling laws that govern the relationship between the centrifuge model and its corresponding prototype, with respect to the problem of hazardous-waste transport, are presented. A centrifuge test, simulating two-dimensional migration of a conservative pollutant species from a landfill site, is described, and results from three such tests are presented. These results are compared with theoretical predictions from an existing one-dimensional transport code. L'article présente les résultats d'un programme de recherches effectuées sur la centrifugeuse a bras équilibré de l'Université de Cambridge pour étudier le transport à long terme des matières contaminantes dans le sol dans les environs des trachées construites pour les recevoir. Les phénomènes qui influencent le transport des déchets dangereux à travers les milieux poreux sont passés en revue et les principes de la modélisation des centrifuges géotechniques brièvement décrits. L'article présente aussi les lois d'échelle qui influencent les relations entre le modèle de la centrifugeuse et son prototype correspondant au problème du transport des déchets dangereux. Un essai à la centrifugeuse est décrit qui simule la migration bidimensionnelle d'une espèce de matière contaminante à toxicité de longue durée dans de telles tranchées. Les résultats de trois essais de ce type sont comparés avec des prédictions théoriques contenues dans un code de transport unidimensionnel déjà publié.

Gamma Heating Measurements in a Mixed Radiation Field

Gamma hearing measurements have been made in a low-Z assembly irradiated with 14-MeV neutrons and (n,n{prime}) gammas produced by a Texas Nuclear Model 9400 neutron generator. The assembly is composed of 144 magnesium sleeves (5cm {times} 5cm {times} 60cm {times} 3 mm thick) filled with graphite to simulate a fusion blanket test module. Heating measurements were made in the mid-line of the assembly using a proportional counter operating in the Continuously-varied Bias-voltage Acquisition (CBA) mode. The neutron induced atomic recoil signal was rejected by observing the signal rise-time differences inherent to radiations of different LET. The experiment was modelled using the one-dimensional radiation transport code ANISN/PC. The operating limits of this technique were identified by comparing measurements made at different positions in the assembly and then comparing these measurements to the calculated flux. 7 refs., 5 figs., 1 tab.

Influence of MHD effects and edge conditions on ITER helium ash accumulation and sustained ignition

Dilution of reacting species by build-up of helium ash and its effect on ignition in the ITER tokamak have been studied in a series of simulations with the one-dimensional BALDUR transport code. Thermal diffusivities, obtained from ITER scaling laws and with radial variations observed in JET, gave τ E ≈ 2–4 s. Refuelling of deuterium and tritium maintained constant electron density, while carbon recycling was 100% and the helium ash recycling was varied from 1.0 to 0.5. Including MHD effects, specifically sawteeth and beta limits, we find that ignition can be sustained for 200 s with R helium = 0.95. These simulations, the only non-zero-dimensional, time-dependent simulations thus far made for ITER plasmas, emphasize that edge plasma conditions, MHD behavior, and helium particle transport are critical synergistic issues for sustained ignition.

Impurity transport in detached plasmas

Transport of metallic impurities in the plasma edge was compared for normal and detached Tokamak plasmas. A neo-classical model, valid for a dirty plasma in the Pfirsch-Schluter regime, was used to calculate the impurity flux terms. Changes in the edge density and temperature profiles, characteristic of detached discharges, were seen to greatly influence the impurity transport. In particular, the inward convective velocity increased significantly because of the detachment. A one-dimensional transport code was used to evaluate the influence of the edge transport modifications on the global impurity confinement time. Code predictions are in qualitative agreement with experimental measurements made on TEXTOR.

Transport analysis of JT-60 plasma with the drift wave turbulence model

Characteristics of the JT-60 plasma in both the Ohmic heating phase and the neutral beam heating phase have been studied numerically by using a one-dimensional tokamak transport code, with the thermal conductivities based on the drift wave turbulence (DWT) model. The numerical results for the central electron temperature Te(0) and the energy confinement time τE show good agreement with the experimental data in the medium line averaged electron density range n̄e ∼ 4 × 1019 m−3, for both Ohmic heating and neutral beam'heating cases. The absorbed power degradation of is also reproduced with this model. On the other hand, the DWT model underestimates the plasma temperatures at low line averaged electron density, especially in the neutral beam heating phase, because of the strong dependence of the thermal conductivity on the electron temperature, and high temperature plasmas cannot be reproduced. This leads to a discrepancy in the n̄e dependence of τE between experiment and calculation. The current dependence of τE is not reproduced either, even when the Venetian blind model is used.

Optimization of the bootstrap current in a large helical system with L = 2

Neoclassical bootstrap currents in the banana and plateau regimes are evaluated for a large helical system with L = 2 and with a major radius of 5 m. Various vacuum magnetic field configurations are studied with a view to optimizing the bootstrap current. In the banana regime, shifting of the magnetic axis and shaping of magnetic surfaces have a remarkable influence on the bootstrap current. It has been found that a small outward shift of the magnetic axis and vertically elongated magnetic surfaces are favourable for a reduction of the bootstrap current. In contrast, in the plateau regime the bootstrap current depends strongly on the toroidal pitch number of the helical winding coils, but shifting of the axis and shaping of magnetic surfaces are not effective. The magnitude of the bootstrap current is estimated for plasmas in a large helical system with parameters given by a one-dimensional radial transport code.

Effect of tearing modes on temperature and density profiles and on the perpendicular transport in the W VII-A stellarator

In the ohmically heated W VII-A stellarator, the behaviour of which is similar to that of a medium sized tokamak, the additional shearless external rotational transform t0 (Δι0/ι0 < 1%, ι = 1/q) improves the stability properties and allows stationary and reproducible helium discharges with large amplitude tearing modes to be produced for 0.10 ≤ ι0 ≤ 0.15. Discharges of this type are used to study, by means of Thomson scattering, the modification of electron temperature and density profiles by large amplitude tearing modes. The two-dimensional shapes of the profiles found experimentally can be attributed to the magnetic islands predicted by tearing mode theory. These shapes are further used to define an effective, locally enhanced radial transport coefficient κ⊥,e in a one-dimensional heat transport code. In this way, the measured temperature profiles can be reproduced quite well and the energy confinement time of discharges with tearing mode activity can be predicted quantitatively. The transport model is used to investigate the explicit dependence of κ⊥,e on the plasma current and to study the importance of plasma current driven instabilities for the energy confinement in the W VII-A stellarator as well as in tokamaks.

Numerical modelling of lower hybrid RF heating and current drive experiments in the Alcator C tokamak

A simulation model is described for lower hybrid (LH) current drive, rampup, heating, and sawtooth stabilization. The model incorporates a one-dimensional radial transport code, parallel velocity Fokker-Planck calculation, and a toroidal ray tracing code. For steady LH current drive it is found that the RF current generation is accurately predicted by a fast electron confinement time of the form ms in the density range of 3 × 1019 m−3 ≲ n̄e ≲ 7 × 1019 m−3 (where ± distinguishes electrons moving parallel (antiparallel) to the current drive direction). Also in this range, the theoretically predicted wave absorption and experimentally measured electron temperatures and stored energy were found to be consistent with an electron thermal diffusivity whose magnitude is independent of ne. To reproduce the experimentally measured values of LH rampup efficiency at n̄e = 3 × 1019 m−3, it was necessary to take . For LH heating at densities of n̄e ≌ 1.4 × 1020 m−3, the power lost due to collisional damping of the LH ray trajectories at the plasma periphery was found to be significant, because of higher edge densities. Studies of LHRF sawtooth stabilization experiments with RF current drive indicated the possibility of creating stable profiles of the safety factor, q, via the generation of positive RF current near the q = 1 surface, thus producing a current ‘pedestal’.

Baldur: A one-dimensional plasma transport code

A version of the BALDUR plasma transport code which calculates the evolution of plasma parameters is documented. This version uses an MHD equilibrium which can be approximated by concentric circular flux surfaces. Transport of up to six species of ionized particles, of electron and ion energy, and of poloidal magnetic field is computed. A wide variety of source terms are calculated including those due to neutral gas, fusion and auxiliary heating. The code is primarily designed for modelling tokamak plasmas.

Numerical Simulation for ICRF Minority-Ion Heating in a Tokamak

Ion cyclotron range of frequencies (ICRF) heating in the two-ion hybrid resonance regime is numerically studied and the results are compared with those of the heating experiments on the JET tokamak. The kinetic one-dimensional analysis of the ICRF wave is coupled with the anisotropic Fokker-Planck equation and the one-dimensional transport code, Spatial transport coefficients are inferred from those of the drift wave model and a phenomenological internal disruption is introduced. Calculated power deposition profiles agree well with experimental results. Degradation of confinement with increasing heating power, profile modification due to the off-axis heatinq and heat pulse propagation after the internal disruption are well reproduced by our simulation model.

Effect of Fluorescence in Deep Penetration of Gamma Rays

Transport calculations have been performed using the one-dimensional gamma-ray transport code ASFIT for materials of high atomic number (Z), such as tin, tungsten, lead, and uranium, for incident energies in the range of 0.030 to 0.5 MeV, where the fluorescent X rays are important. The relative impact of different components of K X rays on the spectra and buildup factors at various depths in the medium has been assessed for a typical case. Approximate analytic results are derived and compared with the computed X-ray contributions. Point isotropic air and medium response buildup factors computed for these materials have been given, filling the gap in the existing standard tables. Since the buildup factors are not amenable for conventional interpolation in this region, the values are given at close intervals of incident photon energy.

Analysis of Ex-Core Detector Response Measured During Nuclear ShipMutsuLand-Loaded Core Critical Experiment

There are some cases where the ex-core neutron detector response is dependent not only on the fission source distribution in a core but also on neutron absorption in the borated water reflector. For example, an unexpectedly large response variation was measured during the nuclear ship Mutsu land-loaded core critical experiment. This large response variation is caused largely by the boron concentration change associated with the change in control rod positioning during the experiment. The conventional Crump-Lee response calculation method has been modified to take into account this boron effect. The correction factor in regard to this effect has been estimated using the one-dimensional transport code ANISN. The detector response variations obtained by means of this new calculation procedure agree well with the measured values recorded during the experiment.

Simulation of the radial transport in CT-6B tokamak during gas puffing

A parameter evolution in CT-6B tokamak during gas puffing is numerically studied using a one-dimensional tokamak transport code. The calculated results show that the gas puffing enhances the average electron density. The transport coefficients obtained from the simulation are compared with those from the measurements performed on CT-6B device.

The optimisation of limiter geometry to reduce impurity influx in Tokamaks

The authors discuss the impurity control limiter (ICL) which has an inverted geometry. The ICL shape is designed to direct the impurities towards the wall. They present the results from a two-dimensional neutral particle code which maps the ionisation of carbon physically sputtered by deuterons from a carbon limiter. This ionisation source is coupled to a one-dimensional impurity transport code which calculates the implied central impurity density. The results demonstrate that the ICL achieves impurity control in two ways. Firstly, many of the sputtered impurities directed towards the wall are not ionised and return to the wall as neutrals. Secondly, much of the ionisation which does occur is located in the scrape-off layer. They conclude that a reduction in central impurity density of a factor of 10 is possible in a Tokamak such as DITE provided that the limiter is the main source of impurities.