Weston Stacey

Georgia Institute of Technology | GT · Nuclear Engineering Program

Fusion alpha heating introduces new phenomena into plasma dynamics and control. On the worrisome side is the well-known fact that the συfus≃Tion2 dependence of the predominantly central fusion heating mechanism, coupled with the less appreciated fact of the predominantly plasma edge location of bremsstrahlung and impurity line and recombination rad...

The relationships among the radial distributions of neutral beam momentum and particle sources, the radial distribution of ion orbit losses, and the resulting radial distributions of toroidal and poloidal rotation velocities and radial pressure gradients and the radial distribution of the ion and electron temperatures are derived from the requireme...

A particle-, momentum-, and energy-conserving, flux surface–averaged fluid theory for the radial particle and energy fluxes and the radial distributions of pressure, density, rotation velocities, and temperatures in the edge plasma that has been derived from fundamental fluid conservation (particle, momentum, energy) relations is summarized. Kineti...

The dependence of the kinetic ion orbit loss of thermalized ions in a tokamak plasma on the charge and mass of these ions is explicitly developed from the underlying ion orbit loss theory.

This paper combines the older neoclassical gyroviscous model for toroidal viscosity in the plasma core, which is based on an axisymmetric magnetic field and obtains reasonable agreement with experiment for toroidal rotation in the plasma core but not in edge plasma, with recent models for neoclassical toroidal viscosity (NTV) based on nonaxisymmetr...

A particle-momentum-energy conserving flux-surface-averaged fluid theory for the radial particle and energy fluxes and the radial distributions of pressure, density, rotation velocities and temperatures in the tokamak edge plasma is derived from fundamental fluid conservation(particle, momentu, energy) relations. Kinetic corrections arising from io...

Theoretical analysis and interpretation of experimental measurements indicate the need to extend the fluid theory used in the tokamak plasma edge to include ion orbit loss of thermalized ions and to retain (mainly) electromagnetic pinch forces in the momentum balance in order to derive transport equations which conserve particles, energy, and momen...

An extended plasma fluid theory including atomic physics, radiation, electromagnetic and themodynamic forces, external sources of particles, momentum and energy, and kinetic ion orbit loss is employed to derive theoretical expressions that display the role of the various factors involved in the determination of the pressure and temperature gradient...

A customized dynamic safety model is developed and used to analyze the safety characteristics of the Subcritical Advanced Burner Reactor (SABR), a fast transmutation reactor driven by a tokamak fusion neutron source. Loss-of-flow accidents (LOFAs), loss–of–heat sink accidents (LOHSAs), and loss-of-power accidents (LOPAs) are analyzed taking into ac...

Investigations of tokamak dynamics, especially as they relate to the challenge of burn control, require an accurate representation of energy and particle confinement times. While the ITER- 98 scaling law represents a correlation of data from a wide range of tokamaks, confinement scaling laws will need to be fine-tuned to specific operational featur...

The Georgia Tech concept of the Subcritical Advanced Burner Reactor (SABR) spent nuclear fuel (SNF) transmutation reactor and supporting analyses to date are summarized. SABR is based on the fast reactor physics and technology prototyped in Experimental Breeder Reactor-II (EBR-II) and proposed for the Integral Fast Reactor and the PRISM Reactor and...

Fluid theory expressions for the radial particle and energy fluxes and the radial distributions of pressure and temperature in the edge plasma are derived from fundamental conservation (particle, energy, momentum) relations, taking into account kinetic corrections arising from ion orbit loss, and integrated to illustrate the dependence of the obser...

A modified Ohm's Law, derived from the conservation of deuterium and carbon ions and electron momentum and the requirement for charge neutrality, yields an expression for the radial electric field, Er, in the edge pedestal region in terms of the motional electric field due to the carbon and deuterium ion rotation velocities as well as pressure grad...

An existing model of collisionless particle, momentum, and energy ion orbit loss from the edge region of a diverted tokamak plasma has been extended. The extended ion orbit loss calculation now treats losses of both thermal ions and fast neutral beam injection ions and includes realistic flux surface and magnetic field representations, particles re...

Recent developments in electromagnetic particle pinch, ion orbit loss, intrinsic rotation, rotation theory and radial electric field theory in the tokamak plasma edge are described. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A fluid model for the tokamak edge pressure profile required by the conservation of particles, momentum and energy in the presence of specified heating and fueling sources and electromagnetic and geometric parameters has been developed. Kinetics effects of ion orbit loss are incorporated into the model. The use of this model as a “transport” constr...

An orthogonalized flux-surface aligned curvilinear coordinate system has been developed from an up-down asymmetric variation of the “Miller” flux-surface equilibrium model. It is found that the new orthogonalized “asymmetric Miller” model representation of equilibrium flux surfaces provides a more accurate match than various other representations o...

The realities of energy development and the perception of and support for magnetic fusion in the US are briefly summarized as background for proposing a strategic opportunity for magnet fusion energy development as fusion neutron sources for subcritical advanced burner (transmutation) reactors for the destruction of long-lived transuranics in spent...

The preferential ion orbit loss of counter-current directed ions leaves a predominantly co-current ion distribution in the thermalized ions flowing outward through the plasma edge of tokamak plasmas, constituting a co-current intrinsic rotation. A methodology for representing this essentially kinetic phenomenon in plasma fluid theory is described a...

A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ω τ -ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systema...

A more detailed calculation strategy for the evaluation of ion orbit loss of thermalized plasma ions in the edge of tokamaks is presented. In both this and previous papers, the direct loss of particles from internal flux surfaces is calculated from the conservation of canonical angular momentum, energy, and magnetic moment. The previous result that...

Evolution of measured profiles of densities, temperatures, and velocities in the edge pedestal region between successive ELM (edge-localized mode) events are analyzed and interpreted in terms of the constraints imposed by particle, momentum and energy balance in order to gain insights regarding the underlying evolution of transport processes in the...

The Braginskii viscous stress tensor formalism was generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry in order to provide a representation for the viscous damping of toroidal rotation in tokamaks arising from various "neoclassical toroidal viscosity" mechanisms. In the process, it was verified t...

The subcritical advanced burner reactor (SABR) concept, which combines IFR-PRISM fast reactor technology and the ITER tokamak fusion physics and technology in a burner reactor for the transmutation of transuranics, has been adapted for a subcritical advanced breeder reactor (SABrR) that produces plutonium. It is found that basically the same fissio...

The conceptual design of the subcritical advanced burner reactor (SABR), a 3000-MW(thermal) annular, modular sodium pool-type fast reactor, fueled by metallic transuranic (TRU) fuel processed from discharged light water reactor fuel and driven by a tokamak D-T fusion neutron source based on ITER physics and technology, has been substantially upgrad...

It is argued that the structure observed in radial profiles in the tokamak edge plasma is determined by the requirements of ion particle, momentum and energy conservation and the underlying transport mechanisms in the presence of sources and losses of particles, energy and momentum. The intent of this paper is to define a systematic formalism that...

A low-confinement mode discharge which optimizes the capability of the new main-ion charge-exchange-recombination spectroscopy system on DIII-D (Luxon 2002 Nucl. Fusion 42 614) to measure deuterium toroidal velocity is interpretted in comparison with the predictions of neoclassical theory, with an emphasis on the plasma edge region. The observed pe...

A moments equation formalism for the interpretation of the experimental ion thermal diffusivity from experimental data is used to determine the radial ion thermal conduction flux that must be used to interpret the measured data. It is shown that the total ion energy flux must be corrected for thermal and rotational energy convection, for the work d...

Theoretical refinements to an existing model for the loss of ions by drifting across the last closed flux surface are presented.

The extended neoclassical rotation theory formulated in Miller flux surface geometry enables unprecedented neoclassical calculations of the poloidal asymmetries in density, rotation velocities, electrostatic potential along the flux surfaces, and of the inertial (Reynolds stress) and gyroviscous transport frequencies, which are strong functions of...

An interpretive methodology improved to account for two non-diffusive transport mechanisms--particle pinch and ion orbit loss--was applied to interpret the difference in transport (i) between a discharge with Resonance Magnetic Perturbations and a High confinement mode discharge with otherwise identical operating parameters and (ii) between the Low...

GTROTA (Georgia Tech ROTAtion) is a code that solves the extended neoclassical rotation equations for tokamak plasmas, derived from the multifluid moment equations (including electromagnetic effects) in generalized toroidal magnetic flux surface geometry. It computes the toroidal and poloidal fluid rotation velocities and the in-out and up-down den...

An investigation of the effect of ion orbit loss of thermal ions and the compensating return ion current directly on the radial ion flux flowing in the plasma, and thereby indirectly on the toroidal and poloidal rotation velocity profiles, the radial electric field, density, and temperature profiles, and the interpretation of diffusive and non-diff...

Joint experiment/theory/modelling research has led to increased confidence in predictions of the pedestal height in ITER. This work was performed as part of a US Department of Energy Joint Research Target in FY11 to identify physics processes that control the H-mode pedestal structure. The study included experiments on C-Mod, DIII-D and NSTX as wel...

Fuel cycle analyses of the transmutation of (a) all of the transuranics (TRUs) in light water reactor (LWR) spent nuclear fuel (SNF) and of (b) the minor actinides (MAs) remaining in SNF (after separation of much of the plutonium for starting up fast reactors) have been performed for the conceptual subcritical advanced burner reactor (SABR) fission...

Resonant Magnetic Perturbation (RMP) fields produced by external control coils are considered a viable option for the suppression of Edge Localized Modes in present and future tokamaks. In DIII-D, the RMPs are generated by six pairs of I-coils, each spanning 60° in toroidal angle, with the currents flowing in opposite directions in adjacent pairs o...

The effect of ion orbit loss on the poloidal distribution of ions, energy and momentum from the plasma edge into the tokamak scrape-off layer (SOL) is analysed for a representative DIII-D (Luxon 2002 Nucl. Fusion 42 614) high-mode discharge. Ion orbit loss is found to produce a significant concentration of the fluxes of particle, energy and momentu...

A neoclassical rotation theory (poloidal and toroidal) is developed from the fluid moment equations, using the Braginskii decomposition of the viscosity tensor extended to generalized curvilinear geometry and a neoclassical calculation of the parallel viscosity coefficient interpolated over collision regimes. Important poloidal dependences are calc...

Boltzmannand Vlasov Equations Drift Kinetic Approximation Fokker–Planck Theory of Collisions Plasma Resistivity Coulomb Collisional Energy Transfer Krook Collision Operators*

Hydromagnetic Instabilities Energy Principle Pinch and Kink Instabilities Interchange (Flute) Instabilities Ballooning Instabilities Drift Wave Instabilities Resistive Tearing Instabilities* Kinetic Instabilities* Sawtooth Oscillations*

Electrostatic Drift Wave Magnetic Fluctuations Wave–Wave Interactions* Drift Wave Eigenmodes* Microinstability thermal diffusivity models* Gyrokineticand Gyrofluid Theory* Zonal Flows*

Configuration, Nomenclature and Physical Processe Simple Divertor Model Divertor Operating Regimes* Impurity Retention Thermal Instability* 2D Fluid Plasma Calculation* Drifts Thermoelectric Currents Detachment Effect of Drifts on Divertor and SOL Plasma Properties* Blob Transport*

Fundamentals* PN Transport and Diffusion Theory* Multidimensional Neutral Transport* Integral Transport Theory* Collision Probability Methods* Interface Current Balance Method Extended Transmission-Escape Probabilities Method* Discrete Ordinates Methods* Monte Carlo Methods* Navier–Stokes Fluid Model* Tokamak Plasma Refueling by Neutral Atom Recycl...

Energy Confinement Tim Radiation Impurities Burning Plasma Dynamic

Inductive Adiabatic Compression* Fast Ions Electromagnetic Waves

Collisional Transport Mechanism Classical Transport Neoclassical Transport – Toroidal Effects in Fluid Theory Multifluid Transport Formalism* Closure of Fluid Transport Equations* Neoclassical Transport–Trapped Particles Extended Neoclassical Transport–Fluid Theory* Electrical Currents Orbit Distortion* Neoclassical Ion Thermal Diffusivity Paleocla...

Disruptions Disruption Density Limi Nondisruptive Density Limit Empirical Density Limit MHD Instability Limits

Neoclassical Viscosity Rotation Calculations Momentum Confinement Times Rotation and Transport in Elongated Geometry

Gyromotion and Drifts Constants of the Motion Diamagnetism*

General Properties Axisymmetric Toroidal Equilibria Large Aspect Ratio Tokamak Equilibri Safety Factor Shafranov Shift* Beta* Magnetic Field Diffusion and Flux Surface Evolution* Anisotropic Pressure Equilibria* Elongated Equilibria*

Sheath Recycling Atomic and Molecular Processes Penetration of Recycling Neutrals Sputtering Impurity Radiation

Plasma Physics and Engineering Constraint International Tokamak Program Fusion Beyond ITER Fusion-Fission Hybrids?

Moments Equations One-Fluid Model Magnetohydrodynamic Mode Anisotropic Pressure Tensor Model* Strong Field, Transport Time Scale Orderin

Fusion Plasma Coulomb Collisions ElectromagneticTheory

H-Mode Edge Plasma Transport in the Plasma Edge Differences Between L-Mode and H-Mode Plasma Edges Effect of Recycling Neutrals E × B Shear Stabilization of Turbulenc Thermal Instabilities Poloidal Velocity Spin-Up* ELM Stability Limits on Edge Pressure Gradients MARFEs Radiative Mantle Edge Operation Boundaries

Waves in an Unmagnetized Plasm Waves in a Uniformly Magnetized Plasma Langmuir Waves and Landau Dampin Vlasov Theory of Plasma Waves* Electrostatic Waves*

Confinement in Mirror Field Closed Toroidal Confinement System

The evolution of diffusive and non-diffusive transport during pedestal buildup following a low-high (L-H) transition has been interpreted from a particle-momentum-energy balance analysis of the measured density, temperature, and rotation velocity profiles in the plasma edge (0.82<ρ<1.0) of a DIII-D [Luxon, Nucl. Fusion 42, 614 (2002)] discharge. In...

A formalism, based on particle, momentum, and energy balance constraints, for the interpretation of diffusive and nondiffusive transport from plasma edge measurements is presented and applied to interpret transport differences between low-mode and high-mode DIII-D [J. Luxon, Nucl. Fusion, Vol. 42, p. 614 (2002)] plasmas. The experimental values of...

A practical calculation model for the intrinsic rotation imparted to the edge plasma by the directionally preferential loss of ions on orbits that cross the last closed flux surface is presented and applied to calculate intrinsic rotation in several DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)] discharges. The intrinsic rotation produced by ion lo...

There are (at least) two classical mechanisms for non-diffusive transport in the edge plasma: (i) particle 'pinch' velocities due to forces such as V × B and Er; and (ii) outward drifts due to ion-orbit loss and X-transport. A theoretical development for the treatment of these non-diffusive transport mechanisms within the context of fluid theory is...

Resonant magnetic perturbation (RMP) fields produced by 3D control coils are considered a viable option for the suppression of edge localized modes in future tokamaks, so an analysis of the diffusive and non-diffusive transport effects of these perturbations in the plasma edge has been performed. Repeated reversals of the toroidal phase of the I-co...

The measured edge profile evolution in DIII-D discharges is analyzed in terms of the implied thermal diffusivities, ion diffusion coefficients and pinch velocities, using the momentum-balance methodology of Ref. [1], extended to take into account ion orbit loss and X-point loss. The evolution of the density, temperature, rotation and radial electri...

The detailed time evolution of thermal diffusivities, electromagnetic forces, pressure gradients, particle pinch and momentum transport frequencies (which determine the diffusion coefficient) have been analyzed during the L-H transition in a DIII-D discharge. Density, temperature, rotation velocity and electric field profiles at times just before a...

An extended neoclassical rotation theory (poloidal and toroidal) is developed from the fluid moment equations, using the Braginskii decomposition of the viscosity tensor extended to generalized curvilinear geometry and a neoclassical calculation of the parallel viscosity coefficient interpolated over collision regimes. Important poloidal dependence...

The potential advantages of Fusion-Fission Hybrid (FFH) reactors (relative to critical fast reactors) for closing the back end of the nuclear fuel cycle are discussed. The choices of fission and fusion technologies for FFH burner reactors that would fission the transuranics remaining in spent fuel discharged from nuclear power reactors are summariz...

The presence of a large pinch velocity in the edge pedestal of high-confinement (H-mode) tokamak plasmas implies that particle transport in the plasma edge must be treated by a generalized pinch-diffusion theory, rather than a pure diffusion theory. An investigation of extending the numerical solution methodology of the standard diffusion theory to...

Rotation of tokamak plasmas is of intrinsic interest and also important for stabilization of MHD instabilities. Neoclassical rotation theory and gyroviscosity both depend on the poloidal dependence of the magnetic flux surface geometry. Gyroviscosity in the circular flux surface formulation [1] was found to lead to over-prediction of toroidal rotat...

The presence of a large pinch velocity in the edge pedestal of high confinement (H-mode) tokamak plasma discharges is important in edge transport, and must be included in theoretical modeling of experiments. The pinch-diffusion relation [1] describing edge transport has been derived from first principles and includes a momentum-balance satisfying p...

A calculation model for X-transport due to the radially outward grad-B and curvature drift of ions trapped poloidally in the null-B(theta) X-region just inside the X-point in diverted tokamaks is presented. Calculations are presented for two representative DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)] shots which indicate that X-transport effects...

Models have been developed for the calculation of i) standard ion orbit loss across the separatrix and of ii) X-loss of ions in the narrow, null-Bθ region extending into the plasma from the X-point in a divertor plasma, which are trapped poloidally while they ∇B drift radially outward through the X-point region (X-loss). Calculations of a DIII-D di...

Radial and toroidal momentum balance requires the ion particle flux in the edge pedestal to satisfy a pinch-diffusion relation, λ= -D∇n+nVr^pinch, rather than the pure diffusion relation used to derive standard diffusion theory. Re-derivation of diffusion theory using the pinch-diffusion relation in the particle continuity equation yields a general...

Rotation of tokamak plasmas is of intrinsic interest and also important for stabilization of MHD modes. Neoclassical rotation theory and gyroviscosity both depend on the poloidal dependence of the magnetic flux surface geometry. The circular [R = Rθ(1+ɛcosθ), B = Bθcosθ] flux surface formulation [1] was found to overpredict toroidal rotation veloci...

Calculation models are presented for treating ion orbit loss effects in interpretive fluid transport calculations for the tokamak edge pedestal. Both standard ion orbit loss of particles following trapped or passing orbits across the separatrix and the X-loss of particles that are poloidally trapped in a narrow null-Bθ region extending inward from...

The evolution of edge pedestal parameters between edge-localized modes (ELMs) is analyzed for an H-mode DIII-D (Luxon 2002 Nucl. Fusion 42 612) discharge. Experimental data are averaged over the same sub-intervals between successive ELMs to develop data that characterize the evolution of density, temperature, rotation velocities, etc over the inter...

Self-consistent calculations of the plasma energy and particle balances, the plasma current required for confinement according to trapped-ion instability theory, the toroidal magnetic field required for MHD-stability, the transformer magnetic field required to create and maintain the plasma current, and the maximum power allowed by either MHD-stabi...

The steady-state operating conditions and stability against temperature-density excursions are evaluated for tokamaks operating in the reactor regime on a D-T cycle. Global ion and alpha-particle balances and global ion and electron energy balances, together with MHD equilibrium and stability constraints, constitute the basic computational model. C...

A brief summary is given of the plenary sessions of the 3rd IAEA Technical Committee Meeting and Workshop on Fusion Reactor Design and Technology. The large tokamak experiments now under construction have brought fusion research to the threshold of fusion reactor power. A number of major in-depth reactor design studies are reported such as the 650-...

A recently developed generalization of neoclassical theory is applied to study the use of neutral-beam injection to drive impurities out of a tokamak plasma. The theory accounts for the direct momentum exchange between beam and plasma, which has been studied previously, and also for the effects of the beam in altering the first-order particle flows...

A summary is given of the experimental, demonstration and commercial fusion reactor concepts presented at the Second IAEA Technical Committee Meeting and Workshop on Fusion Reactor Design. The potential role of fusion power as an inexhaustible energy source is discussed, the advances and trends in fusion reactor design assessed, and the major concl...

A point model of particle densities and temperatures within a CTR is formulated, and equilibrium solutions are obtained for different plausible operating regimes of a D-T reactor of commercial interest. The stability of these equilibrium points against excursions in the overall particle densities and temperatures is determined by linear analysis an...

A formalism is presented for interpreting convective and viscous energy fluxes derived from experimental data and for correcting for them in the interpretation of measurements of the conductive heat flux. The corrections are shown to be significant in two JET pulses, suggesting that they should be taken into account in the experimental determinatio...