ABSTRACT The Quasi-Poloidal Stellarator (QPS) achieves approximate poloidal symmetry in magnetic ... more ABSTRACT The Quasi-Poloidal Stellarator (QPS) achieves approximate poloidal symmetry in magnetic coordinates at low aspect ratio through numerically determined three-dimensional shaping. This symmetry results in a number of novel characteristics with respect to neoclassical plasma flows and currents. To analyze these, a moments based analysis has been developed that utilizes the DKES (Drift Kinetic Equation Solver) code to generate a data base of transport coefficients that relate plasma fluxes, parallel flows, Ohmic and bootstrap currents to thermodynamic forces and electric fields. This analysis has indicated that poloidal flows dominate in most regimes, in contrast to the case in toroidally symmetric devices where toroidal flows dominate. Bootstrap currents are suppressed from their axisymmetric levels and have been checked against asymptotic low collisionality predictions. Parameters and profiles are chosen that lead to unique ion/electron root self-consistent ambipolar electric field solutions over the minor radius. Electric field bifurcations are observed at low densities when the electron temperature >> ion temperature. Acknowledgement This work was performed at Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Dept. of Energy under contract DE-AC05-00OR22725.
In this work, a numerical transport model is used to examine for hysteresis in the development of... more In this work, a numerical transport model is used to examine for hysteresis in the development of an edge poloidal velocity shear layer due to a modeled gas puff. The transport model couples together density, ion temperature, electron temperature, poloidal flow, toroidal flow, radial electric field, and a fluctuation envelope equation which includes a shear-suppression factor. The model has been modified in both the physics and in the numerical integration. The physics has been modified to include a turbulence growth rate for resistive ballooning modes as well as ion temperature gradient modes. The numerical integration has been changed to a modified Runge-Kutta with adaptive time-stepping. For the cases run with parameters consistent with these TJ-II experiments (only RF heating, no neutral beams), the resistive ballooning mode growth rate is dominant in the edge region. In this work, we present results from a series of cases using parameters that are typical of TJ-II discharges an...
Turbulence, and turbulence-driven transport are ubiquitous in magnetically confined plasmas, wher... more Turbulence, and turbulence-driven transport are ubiquitous in magnetically confined plasmas, where there is an intimate relationship between turbulence, transport, destabilizing mechanisms like gradients and currents, and stabilizing mechanisms like shear. We ...
This work examines bootstrap current and its impact on the equilibrium properties in optimized st... more This work examines bootstrap current and its impact on the equilibrium properties in optimized stellarators. Two independent methods are used to calculate the bootstrap current: a fast code based on a calculation in an asymptotically collisionless limit [K. C. Shaing, et al., Phys. Fluids B 1, 148 (1989)] and a fluid moments approach that self- consistently calculates the neoclassical transport
The impact of magnetic geometry on neoclassical flows and viscosities for the Helically Symmetric... more The impact of magnetic geometry on neoclassical flows and viscosities for the Helically Symmetric Experiment (HSX) is investigated using the PENTA code [1,2]. Specifically, two topics are investigated: (1) finite-beta effects and (2) configurational variations. The PENTA code is used to calculate flows in HSX with the vacuum magnetic geometry and with finite-beta magnetic surfaces from the VMEC equilibrium code. This is done for the standard quasi-helically symmetric configuration of HSX, a symmetry-breaking mirror configuration and a hill configuration. The impact of these changes in the magnetic geometry on neoclassical viscosities and flows in HSX will be discussed.[0pt] [1] D. A. Spong, Phys. Plasmas 12, 056114 (2005). [0pt] [2] D. A. Spong, Fusion Sci. Technology 50, 343 (2006).
This report is a summary of discussions held in the transport and turbulence breakout subgroups o... more This report is a summary of discussions held in the transport and turbulence breakout subgroups of the Magnetic Confinement Concepts Working Group (which met in the mornings) and the Plasma Sciences Working Group (which met in the afternoons). It was the judgement of the convenors of these groups, that a combined report was appropriate considering the overlap in subject matter and membership of the two groups. The report is organized to cover the most general topics first, then to move on to more specific topics. IFE and basic processes were primarily the focus of the Plasma Science group, while discussion of specific MFE concepts was carried out in the Magnetic Concepts breakouts. The substantial topic of MFE overarching issues was covered extensively in both sets of sessions.
The effects of a poloidally asymmetric ionization source on both dissipative toroidal drift wave ... more The effects of a poloidally asymmetric ionization source on both dissipative toroidal drift wave stability and the generation of mean sheared parallel flow are examined. The first part of this work extends the development of a local model of ionization-driven drift wave turbulence [Phys. Fluids B 4, 877 (1992)] to include the effects of magnetic shear and poloidal source asymmetry, as well as poloidal mode coupling due to both magnetic drifts and the source asymmetry. Numerical and analytic investigation confirm that ionization effects can destabilize collisional toroidal drift waves. However, the mode structure is determined primarily by the magnetic drifts, and is not overly effected by the poloidal source asymmetry. The ionization source drives a purely inward particle flux, which can explain the anomalously rapid uptake of particles which occurs in response to gas puffing. In the second part of this work, the role poloidal asymmetries in both the source and turbulent particle diffusion play in the generation of sheared mean parallel flow is examined. Analysis indicates that predictions of sonic parallel shear flow [v∥(r)∼cs] are an unphysical result of the assumption of purely parallel flow (i.e., v⊥=0) and the neglect of turbulent parallel momentum transport. Results indicate that the flow produced is subcritical to the parallel shear flow instability when diamagnetic effects are properly considered.
This work examines bootstrap current in quasi-symmetric stellarators with a focus on the Quasi- P... more This work examines bootstrap current in quasi-symmetric stellarators with a focus on the Quasi- Poloidal Stellarator (QPS). In the design of QPS, a code was used to predict the bootstrap current based on a calculation in an asymptotically collisionless limit. This calculation is believed to be a good approximation of the bootstrap current for low density, high electron temperature (n
Quasi-symmetry in three-dimensional magnetic confinement devices provides a path for external con... more Quasi-symmetry in three-dimensional magnetic confinement devices provides a path for external control of the confining magnetic field while achieving confinement comparable to axisymmetric configurations. In a quasi-symmetric toroidal configuration, magnetic field strength in ...
ABSTRACT Theories that calculate the effect of flow shear on the cross phase between transport-ca... more ABSTRACT Theories that calculate the effect of flow shear on the cross phase between transport-causing fluctuations have generally dealt with multiple inhomogeneities of undetermined scale [1]. To treat this complication, the theories have restricted themselves to shear values that are significantly lower than those of experiment. We address here the strong shear limit for cross phase effects by constructing a scaling theory for the conditions of the original scaling theory of amplitude suppression [2], i.e., a passive scalar advected by ExB flow in a plasma whose only inhomogeneity is the mean flow. We show that correlation between the scalar and the potential has a stronger dependence on inverse shear strength than does the product of the amplitudes, indicating that the cosine of the phase angle is reduced by flow shear. We also examine a scalar with a mean gradient and calculate self-consistently the flux that drives transport of the mean scalar. 1. A.S. Ware, et al., Phys. Plasmas 5, 173 (1998). 2. H. Biglari, et al., Phys. Fluids B 2, 1 (1990).
Quasi-poloidal (QP) stellarators have achieved levels of optimization that significantly suppress... more Quasi-poloidal (QP) stellarators have achieved levels of optimization that significantly suppress neoclassical transport relative to anomalous levels. QP symmetry also allows poloidal flow damping to be less than toroidal flow damping. This ordering (reversed from that of tokamaks) should allow more efficient control of the radial electric field with less required momentum input. An analysis of flow dynamics in such systems has been initiated using viscosity coefficients that can be derived from the usual transport coefficients (density/energy diffusion, bootstrap current. resistivity enhancement). The dependencies of these coefficients on plasma parameters such as collisionality and electric field will be analyzed and implications for flow evolution discussed. By varying the modular and vertical field coil currents in proposed QP systems, substantial flexibility has been demonstrated theoretically with respect to neoclassical confinement, quasi-poloidal symmetry, flow damping, and ...
A compact quasi-poloidally symmetric stellarator plasma and coil configuration is described that ... more A compact quasi-poloidally symmetric stellarator plasma and coil configuration is described that has desirable physics and engineering properties and a very low aspect ratio plasma bounded by good magnetic flux surfaces both in vac-uum and at β = 2%. The configuration is robust insofar as variations of the plasma β and consequent bootstrap current leave the bounding flux surface ap-proximately unchanged, thus reducing active positional control requirements. This configuration was developed using a new computational method targeting good vacuum flux surfaces, as a measure of robustness, in the design of magnetic coils. The stellarator plasma and coil design code STELLOPT is used to vary the coil geometry, which produces plasma geometry and profiles that optimize plasma performance with respect to neoclassical transport, infinite-n ballooning stability up to β = 2%, and coil engineering parameters. The normal compo-nent of the vacuum magnetic field is simultaneously minimized at the f...
ABSTRACT The Quasi-Poloidal Stellarator (QPS) achieves approximate poloidal symmetry in magnetic ... more ABSTRACT The Quasi-Poloidal Stellarator (QPS) achieves approximate poloidal symmetry in magnetic coordinates at low aspect ratio through numerically determined three-dimensional shaping. This symmetry results in a number of novel characteristics with respect to neoclassical plasma flows and currents. To analyze these, a moments based analysis has been developed that utilizes the DKES (Drift Kinetic Equation Solver) code to generate a data base of transport coefficients that relate plasma fluxes, parallel flows, Ohmic and bootstrap currents to thermodynamic forces and electric fields. This analysis has indicated that poloidal flows dominate in most regimes, in contrast to the case in toroidally symmetric devices where toroidal flows dominate. Bootstrap currents are suppressed from their axisymmetric levels and have been checked against asymptotic low collisionality predictions. Parameters and profiles are chosen that lead to unique ion/electron root self-consistent ambipolar electric field solutions over the minor radius. Electric field bifurcations are observed at low densities when the electron temperature >> ion temperature. Acknowledgement This work was performed at Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Dept. of Energy under contract DE-AC05-00OR22725.
In this work, a numerical transport model is used to examine for hysteresis in the development of... more In this work, a numerical transport model is used to examine for hysteresis in the development of an edge poloidal velocity shear layer due to a modeled gas puff. The transport model couples together density, ion temperature, electron temperature, poloidal flow, toroidal flow, radial electric field, and a fluctuation envelope equation which includes a shear-suppression factor. The model has been modified in both the physics and in the numerical integration. The physics has been modified to include a turbulence growth rate for resistive ballooning modes as well as ion temperature gradient modes. The numerical integration has been changed to a modified Runge-Kutta with adaptive time-stepping. For the cases run with parameters consistent with these TJ-II experiments (only RF heating, no neutral beams), the resistive ballooning mode growth rate is dominant in the edge region. In this work, we present results from a series of cases using parameters that are typical of TJ-II discharges an...
Turbulence, and turbulence-driven transport are ubiquitous in magnetically confined plasmas, wher... more Turbulence, and turbulence-driven transport are ubiquitous in magnetically confined plasmas, where there is an intimate relationship between turbulence, transport, destabilizing mechanisms like gradients and currents, and stabilizing mechanisms like shear. We ...
This work examines bootstrap current and its impact on the equilibrium properties in optimized st... more This work examines bootstrap current and its impact on the equilibrium properties in optimized stellarators. Two independent methods are used to calculate the bootstrap current: a fast code based on a calculation in an asymptotically collisionless limit [K. C. Shaing, et al., Phys. Fluids B 1, 148 (1989)] and a fluid moments approach that self- consistently calculates the neoclassical transport
The impact of magnetic geometry on neoclassical flows and viscosities for the Helically Symmetric... more The impact of magnetic geometry on neoclassical flows and viscosities for the Helically Symmetric Experiment (HSX) is investigated using the PENTA code [1,2]. Specifically, two topics are investigated: (1) finite-beta effects and (2) configurational variations. The PENTA code is used to calculate flows in HSX with the vacuum magnetic geometry and with finite-beta magnetic surfaces from the VMEC equilibrium code. This is done for the standard quasi-helically symmetric configuration of HSX, a symmetry-breaking mirror configuration and a hill configuration. The impact of these changes in the magnetic geometry on neoclassical viscosities and flows in HSX will be discussed.[0pt] [1] D. A. Spong, Phys. Plasmas 12, 056114 (2005). [0pt] [2] D. A. Spong, Fusion Sci. Technology 50, 343 (2006).
This report is a summary of discussions held in the transport and turbulence breakout subgroups o... more This report is a summary of discussions held in the transport and turbulence breakout subgroups of the Magnetic Confinement Concepts Working Group (which met in the mornings) and the Plasma Sciences Working Group (which met in the afternoons). It was the judgement of the convenors of these groups, that a combined report was appropriate considering the overlap in subject matter and membership of the two groups. The report is organized to cover the most general topics first, then to move on to more specific topics. IFE and basic processes were primarily the focus of the Plasma Science group, while discussion of specific MFE concepts was carried out in the Magnetic Concepts breakouts. The substantial topic of MFE overarching issues was covered extensively in both sets of sessions.
The effects of a poloidally asymmetric ionization source on both dissipative toroidal drift wave ... more The effects of a poloidally asymmetric ionization source on both dissipative toroidal drift wave stability and the generation of mean sheared parallel flow are examined. The first part of this work extends the development of a local model of ionization-driven drift wave turbulence [Phys. Fluids B 4, 877 (1992)] to include the effects of magnetic shear and poloidal source asymmetry, as well as poloidal mode coupling due to both magnetic drifts and the source asymmetry. Numerical and analytic investigation confirm that ionization effects can destabilize collisional toroidal drift waves. However, the mode structure is determined primarily by the magnetic drifts, and is not overly effected by the poloidal source asymmetry. The ionization source drives a purely inward particle flux, which can explain the anomalously rapid uptake of particles which occurs in response to gas puffing. In the second part of this work, the role poloidal asymmetries in both the source and turbulent particle diffusion play in the generation of sheared mean parallel flow is examined. Analysis indicates that predictions of sonic parallel shear flow [v∥(r)∼cs] are an unphysical result of the assumption of purely parallel flow (i.e., v⊥=0) and the neglect of turbulent parallel momentum transport. Results indicate that the flow produced is subcritical to the parallel shear flow instability when diamagnetic effects are properly considered.
This work examines bootstrap current in quasi-symmetric stellarators with a focus on the Quasi- P... more This work examines bootstrap current in quasi-symmetric stellarators with a focus on the Quasi- Poloidal Stellarator (QPS). In the design of QPS, a code was used to predict the bootstrap current based on a calculation in an asymptotically collisionless limit. This calculation is believed to be a good approximation of the bootstrap current for low density, high electron temperature (n
Quasi-symmetry in three-dimensional magnetic confinement devices provides a path for external con... more Quasi-symmetry in three-dimensional magnetic confinement devices provides a path for external control of the confining magnetic field while achieving confinement comparable to axisymmetric configurations. In a quasi-symmetric toroidal configuration, magnetic field strength in ...
ABSTRACT Theories that calculate the effect of flow shear on the cross phase between transport-ca... more ABSTRACT Theories that calculate the effect of flow shear on the cross phase between transport-causing fluctuations have generally dealt with multiple inhomogeneities of undetermined scale [1]. To treat this complication, the theories have restricted themselves to shear values that are significantly lower than those of experiment. We address here the strong shear limit for cross phase effects by constructing a scaling theory for the conditions of the original scaling theory of amplitude suppression [2], i.e., a passive scalar advected by ExB flow in a plasma whose only inhomogeneity is the mean flow. We show that correlation between the scalar and the potential has a stronger dependence on inverse shear strength than does the product of the amplitudes, indicating that the cosine of the phase angle is reduced by flow shear. We also examine a scalar with a mean gradient and calculate self-consistently the flux that drives transport of the mean scalar. 1. A.S. Ware, et al., Phys. Plasmas 5, 173 (1998). 2. H. Biglari, et al., Phys. Fluids B 2, 1 (1990).
Quasi-poloidal (QP) stellarators have achieved levels of optimization that significantly suppress... more Quasi-poloidal (QP) stellarators have achieved levels of optimization that significantly suppress neoclassical transport relative to anomalous levels. QP symmetry also allows poloidal flow damping to be less than toroidal flow damping. This ordering (reversed from that of tokamaks) should allow more efficient control of the radial electric field with less required momentum input. An analysis of flow dynamics in such systems has been initiated using viscosity coefficients that can be derived from the usual transport coefficients (density/energy diffusion, bootstrap current. resistivity enhancement). The dependencies of these coefficients on plasma parameters such as collisionality and electric field will be analyzed and implications for flow evolution discussed. By varying the modular and vertical field coil currents in proposed QP systems, substantial flexibility has been demonstrated theoretically with respect to neoclassical confinement, quasi-poloidal symmetry, flow damping, and ...
A compact quasi-poloidally symmetric stellarator plasma and coil configuration is described that ... more A compact quasi-poloidally symmetric stellarator plasma and coil configuration is described that has desirable physics and engineering properties and a very low aspect ratio plasma bounded by good magnetic flux surfaces both in vac-uum and at β = 2%. The configuration is robust insofar as variations of the plasma β and consequent bootstrap current leave the bounding flux surface ap-proximately unchanged, thus reducing active positional control requirements. This configuration was developed using a new computational method targeting good vacuum flux surfaces, as a measure of robustness, in the design of magnetic coils. The stellarator plasma and coil design code STELLOPT is used to vary the coil geometry, which produces plasma geometry and profiles that optimize plasma performance with respect to neoclassical transport, infinite-n ballooning stability up to β = 2%, and coil engineering parameters. The normal compo-nent of the vacuum magnetic field is simultaneously minimized at the f...
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