Maintaining conservation laws in the fully discrete setting is critical for accurate long-time be... more Maintaining conservation laws in the fully discrete setting is critical for accurate long-time behavior of numerical simulations and requires accounting for discrete conservation properties in both space and time. This paper derives arbitrary order finite element exterior calculus spatial discretizations for the two-dimensional (2D) Navier-Stokes and drift-reduced magnetohydrodynamic equations that conserve both energy and enstrophy to machine precision when coupled with generally symplectic time-integration methods. Both continuous and discontinuous-Galerkin (DG) weak formulations can ensure conservation, but only generally symplectic time integration methods, such as the implicit midpoint method, permit exact conservation in time. Moreover, the symplectic implicit midpoint method yields an order of magnitude speedup over explicit schemes. The methods are implemented using the MFEM library and the solutions are verified for an extensive suite of 2D neutral fluid turbulence test problems. Numerical solutions are verified via comparison to a semi-analytic linear eigensolver as well as to the finite difference Global Drift Ballooning (GDB) code. However, it is found that turbulent simulations that conserve both energy and enstrophy tend to have too much power at high wavenumber and that this part of the spectrum should be controlled by reintroducing artificial dissipation. The DG formulation allows upwinding of the advection operator which dissipates enstrophy while still maintaining conservation of energy. Coupling upwinded DG with implicit symplectic integration appears to offer the best compromise of allowing mid-range wavenumbers to reach the appropriate amplitude while still controlling the high-wavenumber part of the spectrum.
Abstract A model of ion temperature anisotropy for 2D plasma transport in the scrape-off layer (S... more Abstract A model of ion temperature anisotropy for 2D plasma transport in the scrape-off layer (SOL) of tokamaks is described and implemented in the UEDGE fluid transport code. Two ion energy equations are used to describe the evolution of the separate parallel and perpendicular ion temperatures. The temperature anisotropy generates viscous forces in both parallel and perpendicular directions that modify the parallel force balance equation and add an additional cross-magnetic-field drift velocity. Using the full set of UEDGE plasma and neutral equations (particle continuity, momentum, and energy), simulations are performed for both a 1D poloidal case and a 2D (radial and poloidal) single-null tokamak geometry case to highlight the 2D effects. The results show that ion parallel flows near the magnetic X-point in a comparatively low collisionality regime can be overestimated by the standard isotropic Braginskii model. The 2D ion temperature anisotropy varies substantially near the X-point and also near the divertor target plates, due to ionization sources. Moving radially outwards at the outer midplane, the anisotropy decreases between the core boundary and the magnetic separatrix and then it increases while moving across the SOL to the chamber wall.
Motivated by recent discussions on the possible role of quantum computation in plasma simulations... more Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here, we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov–Maxwell kinetic theory. The celebrated Koopman–von Neumann construction is provided with two different Hamiltonian structures: one is canonical and recovers the usual Clebsch representation of the Vlasov density, the other is non-canonical and appears to overcome certain issues emerging in the canonical formalism. Furthermore, the canonical structure is restored for a variant of the Koopman–von Neumann construction that carries a different phase dynamics. Going back to van Hove's prequantum theory, the corresponding Koopman–van Hove equation provides an alternative Clebsch representation which is then coupled to the electromagnetic fields. Finally, the role of gauge transformations in the new context is discussed in detail.
Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenva... more Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems Hv = λv, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to generalized eigenvalue problems Av = λBv, which arise in many areas of science and engineering. We answer this question affirmatively. A restricted class of generalized eigenvalue could be solved as efficiently as standard eigenvalue problems. A paradigmatic example is provided by Sturm-Liouville problems. Moreover, this method could be used for linear ideal magnetohydrodynamics to determine the stability of magnetically confined plasmas used in fusion reactors, providing a route to fast stability calculations in design optimization or feedback control.
This article reports on the first dedicated 1D+2V heat pulse propagation studies using the COGENT... more This article reports on the first dedicated 1D+2V heat pulse propagation studies using the COGENT guiding center kinetic code. The model uses magnetized kinetic ions and a simple Boltzmann electron model. Results agree with previous kinetic and fluid modeling benchmark studies that correspond to the parameters of edge localized modes (ELMs) observed on the JET tokamak. The plasma parameters for the edge pedestal and ensuing ELM dynamics are in the low collisionality regime. Hence, the dominant balance between the assumed Maxwellian ELM source and collisionless parallel advection causes the ion PDF to develop a significantly anisotropic velocity distribution. Adding nonlinear Coulomb ion-ion collisions to the model acts to smooth the sharp features of the ion distribution function, but the anisotropy remains robust due to the low collisionality.
Jacobian-free Newton-Krylov (JFNK) algorithms are a potentially powerful class of methods for sol... more Jacobian-free Newton-Krylov (JFNK) algorithms are a potentially powerful class of methods for solving the problem of coupling codes that address dfferent physics models. As communication capability between individual submodules varies, different choices of coupling algorithms are required. The more communication that is available, the more possible it becomes to exploit the simple sparsity pattern of the Jacobian, albeit of a large system. The less communication that is available, the more dense the Jacobian matrices become and new types of preconditioners must be sought to efficiently take large time steps. In general, methods that use constrained or reduced subsystems can offer a compromise in complexity. The specific problem of coupling a fluid plasma code to a kinetic neutrals code is discussed as an example.
An efficient and versatile non-Fourier method for the computation of Landau-fluid (LF) closure op... more An efficient and versatile non-Fourier method for the computation of Landau-fluid (LF) closure operators [Hammett and Perkins, Phys. Rev. Lett. 64, 3019 (1990)] is presented, based on an approximation by a sum of modified-Helmholtz-equation solves (SMHS) in configuration space. This method can yield fast-Fourier-like scaling of the computational time requirements and also provides a very compact data representation of these operators, even for plasmas with large spatial nonuniformity. As a result, the method can give significant savings compared with direct application of "delocalization kernels" [e.g., Schurtz et al., Phys. Plasmas 7, 4238 (2000)], both in terms of computational cost and memory requirements. The method is of interest for the implementation of Landau-fluid models in situations where the spatial nonuniformity, particular geometry, or boundary conditions render a Fourier implementation difficult or impossible. Systematic procedures have been developed to optimize the resulting operators for accuracy and computational cost. The four-moment Landau-fluid model of Hammett and Perkins has been implemented in the BOUTþþ code using the SMHS method for LF closure. Excellent agreement has been obtained for the one-dimensional plasma density response function between driven initial-value calculations using this BOUTþþ implementation and matrix eigenvalue calculations using both Fourier and SMHS non-Fourier implementations of the LF closures. The SMHS method also forms the basis for the implementation, which has been carried out in the BOUTþþ code, of the parallel and toroidal drift-resonance LF closures. The method is a key enabling tool for the extension of gyro-Landau-fluid models [e.g., Beer and Hammett, Phys. Plasmas 3, 4046 (1996)] to codes that treat regions with strong profile variation, such as the tokamak edge and scrapeoff-layer.
The bunching instability of particles trapped in Langmuir waves is studied using Vlasov simulatio... more The bunching instability of particles trapped in Langmuir waves is studied using Vlasov simulations. A measure of particle bunching is defined and used to extract the growth rate from numerical simulations, which are compared with theory [Dodin et al., Phys. Rev. Lett., 110, 215006 (2013)]. In addition, the general theory of trapped particle instability in 1D is revisited and a more accurate description of the dispersion relation is obtained. Excellent agreement between numerical and theoretical predictions of growth rates of the bunching instability is shown over a range of parameters.
An unambiguous signal of the negative mass instability (NMI) of large amplitude Langmuir waves ha... more An unambiguous signal of the negative mass instability (NMI) of large amplitude Langmuir waves has been observed for the first time using a 1D-1V Vlasov simulation code. During the NMI, recently proposed by Dodin (PRL 110, 215006 (2013)), particles trapped in the potential well move to different trapped orbits with different bounce frequencies due to mutual Coulomb repulsion and potentially undergo phase bunching. The NMI in Langmuir waves has been studied using the Vlasov simulation with initial conditions conducive to comparison with theoretical estimates of the growth rate. In order to investigate the instability, Fourier analysis of the trapped particle distribution has been performed in action-angle coordinates. Theoretical and numerical growth rates of the NMI are in good agreement when the trapped particle population is initialized as a delta-like function in energy. The mechanism of nonlinear saturation of the NMI is also discussed. This work was performed under the auspices of the
A critical requirement for tokamak fusion reactors is the control of the divertor heat load, both... more A critical requirement for tokamak fusion reactors is the control of the divertor heat load, both the time-averaged value and the impulsive fluxes that accompany edge-localized modes. We propose driving toroidally varying currents through the scrape-off layer (SOL) plasma both to broaden the SOL by inducing radial convection and to control the edge pressure gradient by inducing resonant magnetic perturbations. The generation of additional convective transport via steady-state convective cells or increased turbulence drive requires that the electric potential perturbations exceed a threshold in amplitude that depends on wavelength. The generation of a coherent magnetic perturbation is optimized by choosing the appropriate width and phasing of the biasing region at the target plate in order to optimize the profile of the SOL current. Longer wavelength modes produce a larger effect because they are not sheared as strongly by the magnetic X-point. Generation of the necessary currents is challenging due to the possibly substantial power requirements and the possible need for internal insulators. We analyze passive current-drive mechanisms that rely on puffing and pumping of neutral gas in a toroidally asymmetric fashion using the UEDGE code to model the ITER divertor.
The response of an H-mode plasma to magnetic perturbations that are resonant in the edge is evalu... more The response of an H-mode plasma to magnetic perturbations that are resonant in the edge is evaluated using a fluid model. With two exceptions, the plasma rotation suppresses the formation of magnetic islands, holding their widths to less than a tenth of those predicted by the vacuum approximation. The two exceptions are at the foot of the pedestal, where the plasma becomes more resistive, and at the surface where the perpendicular component of the electron velocity reverses. The perturbations exert a force on the plasma so as to brake the perpendicular component of the electron rotation. In the pedestal, the corresponding Maxwell stress drives the radial electric field in such a way as to accelerate ion rotation. Despite the suppression of the islands, the perturbations give rise to particle fluxes caused by magnetic flutter, with a negligible contribution from E × B convection. In the pedestal, the fluxes are such as to reduce the density.
The effect of resonant magnetic perturbations on heat transport in DIII-D H-mode plasmas has been... more The effect of resonant magnetic perturbations on heat transport in DIII-D H-mode plasmas has been calculated by combining the TRIP3D field line tracing code with the E3D two-fluid transport code. Simulations show that the divertor heat flux distribution becomes non-axisymmetric because heat flux is efficiently guided to the divertor along the three-dimensional invariant manifolds of the magnetic field. Calculations demonstrate that heat flux is spread over a wider area of the divertor target, thereby reducing the peak heat flux delivered during steady-state operation. Filtered optical cameras have observed non-axisymmetric particle fluxes at the strike point and Langmuir probes have observed non-axisymmetric floating potentials. On the other hand, the predicted magnitude of stochastic thermal transport is too large to match the pedestal plasma profiles measured by Thomson scattering and charge exchange recombination spectroscopy. The Braginskii thermal conductivity overestimates the...
Effects of linear plasma response currents on non-axisymmetric magnetic field perturbations from ... more Effects of linear plasma response currents on non-axisymmetric magnetic field perturbations from the I-coil used for edge localized mode mitigation in DIII-D tokamak are analysed with the help of a kinetic plasma response model developed for cylindrical geometry. It is shown that these currents eliminate the ergodization of the magnetic field in the core plasma and reduce the size of the ergodic layer at the edge. A simple balance model is proposed which qualitatively reproduces the evolution of the plasma parameters in the pedestal region with the onset of the perturbation. It is suggested that the experimentally observed density pump-out effect in the long mean free path regime is the result of a combined action of ion orbit losses and magnetic field ergodization at the edge.
A critical issue for fusion plasma research is the erosion of the first wall of the experimental ... more A critical issue for fusion plasma research is the erosion of the first wall of the experimental device due to impulsive heating from repetitive edge magneto-hydrodynamic (MHD) instabilities known as "edge-localized modes" (ELMs). Here, we show that the addition of small resonant magnetic field perturbations completely eliminates ELMs while maintaining a steady-state highconfinement (H-mode) plasma. These perturbations induce a chaotic behaviour in the magnetic field lines, which reduces the edge pressure gradient below the ELM instability threshold. The pressure gradient reduction results from a reduction in particle content of the plasma, rather than an increase in the electron thermal transport. This is inconsistent with the predictions of stochastic electron heat transport theory. These results provide a first experimental test of stochastic transport theory in a highly rotating, hot, collisionless plasma and demonstrate a promising solution to the critical issue of controlling edge instabilities in fusion plasma devices.
This is a preprint of a paper to be presented at the 17th Plasma Surface Interactions in Controll... more This is a preprint of a paper to be presented at the 17th Plasma Surface Interactions in Controlled Fusion Devices, May 22-26, 2006, in Hefei, China, and to be published in the J. Nucl. Mater.
In this contribution, we report on experimental results on edge transport in limiter H-mode plasm... more In this contribution, we report on experimental results on edge transport in limiter H-mode plasmas in TEXTOR under the influence of the Dynamic Ergodic Divertor (DED). These plasmas are characterized by a pedestal structure mainly visible in the electron density, resulting in increased electron pressure gradients of up to 30kPa/m over a pedestal width of 25 mm at high pedestal collisionalities (ν e * = 1 − 10), and with high frequency ELMs in the range of 300-1500 Hz. Under the influence of DED the pedestal pressure is gradually reduced and completely collapses to L-mode when the laminar zone extends all the way across the pedestal width. Toroidal plasma rotation is maintained at H-mode levels by the torque introduced by DED in the stochastic region. The perturbed magnetic topology has been optimized to access conditions with a density pump-out which are strongly governed by wall pumping capabilities in TEXTOR.
Maintaining conservation laws in the fully discrete setting is critical for accurate long-time be... more Maintaining conservation laws in the fully discrete setting is critical for accurate long-time behavior of numerical simulations and requires accounting for discrete conservation properties in both space and time. This paper derives arbitrary order finite element exterior calculus spatial discretizations for the two-dimensional (2D) Navier-Stokes and drift-reduced magnetohydrodynamic equations that conserve both energy and enstrophy to machine precision when coupled with generally symplectic time-integration methods. Both continuous and discontinuous-Galerkin (DG) weak formulations can ensure conservation, but only generally symplectic time integration methods, such as the implicit midpoint method, permit exact conservation in time. Moreover, the symplectic implicit midpoint method yields an order of magnitude speedup over explicit schemes. The methods are implemented using the MFEM library and the solutions are verified for an extensive suite of 2D neutral fluid turbulence test problems. Numerical solutions are verified via comparison to a semi-analytic linear eigensolver as well as to the finite difference Global Drift Ballooning (GDB) code. However, it is found that turbulent simulations that conserve both energy and enstrophy tend to have too much power at high wavenumber and that this part of the spectrum should be controlled by reintroducing artificial dissipation. The DG formulation allows upwinding of the advection operator which dissipates enstrophy while still maintaining conservation of energy. Coupling upwinded DG with implicit symplectic integration appears to offer the best compromise of allowing mid-range wavenumbers to reach the appropriate amplitude while still controlling the high-wavenumber part of the spectrum.
Abstract A model of ion temperature anisotropy for 2D plasma transport in the scrape-off layer (S... more Abstract A model of ion temperature anisotropy for 2D plasma transport in the scrape-off layer (SOL) of tokamaks is described and implemented in the UEDGE fluid transport code. Two ion energy equations are used to describe the evolution of the separate parallel and perpendicular ion temperatures. The temperature anisotropy generates viscous forces in both parallel and perpendicular directions that modify the parallel force balance equation and add an additional cross-magnetic-field drift velocity. Using the full set of UEDGE plasma and neutral equations (particle continuity, momentum, and energy), simulations are performed for both a 1D poloidal case and a 2D (radial and poloidal) single-null tokamak geometry case to highlight the 2D effects. The results show that ion parallel flows near the magnetic X-point in a comparatively low collisionality regime can be overestimated by the standard isotropic Braginskii model. The 2D ion temperature anisotropy varies substantially near the X-point and also near the divertor target plates, due to ionization sources. Moving radially outwards at the outer midplane, the anisotropy decreases between the core boundary and the magnetic separatrix and then it increases while moving across the SOL to the chamber wall.
Motivated by recent discussions on the possible role of quantum computation in plasma simulations... more Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here, we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov–Maxwell kinetic theory. The celebrated Koopman–von Neumann construction is provided with two different Hamiltonian structures: one is canonical and recovers the usual Clebsch representation of the Vlasov density, the other is non-canonical and appears to overcome certain issues emerging in the canonical formalism. Furthermore, the canonical structure is restored for a variant of the Koopman–von Neumann construction that carries a different phase dynamics. Going back to van Hove's prequantum theory, the corresponding Koopman–van Hove equation provides an alternative Clebsch representation which is then coupled to the electromagnetic fields. Finally, the role of gauge transformations in the new context is discussed in detail.
Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenva... more Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems Hv = λv, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to generalized eigenvalue problems Av = λBv, which arise in many areas of science and engineering. We answer this question affirmatively. A restricted class of generalized eigenvalue could be solved as efficiently as standard eigenvalue problems. A paradigmatic example is provided by Sturm-Liouville problems. Moreover, this method could be used for linear ideal magnetohydrodynamics to determine the stability of magnetically confined plasmas used in fusion reactors, providing a route to fast stability calculations in design optimization or feedback control.
This article reports on the first dedicated 1D+2V heat pulse propagation studies using the COGENT... more This article reports on the first dedicated 1D+2V heat pulse propagation studies using the COGENT guiding center kinetic code. The model uses magnetized kinetic ions and a simple Boltzmann electron model. Results agree with previous kinetic and fluid modeling benchmark studies that correspond to the parameters of edge localized modes (ELMs) observed on the JET tokamak. The plasma parameters for the edge pedestal and ensuing ELM dynamics are in the low collisionality regime. Hence, the dominant balance between the assumed Maxwellian ELM source and collisionless parallel advection causes the ion PDF to develop a significantly anisotropic velocity distribution. Adding nonlinear Coulomb ion-ion collisions to the model acts to smooth the sharp features of the ion distribution function, but the anisotropy remains robust due to the low collisionality.
Jacobian-free Newton-Krylov (JFNK) algorithms are a potentially powerful class of methods for sol... more Jacobian-free Newton-Krylov (JFNK) algorithms are a potentially powerful class of methods for solving the problem of coupling codes that address dfferent physics models. As communication capability between individual submodules varies, different choices of coupling algorithms are required. The more communication that is available, the more possible it becomes to exploit the simple sparsity pattern of the Jacobian, albeit of a large system. The less communication that is available, the more dense the Jacobian matrices become and new types of preconditioners must be sought to efficiently take large time steps. In general, methods that use constrained or reduced subsystems can offer a compromise in complexity. The specific problem of coupling a fluid plasma code to a kinetic neutrals code is discussed as an example.
An efficient and versatile non-Fourier method for the computation of Landau-fluid (LF) closure op... more An efficient and versatile non-Fourier method for the computation of Landau-fluid (LF) closure operators [Hammett and Perkins, Phys. Rev. Lett. 64, 3019 (1990)] is presented, based on an approximation by a sum of modified-Helmholtz-equation solves (SMHS) in configuration space. This method can yield fast-Fourier-like scaling of the computational time requirements and also provides a very compact data representation of these operators, even for plasmas with large spatial nonuniformity. As a result, the method can give significant savings compared with direct application of "delocalization kernels" [e.g., Schurtz et al., Phys. Plasmas 7, 4238 (2000)], both in terms of computational cost and memory requirements. The method is of interest for the implementation of Landau-fluid models in situations where the spatial nonuniformity, particular geometry, or boundary conditions render a Fourier implementation difficult or impossible. Systematic procedures have been developed to optimize the resulting operators for accuracy and computational cost. The four-moment Landau-fluid model of Hammett and Perkins has been implemented in the BOUTþþ code using the SMHS method for LF closure. Excellent agreement has been obtained for the one-dimensional plasma density response function between driven initial-value calculations using this BOUTþþ implementation and matrix eigenvalue calculations using both Fourier and SMHS non-Fourier implementations of the LF closures. The SMHS method also forms the basis for the implementation, which has been carried out in the BOUTþþ code, of the parallel and toroidal drift-resonance LF closures. The method is a key enabling tool for the extension of gyro-Landau-fluid models [e.g., Beer and Hammett, Phys. Plasmas 3, 4046 (1996)] to codes that treat regions with strong profile variation, such as the tokamak edge and scrapeoff-layer.
The bunching instability of particles trapped in Langmuir waves is studied using Vlasov simulatio... more The bunching instability of particles trapped in Langmuir waves is studied using Vlasov simulations. A measure of particle bunching is defined and used to extract the growth rate from numerical simulations, which are compared with theory [Dodin et al., Phys. Rev. Lett., 110, 215006 (2013)]. In addition, the general theory of trapped particle instability in 1D is revisited and a more accurate description of the dispersion relation is obtained. Excellent agreement between numerical and theoretical predictions of growth rates of the bunching instability is shown over a range of parameters.
An unambiguous signal of the negative mass instability (NMI) of large amplitude Langmuir waves ha... more An unambiguous signal of the negative mass instability (NMI) of large amplitude Langmuir waves has been observed for the first time using a 1D-1V Vlasov simulation code. During the NMI, recently proposed by Dodin (PRL 110, 215006 (2013)), particles trapped in the potential well move to different trapped orbits with different bounce frequencies due to mutual Coulomb repulsion and potentially undergo phase bunching. The NMI in Langmuir waves has been studied using the Vlasov simulation with initial conditions conducive to comparison with theoretical estimates of the growth rate. In order to investigate the instability, Fourier analysis of the trapped particle distribution has been performed in action-angle coordinates. Theoretical and numerical growth rates of the NMI are in good agreement when the trapped particle population is initialized as a delta-like function in energy. The mechanism of nonlinear saturation of the NMI is also discussed. This work was performed under the auspices of the
A critical requirement for tokamak fusion reactors is the control of the divertor heat load, both... more A critical requirement for tokamak fusion reactors is the control of the divertor heat load, both the time-averaged value and the impulsive fluxes that accompany edge-localized modes. We propose driving toroidally varying currents through the scrape-off layer (SOL) plasma both to broaden the SOL by inducing radial convection and to control the edge pressure gradient by inducing resonant magnetic perturbations. The generation of additional convective transport via steady-state convective cells or increased turbulence drive requires that the electric potential perturbations exceed a threshold in amplitude that depends on wavelength. The generation of a coherent magnetic perturbation is optimized by choosing the appropriate width and phasing of the biasing region at the target plate in order to optimize the profile of the SOL current. Longer wavelength modes produce a larger effect because they are not sheared as strongly by the magnetic X-point. Generation of the necessary currents is challenging due to the possibly substantial power requirements and the possible need for internal insulators. We analyze passive current-drive mechanisms that rely on puffing and pumping of neutral gas in a toroidally asymmetric fashion using the UEDGE code to model the ITER divertor.
The response of an H-mode plasma to magnetic perturbations that are resonant in the edge is evalu... more The response of an H-mode plasma to magnetic perturbations that are resonant in the edge is evaluated using a fluid model. With two exceptions, the plasma rotation suppresses the formation of magnetic islands, holding their widths to less than a tenth of those predicted by the vacuum approximation. The two exceptions are at the foot of the pedestal, where the plasma becomes more resistive, and at the surface where the perpendicular component of the electron velocity reverses. The perturbations exert a force on the plasma so as to brake the perpendicular component of the electron rotation. In the pedestal, the corresponding Maxwell stress drives the radial electric field in such a way as to accelerate ion rotation. Despite the suppression of the islands, the perturbations give rise to particle fluxes caused by magnetic flutter, with a negligible contribution from E × B convection. In the pedestal, the fluxes are such as to reduce the density.
The effect of resonant magnetic perturbations on heat transport in DIII-D H-mode plasmas has been... more The effect of resonant magnetic perturbations on heat transport in DIII-D H-mode plasmas has been calculated by combining the TRIP3D field line tracing code with the E3D two-fluid transport code. Simulations show that the divertor heat flux distribution becomes non-axisymmetric because heat flux is efficiently guided to the divertor along the three-dimensional invariant manifolds of the magnetic field. Calculations demonstrate that heat flux is spread over a wider area of the divertor target, thereby reducing the peak heat flux delivered during steady-state operation. Filtered optical cameras have observed non-axisymmetric particle fluxes at the strike point and Langmuir probes have observed non-axisymmetric floating potentials. On the other hand, the predicted magnitude of stochastic thermal transport is too large to match the pedestal plasma profiles measured by Thomson scattering and charge exchange recombination spectroscopy. The Braginskii thermal conductivity overestimates the...
Effects of linear plasma response currents on non-axisymmetric magnetic field perturbations from ... more Effects of linear plasma response currents on non-axisymmetric magnetic field perturbations from the I-coil used for edge localized mode mitigation in DIII-D tokamak are analysed with the help of a kinetic plasma response model developed for cylindrical geometry. It is shown that these currents eliminate the ergodization of the magnetic field in the core plasma and reduce the size of the ergodic layer at the edge. A simple balance model is proposed which qualitatively reproduces the evolution of the plasma parameters in the pedestal region with the onset of the perturbation. It is suggested that the experimentally observed density pump-out effect in the long mean free path regime is the result of a combined action of ion orbit losses and magnetic field ergodization at the edge.
A critical issue for fusion plasma research is the erosion of the first wall of the experimental ... more A critical issue for fusion plasma research is the erosion of the first wall of the experimental device due to impulsive heating from repetitive edge magneto-hydrodynamic (MHD) instabilities known as "edge-localized modes" (ELMs). Here, we show that the addition of small resonant magnetic field perturbations completely eliminates ELMs while maintaining a steady-state highconfinement (H-mode) plasma. These perturbations induce a chaotic behaviour in the magnetic field lines, which reduces the edge pressure gradient below the ELM instability threshold. The pressure gradient reduction results from a reduction in particle content of the plasma, rather than an increase in the electron thermal transport. This is inconsistent with the predictions of stochastic electron heat transport theory. These results provide a first experimental test of stochastic transport theory in a highly rotating, hot, collisionless plasma and demonstrate a promising solution to the critical issue of controlling edge instabilities in fusion plasma devices.
This is a preprint of a paper to be presented at the 17th Plasma Surface Interactions in Controll... more This is a preprint of a paper to be presented at the 17th Plasma Surface Interactions in Controlled Fusion Devices, May 22-26, 2006, in Hefei, China, and to be published in the J. Nucl. Mater.
In this contribution, we report on experimental results on edge transport in limiter H-mode plasm... more In this contribution, we report on experimental results on edge transport in limiter H-mode plasmas in TEXTOR under the influence of the Dynamic Ergodic Divertor (DED). These plasmas are characterized by a pedestal structure mainly visible in the electron density, resulting in increased electron pressure gradients of up to 30kPa/m over a pedestal width of 25 mm at high pedestal collisionalities (ν e * = 1 − 10), and with high frequency ELMs in the range of 300-1500 Hz. Under the influence of DED the pedestal pressure is gradually reduced and completely collapses to L-mode when the laminar zone extends all the way across the pedestal width. Toroidal plasma rotation is maintained at H-mode levels by the torque introduced by DED in the stochastic region. The perturbed magnetic topology has been optimized to access conditions with a density pump-out which are strongly governed by wall pumping capabilities in TEXTOR.
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