S. Benkadda | Université d'Aix-Marseille / CNRS (original) (raw)

Papers by S. Benkadda

Journal of Plasma Physics

Challenges in plasma physics are wide. Investigation and advances are made in experiments but at ... more Challenges in plasma physics are wide. Investigation and advances are made in experiments but at the same time, to understand and to reach the experimental limits, accurate numerical simulations are required from systems of nonlinear equations. The numerical challenges of solving the associated fluid equations are discussed in this paper. Using the framework of the finite difference discretization, the most widely used methods for the problems linked to the diffusion or advection operators are presented.

AIP Conference Proceedings, 2008

ABSTRACT In divertor tokamak plasmas, an Edge Transport Barrier forms during the L-H transition. ... more ABSTRACT In divertor tokamak plasmas, an Edge Transport Barrier forms during the L-H transition. A poloidal shear flow has been shown to play a crucial role in the barrier sustainement. The H regime, obtained for a critical value of the heating power, is promising for the next generation of tokamak experiments such as ITER. However, an instability known as Edge Localized Mode (ELM) develops as the power is increased further. ELMs are characterized by intermittent bursts in the radial heat flux, therefore causing the transport barrier to relax quasi-periodically. Over the last decade, the possibility of controlling ELMs has become more and more plausible, as recent experiments were carried out on DIII-D using I-coils, on JET using error field correction coils, and on TEXTOR using an ergodic divertor. These experimental studies demonstrate a qualitative control over the ELMs by imposing a magnetostatic perturbation at the plasma edge. However, in order to get any quantitative result, much work has to be done in the understanding of ELM dynamics. In this work, we present results from numerical simulations of Resistive Ballooning Mode (RBM) turbulence reproducing the stabilization of barrier relaxations by a static magnetic perturbation. We focus our study on the edge region around the resonant surface q = 3. We use the TEXTOR tokamak geometry, and plasma parameters close to those used in typical experiments on this machine.

The Proper Orthogonal Decomposition (POD), also known as Karhunen-Loeve expansion, and the wavele... more The Proper Orthogonal Decomposition (POD), also known as Karhunen-Loeve expansion, and the wavelet decomposition are two useful techniques to extract coherent structures from data sets. In this work we present a comparative study of the application of both techniques to plasma turbulence. We focus on two-dimensional resistive drift-wave turbulence described by the Hasegawa-Wakatani model. This relatively simple model contains key elements for the study of turbulence including the possibility of cross-field transport and the spontaneous formation of coherent structures. In the POD context, the extraction of the coherent structures is based on low-order truncations of the singular value decomposition of the data sets. The wavelet method is based on the thresholding of the wavelet coefficients. The data is decomposed into an orthogonal wavelet series, a thresholding is applied and the coherent vortices are reconstructed from few strong coefficients. Both approaches are compared in terms of compression rate, retained energy, and enstrophy level of the coherent vortices.

The control of transport barrier relaxation oscillations by resonant magnetic perturbations (RMPs... more The control of transport barrier relaxation oscillations by resonant magnetic perturbations (RMPs) is investigated with three-dimensional turbulence simulations of the tokamak edge. It is shown that single har-monics RMPs (single magnetic island chains) stabilize barrier relaxations. In contrast to the control by multiple harmonics RMPs, these perturbations always lead to a degradation of the energy confinement. The convective energy flux associated with the non-axisymmetric plasma equilibrium in presence of magnetic islands is found to play a key role in the erosion of the transport barrier that leads to the stabilization of the relaxations.

Physical Review E, 2000

A general method by which to investigate nonlinear dynamical systems close to a stability thresho... more A general method by which to investigate nonlinear dynamical systems close to a stability threshold is presented. This method combines a proper orthogonal decomposition and a subsequent Galerkin projection. This technique is applied to three-dimensional resistive ballooning plasma fluctuations in a tokamak. The corresponding dynamical system belongs to a large family of convective fluid systems including Rayleigh-Benard convection. A proper orthogonal decomposition of the fluctuating signal obtained by numerical simulation shows that the relevant modes are close to the linear (global) modes. The Galerkin projection provides a low-dimensional system that allows the study of shear flow generation, its subsequent fluctuation reduction, and the evolution to oscillating states.

ABSTRACT Plasma flow in toroidal geometry results in non‐trivial coupling of plasma flow, radial ... more ABSTRACT Plasma flow in toroidal geometry results in non‐trivial coupling of plasma flow, radial electric field and radial plasma pressure gradient. This coupling originates from combination of inertial and gyroviscous forces in toroidal geometry. Such effects have been recently studied as a sources of symmetry breaking and toroidal flow pinches. It is shown here that combination of geodesic curvature, radial electric field and pressure gradient leads to the instability of toroidal flow. An equilibrium profile of the toroidal rotation is determined from the balance of inertial and gyroviscous forces.

In this work, we study the interaction between a tearing mode and a pressure gradient instability... more In this work, we study the interaction between a tearing mode and a pressure gradient instability (resistive interchange) by solving reduced MHD equations numerically. The numerical study shows existence of regimes where thetearing instability is driven by the pressure gradient. An interplay between the pressure and the magnetic flux controls the dynamics of the saturated state. A secondary instability, triggered by interchange unstable modes, produces convective cells which modify the nature of the magnetic island. The system reaches a new state where small scales are produced and the diamagnetic effect is strongly enhanced as well as the poloidal rotation.

The dynamics of a global reconnection in the presence of a poloidal shear flow which is located i... more The dynamics of a global reconnection in the presence of a poloidal shear flow which is located in between magnetic islands is investigated. Different linear regimes are identified according to the value of the resistivity and the distance between the low-order resonant surfaces. It is found that the presence of a small shear flow affects and significantly delays the global reconnection processes. It is shown that this delay is linked to a breaking of symmetry imposed by the existence of the shear flow and the generation of a mean poloidal flow in the resistive layers. Comment: 6 pages, 10 figures, APFA/APPTC 2009 Conference

Plasmas in nature as well as in laboratory devices often harbor large scale magnetic structures t... more Plasmas in nature as well as in laboratory devices often harbor large scale magnetic structures that play an important role in the global dynamics of the system. Some well known examples of such structures are solar flares or coronal loops in the sun and magnetic islands in a tokamak plasma [1]. Quite frequently these structures coexist with fine scale micro-structures associated with turbulent fluctuations arising from various microinstabilities in the system as interchange instability for example. Until recently, considering that magnetic fluctuations are weak in fusion plasmas, micro turbulence has been investigated from an electrostatic point of view. The origine of large scales magnetic structures were exclusively attributed to mechanisms unlinked to the plasma turbulent nature. In our work, we show that, in fact, the whole dynamics of the system is the result of a complex multiscale interaction process. Thus a large scale magnetic island may result not only from a macroscopic ...

Nonlinear 3D simulations are performed. A RMHD model describing the simultaneous evolution of the... more Nonlinear 3D simulations are performed. A RMHD model describing the simultaneous evolution of the interchange turbulence and the tearing instability is used. We show that, through nonlinear generation of radially extended modes, turbulence generated at the plasma edge can lead to the formation of seed islands in the vicinity of the q=2 surface. The special role of the zonal flow in that context is explicited.

ABSTRACT Interchange and geodesic acoustic type modes are considered within the unified approach ... more ABSTRACT Interchange and geodesic acoustic type modes are considered within the unified approach of two-fluid theory. It is assumed that electrons are in the adiabatic, phikvTi. Appropriate moment equations are used for both components taking into account the the magnetic field curvature, which is modeled by the addition of the constant gravity forces, as well as electromagnetic effects. Both electron and ion drift effects are taken into account including the finite Larmor radius (FLR) effects for ions due to gyroviscosity. Within this approach , ion temperature gradient, interchange, and geodesic acoustic modes are recovered. It is shown that geodesic acoustic modes are intrinsically related to interchange modes. Both types of modes occur as a result of the essential balance between the radial diamagnetic and inertial (polarization) currents. It is shown that coupling of drift and geodesic curvature effects leads to the destabilization of geodesic acoustic modes.

Nonequilibrium Phenomena in Plasmas, 2005

ABSTRACT

We present in this work, a systematic study of the passive particle behavior in a flow that exhib... more We present in this work, a systematic study of the passive particle behavior in a flow that exhibits bifurcations in the transition to a turbulent regime. We consider the flow related to a variant of the Charney-Hasegawa-Mima equation. This equation has numerous applications to different plasma fusion problems and is related to the so-called drift-dissipative instability, and to the Rossby-wave dynamics in geophysics.

Plasma Physics Reports, 2001

Plasma Physics and Controlled Fusion, 2007

A promising operational regime of future fusion reactors is characterized by an edge transport ba... more A promising operational regime of future fusion reactors is characterized by an edge transport barrier, i.e. a localized steepening of density and temperature gradients. Typically, such a barrier is unstable and relaxes quasi-periodically. In this work, we show that complete barrier relaxation cycles can be reproduced by three-dimensional turbulence simulations. In these simulations, a barrier forms due to an imposed

Plasma Physics and Controlled Fusion, 2011

ABSTRACT

Journal of Plasma Physics

Challenges in plasma physics are wide. Investigation and advances are made in experiments but at ... more Challenges in plasma physics are wide. Investigation and advances are made in experiments but at the same time, to understand and to reach the experimental limits, accurate numerical simulations are required from systems of nonlinear equations. The numerical challenges of solving the associated fluid equations are discussed in this paper. Using the framework of the finite difference discretization, the most widely used methods for the problems linked to the diffusion or advection operators are presented.

AIP Conference Proceedings, 2008

ABSTRACT In divertor tokamak plasmas, an Edge Transport Barrier forms during the L-H transition. ... more ABSTRACT In divertor tokamak plasmas, an Edge Transport Barrier forms during the L-H transition. A poloidal shear flow has been shown to play a crucial role in the barrier sustainement. The H regime, obtained for a critical value of the heating power, is promising for the next generation of tokamak experiments such as ITER. However, an instability known as Edge Localized Mode (ELM) develops as the power is increased further. ELMs are characterized by intermittent bursts in the radial heat flux, therefore causing the transport barrier to relax quasi-periodically. Over the last decade, the possibility of controlling ELMs has become more and more plausible, as recent experiments were carried out on DIII-D using I-coils, on JET using error field correction coils, and on TEXTOR using an ergodic divertor. These experimental studies demonstrate a qualitative control over the ELMs by imposing a magnetostatic perturbation at the plasma edge. However, in order to get any quantitative result, much work has to be done in the understanding of ELM dynamics. In this work, we present results from numerical simulations of Resistive Ballooning Mode (RBM) turbulence reproducing the stabilization of barrier relaxations by a static magnetic perturbation. We focus our study on the edge region around the resonant surface q = 3. We use the TEXTOR tokamak geometry, and plasma parameters close to those used in typical experiments on this machine.

The Proper Orthogonal Decomposition (POD), also known as Karhunen-Loeve expansion, and the wavele... more The Proper Orthogonal Decomposition (POD), also known as Karhunen-Loeve expansion, and the wavelet decomposition are two useful techniques to extract coherent structures from data sets. In this work we present a comparative study of the application of both techniques to plasma turbulence. We focus on two-dimensional resistive drift-wave turbulence described by the Hasegawa-Wakatani model. This relatively simple model contains key elements for the study of turbulence including the possibility of cross-field transport and the spontaneous formation of coherent structures. In the POD context, the extraction of the coherent structures is based on low-order truncations of the singular value decomposition of the data sets. The wavelet method is based on the thresholding of the wavelet coefficients. The data is decomposed into an orthogonal wavelet series, a thresholding is applied and the coherent vortices are reconstructed from few strong coefficients. Both approaches are compared in terms of compression rate, retained energy, and enstrophy level of the coherent vortices.

The control of transport barrier relaxation oscillations by resonant magnetic perturbations (RMPs... more The control of transport barrier relaxation oscillations by resonant magnetic perturbations (RMPs) is investigated with three-dimensional turbulence simulations of the tokamak edge. It is shown that single har-monics RMPs (single magnetic island chains) stabilize barrier relaxations. In contrast to the control by multiple harmonics RMPs, these perturbations always lead to a degradation of the energy confinement. The convective energy flux associated with the non-axisymmetric plasma equilibrium in presence of magnetic islands is found to play a key role in the erosion of the transport barrier that leads to the stabilization of the relaxations.

Physical Review E, 2000

A general method by which to investigate nonlinear dynamical systems close to a stability thresho... more A general method by which to investigate nonlinear dynamical systems close to a stability threshold is presented. This method combines a proper orthogonal decomposition and a subsequent Galerkin projection. This technique is applied to three-dimensional resistive ballooning plasma fluctuations in a tokamak. The corresponding dynamical system belongs to a large family of convective fluid systems including Rayleigh-Benard convection. A proper orthogonal decomposition of the fluctuating signal obtained by numerical simulation shows that the relevant modes are close to the linear (global) modes. The Galerkin projection provides a low-dimensional system that allows the study of shear flow generation, its subsequent fluctuation reduction, and the evolution to oscillating states.

ABSTRACT Plasma flow in toroidal geometry results in non‐trivial coupling of plasma flow, radial ... more ABSTRACT Plasma flow in toroidal geometry results in non‐trivial coupling of plasma flow, radial electric field and radial plasma pressure gradient. This coupling originates from combination of inertial and gyroviscous forces in toroidal geometry. Such effects have been recently studied as a sources of symmetry breaking and toroidal flow pinches. It is shown here that combination of geodesic curvature, radial electric field and pressure gradient leads to the instability of toroidal flow. An equilibrium profile of the toroidal rotation is determined from the balance of inertial and gyroviscous forces.

In this work, we study the interaction between a tearing mode and a pressure gradient instability... more In this work, we study the interaction between a tearing mode and a pressure gradient instability (resistive interchange) by solving reduced MHD equations numerically. The numerical study shows existence of regimes where thetearing instability is driven by the pressure gradient. An interplay between the pressure and the magnetic flux controls the dynamics of the saturated state. A secondary instability, triggered by interchange unstable modes, produces convective cells which modify the nature of the magnetic island. The system reaches a new state where small scales are produced and the diamagnetic effect is strongly enhanced as well as the poloidal rotation.

The dynamics of a global reconnection in the presence of a poloidal shear flow which is located i... more The dynamics of a global reconnection in the presence of a poloidal shear flow which is located in between magnetic islands is investigated. Different linear regimes are identified according to the value of the resistivity and the distance between the low-order resonant surfaces. It is found that the presence of a small shear flow affects and significantly delays the global reconnection processes. It is shown that this delay is linked to a breaking of symmetry imposed by the existence of the shear flow and the generation of a mean poloidal flow in the resistive layers. Comment: 6 pages, 10 figures, APFA/APPTC 2009 Conference

Plasmas in nature as well as in laboratory devices often harbor large scale magnetic structures t... more Plasmas in nature as well as in laboratory devices often harbor large scale magnetic structures that play an important role in the global dynamics of the system. Some well known examples of such structures are solar flares or coronal loops in the sun and magnetic islands in a tokamak plasma [1]. Quite frequently these structures coexist with fine scale micro-structures associated with turbulent fluctuations arising from various microinstabilities in the system as interchange instability for example. Until recently, considering that magnetic fluctuations are weak in fusion plasmas, micro turbulence has been investigated from an electrostatic point of view. The origine of large scales magnetic structures were exclusively attributed to mechanisms unlinked to the plasma turbulent nature. In our work, we show that, in fact, the whole dynamics of the system is the result of a complex multiscale interaction process. Thus a large scale magnetic island may result not only from a macroscopic ...

Nonlinear 3D simulations are performed. A RMHD model describing the simultaneous evolution of the... more Nonlinear 3D simulations are performed. A RMHD model describing the simultaneous evolution of the interchange turbulence and the tearing instability is used. We show that, through nonlinear generation of radially extended modes, turbulence generated at the plasma edge can lead to the formation of seed islands in the vicinity of the q=2 surface. The special role of the zonal flow in that context is explicited.

ABSTRACT Interchange and geodesic acoustic type modes are considered within the unified approach ... more ABSTRACT Interchange and geodesic acoustic type modes are considered within the unified approach of two-fluid theory. It is assumed that electrons are in the adiabatic, phikvTi. Appropriate moment equations are used for both components taking into account the the magnetic field curvature, which is modeled by the addition of the constant gravity forces, as well as electromagnetic effects. Both electron and ion drift effects are taken into account including the finite Larmor radius (FLR) effects for ions due to gyroviscosity. Within this approach , ion temperature gradient, interchange, and geodesic acoustic modes are recovered. It is shown that geodesic acoustic modes are intrinsically related to interchange modes. Both types of modes occur as a result of the essential balance between the radial diamagnetic and inertial (polarization) currents. It is shown that coupling of drift and geodesic curvature effects leads to the destabilization of geodesic acoustic modes.

Nonequilibrium Phenomena in Plasmas, 2005

ABSTRACT

We present in this work, a systematic study of the passive particle behavior in a flow that exhib... more We present in this work, a systematic study of the passive particle behavior in a flow that exhibits bifurcations in the transition to a turbulent regime. We consider the flow related to a variant of the Charney-Hasegawa-Mima equation. This equation has numerous applications to different plasma fusion problems and is related to the so-called drift-dissipative instability, and to the Rossby-wave dynamics in geophysics.

Plasma Physics Reports, 2001

Plasma Physics and Controlled Fusion, 2007

A promising operational regime of future fusion reactors is characterized by an edge transport ba... more A promising operational regime of future fusion reactors is characterized by an edge transport barrier, i.e. a localized steepening of density and temperature gradients. Typically, such a barrier is unstable and relaxes quasi-periodically. In this work, we show that complete barrier relaxation cycles can be reproduced by three-dimensional turbulence simulations. In these simulations, a barrier forms due to an imposed

Plasma Physics and Controlled Fusion, 2011

ABSTRACT