Study of turbulence associated with trapped particles in fusion plasmas

Les micro-instabilités ioniques et électroniques présentes dans les plasmas de fusion sont à l’origine de la turbulence. Le transport anormal de particules et d’énergie, induit par cette turbulence, joue un rôle néfaste pour les performances des machines à fusion nucléaire comme le tokamak. C’est dans ce cadre général que s’inscrit ce travail visant à une meilleure compréhension de la turbulence et des phénomènes de transport sous-jacents. On sait que la dynamique des particules piégées joue un rôle très important dans l’établissement de la turbulence au travers des instabilités ioniques TIM (Trapped Ion Modes) et électroniques TEM (Trapped Electron Modes). Nous nous attachons donc dans ce travail au développement d’un modèle décrivant ces particules piégées (ions et électrons) de manière cinétique. L’échelle de temps à laquelle nous nous plaçons est de l’ordre de la période de précession toroïdale des particules piégées, période typique de la turbulence TIM/TEM. L’originalité de ce modèle réside dans la réduction de la dimension du problème (de 6D à 4D) par la moyenne sur les deux échelles de temps rapides associées aux particules piégées, respectivement le mouvement cyclotronique et le mouvement de rebond. De plus, l’utilisation des variables d’angle et d’action permet de transformer deux variables en paramètres. Le modèle final ainsi obtenu est 4D, dont deux dimensions interviennent sous la forme de paramètres. L’analyse linéaire du modèle nous permet de connaître les gradients de température et de densité permettant le déclenchement des instabilités TIM et TEM. Il nous permet également de connaître les taux de croissance et les pulsations associés à ces deux instabilités. Ensuite, nous nous appuyons sur le code global TERESA 4D décrivant les ions piégés cinétiques pour y inclure la résolution non-linéaire du modèle décrivant les ions et les électrons piégés cinétiques. Les échelles spatio-temporelles de la turbulence induite par les électrons et celle induite par les ions étant du même ordre de grandeur, cela nous permet d’intégrer à ce code une réponse cinétique des électrons avec un très faible coût numérique supplémentaire par rapport à la version existante. A l’aide de ce nouveau code nous pouvons observer une turbulence générée à la fois par les TIM et les TEM, ceci avec peu de ressources numériques. Nous pouvons obtenir des turbulences présentant différentes structures typiques observées dans les tokamak. C’est le cas des écoulements zonaux et des streamers ayant un rôle majeur dans le transport de particules et d’énergie. En vue d’une meilleure compréhension, voire d’un meilleur contrôle du transport, l’influence de différents paramètres, comme la largeur banane ou le rapport de température ionique sur la température électronique, est étudiée.In tokamak plasmas, it is recognized that ion and electron micro- instabilities are held responsible for turbulence giving rise to anomalous transport. These limit particle and energy confinements in tokamak devices. This is the context of this work. The main objective is to have a better understanding of turbulence and thus of anomalous transport. It is known that the behaviour of trapped particles plays a major role in the development of turbulence via trapped ion mode (TIM) instability and trapped electron mode (TEM) instability. This work focus on the development of a model describing kinetic trapped particles (ions and electrons). The involved time scale is of the order of the trapped particle precession frequency which corresponds to characteristic frequency of TIM/TEM turbulence. The originality of this model is the reduction of the dimension from6D to 4D. This reduction is made by averaging over both the fast cyclotron motion and the bounce motion. In addition, using a set of action-angle variables allows one to deal with two parameters instead of two variables. The final model is 4D, dealing with two parameters and 2D space coordinates. The temperature and density gradients which trigger TIM and TEM instabilities are given by the linear analysis of the model. This analysis allows us to calculate the growth rates and frequencies associated with these instabilities. In order to solve the non-linear model describing both trapped kinetic ions and trapped kinetic electrons, we use the existing global code TERESA 4D including only trapped kinetic ions. The spatial and temporal scales associated to TIM and TEM turbulence are of the same order of magnitude. It allows us to include trapped electron kinetic response with very low numerical cost compared to the existing version. The TIM/TEM turbulence can be generated by this new code with low computational resources. Different typical structures observed in tokamak can be studied. This is the case of zonal flow and streamer structures which play a major role in anomalous transport. Finally, the influence of different parameters, such as banana width or electron to ion temperature ratio, is considered

Étude de la turbulence liée aux particules piégées dans les plasmas de fusion

In tokamak plasmas, it is recognized that ion and electron micro- instabilities are held responsible for turbulence giving rise to anomalous transport. These limit particle and energy confinements in tokamak devices. This is the context of this work. The main objective is to have a better understanding of turbulence and thus of anomalous transport. It is known that the behaviour of trapped particles plays a major role in the development of turbulence via trapped ion mode (TIM) instability and trapped electron mode (TEM) instability. This work focus on the development of a model describing kinetic trapped particles (ions and electrons). The involved time scale is of the order of the trapped particle precession frequency which corresponds to characteristic frequency of TIM/TEM turbulence. The originality of this model is the reduction of the dimension from6D to 4D. This reduction is made by averaging over both the fast cyclotron motion and the bounce motion. In addition, using a set of action-angle variables allows one to deal with two parameters instead of two variables. The final model is 4D, dealing with two parameters and 2D space coordinates. The temperature and density gradients which trigger TIM and TEM instabilities are given by the linear analysis of the model. This analysis allows us to calculate the growth rates and frequencies associated with these instabilities. In order to solve the non-linear model describing both trapped kinetic ions and trapped kinetic electrons, we use the existing global code TERESA 4D including only trapped kinetic ions. The spatial and temporal scales associated to TIM and TEM turbulence are of the same order of magnitude. It allows us to include trapped electron kinetic response with very low numerical cost compared to the existing version. The TIM/TEM turbulence can be generated by this new code with low computational resources. Different typical structures observed in tokamak can be studied. This is the case of zonal flow and streamer structures which play a major role in anomalous transport. Finally, the influence of different parameters, such as banana width or electron to ion temperature ratio, is considered.Les micro-instabilités ioniques et électroniques présentes dans les plasmas de fusion sont à l’origine de la turbulence. Le transport anormal de particules et d’énergie, induit par cette turbulence, joue un rôle néfaste pour les performances des machines à fusion nucléaire comme le tokamak. C’est dans ce cadre général que s’inscrit ce travail visant à une meilleure compréhension de la turbulence et des phénomènes de transport sous-jacents. On sait que la dynamique des particules piégées joue un rôle très important dans l’établissement de la turbulence au travers des instabilités ioniques TIM (Trapped Ion Modes) et électroniques TEM (Trapped Electron Modes). Nous nous attachons donc dans ce travail au développement d’un modèle décrivant ces particules piégées (ions et électrons) de manière cinétique. L’échelle de temps à laquelle nous nous plaçons est de l’ordre de la période de précession toroïdale des particules piégées, période typique de la turbulence TIM/TEM. L’originalité de ce modèle réside dans la réduction de la dimension du problème (de 6D à 4D) par la moyenne sur les deux échelles de temps rapides associées aux particules piégées, respectivement le mouvement cyclotronique et le mouvement de rebond. De plus, l’utilisation des variables d’angle et d’action permet de transformer deux variables en paramètres. Le modèle final ainsi obtenu est 4D, dont deux dimensions interviennent sous la forme de paramètres. L’analyse linéaire du modèle nous permet de connaître les gradients de température et de densité permettant le déclenchement des instabilités TIM et TEM. Il nous permet également de connaître les taux de croissance et les pulsations associés à ces deux instabilités. Ensuite, nous nous appuyons sur le code global TERESA 4D décrivant les ions piégés cinétiques pour y inclure la résolution non-linéaire du modèle décrivant les ions et les électrons piégés cinétiques. Les échelles spatio-temporelles de la turbulence induite par les électrons et celle induite par les ions étant du même ordre de grandeur, cela nous permet d’intégrer à ce code une réponse cinétique des électrons avec un très faible coût numérique supplémentaire par rapport à la version existante. A l’aide de ce nouveau code nous pouvons observer une turbulence générée à la fois par les TIM et les TEM, ceci avec peu de ressources numériques. Nous pouvons obtenir des turbulences présentant différentes structures typiques observées dans les tokamak. C’est le cas des écoulements zonaux et des streamers ayant un rôle majeur dans le transport de particules et d’énergie. En vue d’une meilleure compréhension, voire d’un meilleur contrôle du transport, l’influence de différents paramètres, comme la largeur banane ou le rapport de température ionique sur la température électronique, est étudiée

Stimulated zonal flow generation in the case of TEM and TIM microturbulence

International audienceIn this paper we show that in some parameter range in gyrokinetic simulations, it is possible to apply a control method to stimulate the appearance of zonal flows while minimizing the duration of the control process and the impact on plasma parameters. For this purpose, a gyrokinetic code considering only trapped particles is used. The starting point of our work is a situation where zonal flows transiently appear after the nonlinear phase of saturation of TEM (Trapped Electron Modes) or TIM (Trapped Ion Modes) micro-instabilities. These are observed to be strongly reduced in a later phase, permitting streamers to govern the plasma behavior in the steady-state. By intervening during this latter state (after this transient growth and decay of zonal flow), i.e. by increasing the ion/electron temperature ratio for a short time, it is found to be possible to bifurcate to a new steady-state, in which zonal flows are strongly present and are maintained indefinitely, thereby allowing a significant reduction in radial heat fluxes

Self-generated zonal flows in the plasma turbulence driven by trapped-ion and trapped-electron instabilities

Équipe 107 : Physique des plasmas chaudsInternational audienceThis paper presents a study of zonal flows generated by trapped-electron mode and trapped-ion mode micro turbulence as a function of two plasma parameters-banana width and electron temperature. For this purpose, a gyrokinetic code considering only trapped particles is used. First, an analytical equation giving the predicted level of zonal flows is derived from the quasi-neutrality equation of our model, as a function of the density fluctuation levels and the banana widths. Then, the influence of the banana width on the number of zonal flows occurring in the system is studied using the gyrokinetic code. Finally, the impact of the temperature ratio Te/Ti on the reduction of zonal flows is shown and a close link is highlighted between reduction and different gyro-and-bounce-average ion and electron density fluctuation levels. This reduction is found to be due to the amplitudes of gyro-and-bounce-average density perturbations ne and ni gradually becoming closer, which is in agreement with the analytical results given by the quasi-neutrality equation

A gyro-kinetic model for trapped electron and ion modes

Équipe 107 : Physique des plasmas chaudsInternational audienceIn tokamak plasmas, it is recognized that ITG (ion temperature gradient instability) and trapped electron modes (TEM) are held responsible for turbulence giving rise to anomalous transport. The present work focuses on the building of a model including trapped kinetic ions and trapped kinetic electrons. For this purpose, the dimensionality is reduced by averaging the motion over the cyclotron motion and the ``banana'' orbits, according to the fact that the instabilities are characterized by frequencies of the order of the low trapped particle precession frequency. Moreover, a set of action-angle variables is used. The final model is 4D (two-dimensional phase space parametrized by the two first adiabatic invariants namely the particle energy and the trapping parameter). In this paper, the trapped ion and electron modes (TIM and TEM) are studied by using a linear analysis of the model. This work is currently performed in order to include trapped electrons in an existing semi lagrangian code for which TIM modes are already taken into account. This study can be considered as a first step in order to include kinetic trapped electrons in the 5D gyrokinetic code GYSELA

A new encapsulation method of InP during post implantation annealing

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Collision rates estimated from exact N -body simulations of a one-dimensional plasma

In a plasma, the charged particles interact via long-range forces and this interaction causes the plasma to exhibit collective effects. If the graininess or coupling parameter g goes to zero (ideal collisionless plasma), two-body collisions are negligible while collective effects dominate the dynamics. In contrast, when g ≈ 1 collisions play a significant role. To study the transition between a collisionless and a collisional regime, a N-body code was developed and used in this work. The code solves exactly, in one spatial dimension, the dynamics of N infinite parallel plane sheets for both ion and electron populations. We illustrate the transition between individual and collective effects by studying two basic plasma phenomena, the twostream instability and Langmuir waves, for different values of g. The numerical collision rates given by the N-body code increase linearly with g for both phenomena, although with proportionality factors that differ by roughly a factor of two, a discrepancy that may be accounted for by the different initial conditions. All in all, the usual collision rates published in the literature (Spitzer collisionality) appear to compare rather well with the rates observed in our simulations

Collision rates estimated from exact N -body simulations of a one-dimensional plasma

International audienceIn a plasma, the charged particles interact via long-range forces, and this interaction causes the plasma to exhibit collective effects. If the graininess or coupling parameter g goes to zero (ideal collisionless plasma), two-body collisions are negligible, while collective effects dominate the dynamics. In contrast, when [Formula: see text] collisions play a significant role. To study the transition between a collisionless and a collisional regime, a N-body code was developed and used in this work. The code solves exactly, in one spatial dimension, the dynamics of N infinite parallel plane sheets for both ion and electron populations. We illustrate the transition between individual and collective effects by studying two basic plasma phenomena, the two-stream instability and Langmuir waves, for different values of g. The numerical collision rates given by the N-body code increase linearly with g for both phenomena, although with proportionality factors that differ by roughly a factor of two, a discrepancy that may be accounted for by the different initial conditions. All in all, the usual collision rates published in the literature (Spitzer collisionality) appear to compare rather well with the rates observed in our simulations

Collision rates estimated from exact N -body simulations of a one-dimensional plasma

In a plasma, the charged particles interact via long-range forces and this interaction causes the plasma to exhibit collective effects. If the graininess or coupling parameter g goes to zero (ideal collisionless plasma), two-body collisions are negligible while collective effects dominate the dynamics. In contrast, when g ≈ 1 collisions play a significant role. To study the transition between a collisionless and a collisional regime, a N-body code was developed and used in this work. The code solves exactly, in one spatial dimension, the dynamics of N infinite parallel plane sheets for both ion and electron populations. We illustrate the transition between individual and collective effects by studying two basic plasma phenomena, the twostream instability and Langmuir waves, for different values of g. The numerical collision rates given by the N-body code increase linearly with g for both phenomena, although with proportionality factors that differ by roughly a factor of two, a discrepancy that may be accounted for by the different initial conditions. All in all, the usual collision rates published in the literature (Spitzer collisionality) appear to compare rather well with the rates observed in our simulations

Collision rates estimated from exact N -body simulations of a one-dimensional plasma

In a plasma, the charged particles interact via long-range forces and this interaction causes the plasma to exhibit collective effects. If the graininess or coupling parameter g goes to zero (ideal collisionless plasma), two-body collisions are negligible while collective effects dominate the dynamics. In contrast, when g ≈ 1 collisions play a significant role. To study the transition between a collisionless and a collisional regime, a N-body code was developed and used in this work. The code solves exactly, in one spatial dimension, the dynamics of N infinite parallel plane sheets for both ion and electron populations. We illustrate the transition between individual and collective effects by studying two basic plasma phenomena, the twostream instability and Langmuir waves, for different values of g. The numerical collision rates given by the N-body code increase linearly with g for both phenomena, although with proportionality factors that differ by roughly a factor of two, a discrepancy that may be accounted for by the different initial conditions. All in all, the usual collision rates published in the literature (Spitzer collisionality) appear to compare rather well with the rates observed in our simulations