Magnetorotational instability (MRI) is one of the most important and most common instabilities in astrophysics. Today it is widely accepted that it serves as a major source of turbulent viscosity in accretion disks, the most energy efficient objects in the universe. The importance of the MRI for astrophysics has been realized only in recent fifteen years. However, originally it was discovered much earlier, in 1959, in a very different context. Theoretical flow of a conducting liquid confined between differentially rotating cylinders in the presence of an external magnetic field was analyzed. The central conclusion is that the additional magnetic field parallel to the axis of rotation can destabilize otherwise stable flow. Theory of non-magnetized fluid motion between rotating cylinders has much longer history, though. It has been studied already in 1888 and today such setup is usually referred as a Taylor-Couette flow. To prove experimentally the existence of MRI in a magnetized Taylor-Couette flow is a demanding task and different MHD groups around the world try to achieve it. The main problem lies in the fact that laboratory liquid metals which are used in such experiments are characterized by small magnetic Prandtl number. Consequently rotation rates of the cylinders must be extremely large and vast amount of technical problems emerge. One of the most important difficulties is an influence of plates enclosing the cylinders in any experiment. For fast rotation the plates tend to dominate the whole flow and the MRI can not be observed. In this thesis we discuss a special helical configuration of the applied magnetic field which allows the critical rotation rates to be much smaller. If only the axial magnetic field is present, the cylinders must rotate with angular velocities corresponding to Reynolds numbers of order Re ≈ 10^6. With the helical field this number is dramatically reduced to Re ≈ 10^3. The azimuthal component of the magnetic field can be easily generated by letting an electric current through the axis of rotation, In a Taylor-Couette flow the (primary) instability manifests itself as Taylor vortices. The specific geometry of the helical magnetic field leads to a traveling wave solution and the vortices are drifting in a direction determined by rotation and the magnetic field. In an idealized study for infinitely long cylinders this is not a problem. However, if the cylinders have finite length and are bounded vertically by the plates the situation is different. In this dissertation it is shown, with use of numerical methods, that the traveling wave solution also exists for MHD Taylor-Couette flow at finite aspect ratio H/D, H being height of the cylinders, D width of the gap between them. The nonlinear simulations provide amplitudes of fluid velocity which are helpful in designing an experiment. Although the plates disturb the flow, parameters like the drift velocity indicate that the helical MRI operates in this case. The idea of the helical MRI was implemented in a very recent experiment PROMISE. The results provided, for the first time, an evidence that the (helical) MRI indeed exists. Nevertheless, the influence of the vertical endplates was evident and the experiment can be, in principle, improved. Exemplary methods of reduction of the end-effect are here proposed. Near the vertical boundaries develops an Ekman-Hartmann layer. Study of this layer for the MHD Taylor-Couette system as well as its impact on the global flow properties is presented. It is shown that the plates, especially if they are conducting, can disturb the flow far more then previously thought also for relatively slow rotation rates. / Die magnetische Scherinstabilitaet (engl. MRI) ist eine sehr häufig in der Astrophysik anzutreffende Instabilität. Es wird heute weithin angenommen, dass sie die Ursache für die turbulente Viskosität in Akkretionsscheiben ist, den Objekten mit der höchsten Energieeffizienz im Kosmos. Die Bedeutung der MRI ist erst in den letzten fünfzehn Jahren klargeworden. Entdeckt wurde sie jedoch schon viel früher, im Jahre 1959 in einem völlig anderen physikalischen Kontext. Die Strömung in einer leitfähigen Flüssigkeit zwischen differentiell rotierenden Zylindern unter dem Einfluss eines externen Magnetfeldes wurde theoretisch untersucht. Die Schlussfolgerung war, dass das zugesetzte Magnetfeld eine sonst stabile Strömung destabilisieren kann. Die Geschichte der Theorie von Strömungen zwischen Zylindern reicht bis ins Jahr 1888 zurück. Heute wird ein solcher Aufbau üblicherweise als Taylor-Couette-Strömung bezeichnet. Ein System rotierender Zylinder, zwischen denen sich flüssiges Metall befindet, war Gegenstand des kürzlich durchgeführten Experiments PROMISE. Die Ergebnisse belegen zum ersten Mal experimentell die Existenz der MRI. Um die notwendigen Drehzahlen gering zu halten, wurde ein spezielles, helikales Magnetfeld angelegt. Gegenstand dieser Dissertation ist die theoretische Behandlung der magnetohydrodynamischen Taylor-Couette-Strömung, ähnlich der des Experiments PROMISE. Insbesondere der Einfluss der vertikalen Ränder (Deckel) wird untersucht. Es wird gezeigt, dass die MRI auch in Zylindern mit endlicher Höhe und mit begrenzenden Deckeln einsetzt. In der Nähe der vertikalen Ränder bildet sich eine Ekman-Hartmann-Schicht. Die Untersuchung dieser Schicht im Zusammenhang mit dem MHD-Taylor-Couette-System sowie ihr Einfluss auf die globalen Strömungseigenschaften werden vorgestellt. Es wird gezeigt, dass die Deckel - insbesondere wenn sie elektrisch leitend sind - die Strömung stärker beeinflussen können als bisher angenommen, selbst bei den geringen Drehzahlen. Es werden Methoden zur Verringerung dieser unerwünschten Effekte vorgeschlagen.

Untersuchung konvektiver Transportprozesse innerhalb einer auf der Lorentz-Kraft basierenden Strömung während der elektrolytischen Abscheidung.

Cette thèse est dédiée aux processus de transport de moment cinétique et de flux magnétique dans les disques faiblement magnétisés et faiblement ionisés ; l’influence des effets microphysiques sur la dynamique du disque à grande échelle y est centrale. Dans un premier temps, j’exclue les effets de stratification et j’examine l’impact des effets MHD non-idéaux sur la turbulence dans le plan du disque. Je montre que l’écoulement peut spontanément s’organiser si la fraction d’ionisation est assez faible ; dans ce cas, l’accrétion est stoppée, et le disque exhibe des anneaux axisymétriques susceptibles d’affecter la formation planétaire. Dans un second temps, je caractérise l’interaction du disque avec un vent magnétisé via un modèle global de disque stratifié. Ce modèle est le premier à décrire globalement les effets MHD non-idéaux d’après un réseau chimique simplifié. Il révèle que le disque est essentiellement non-turbulent, et que le champ magnétique peut adopter différentes configurations globales, affectant drastiquement les processus de transport. Un nouveau processus d’auto-organisation est identifié, produisant aussi des structures axisymétriques, tandis que le précédent est invalidé par l’action du vent. Les propriétés des vents magnéto-thermiques sont examinées pour différentes magnétisations, permettant de discriminer les vents magnétisés des vents photo-évaporés par leur efficacité d’éjection. / This thesis is devoted to the transport of angular momentum and magnetic flux through weakly ionized and weakly magnetized accretion disks ; the role of microphysical effects on the large- scale dynamics of the disk is of primary importance. As a first step, I exclude stratification effects and examine the impact of non-ideal MHD effects on the turbulent properties near the disk midplane. I show that the flow can spontaneously organize itself if the ionization fraction is low enough ; in this case, accretion is halted and the disk exhibits axisymmetric structures, with possible consequences on planetary formation. As a second step, I study the disk-wind interaction via a global model of stratified disk. This model is the first to compute non-ideal MHD effects from a simplified chemical network in a global geometry. It reveals that the flow is essentially laminar, and that the magnetic field can adopt different global configurations, drastically affecting the transport processes. A new self-organization process is identified, also leading to the formation of axisymmetric structures, whereas the previous mechanism is discarded by the action of the wind. The properties of magneto-thermal winds are examined for various magnetizations, allowing discrimination between magnetized and photo-evaporative winds based upon their ejection efficiency.

This thesis presents the magnetic fields of the COMPASS tokamak and work done during the COMPASS reinstallation in the Czech Republic. The geometry, vacuum magnetic fields and Power Supplies for the poloidal field coils circuits are described in the technical part of the thesis. The design of Power Supplies filters and improvements in the controller algorithm are also introduced. The MHD equilibrium reconstruction code EFIT++ and implementation of the induced currents model are described in the physical part of the thesis. The EFIT++ code was adapted for COMPASS. The utilization of the EFIT++ code for the COMPASS operation is shown. The global power balance in the non-stationary phases of the tokamak discharge is explained and examples are shown. The attached articles describe Power Supplies and tokamak feedback system developed for the COMPASS plasma control. Powered by TCPDF (www.tcpdf.org)

Le contexte économique et écologique difficile ainsi que la réglementation en matière d'émissions de CO2 poussent les industriels de l'automobile à améliorer les moteurs à allumage commandé. L'une des voies d'amélioration envisagées est l'admission de mélanges pauvres ou fortement dilués par des gaz d'échappement (EGR) dans la chambre de combustion. La difficulté de ce type de fonctionnement est l'initiation de l'allumage. Afin de pallier ce problème, les systèmes d'allumage sont étudiés et tout particulièrement l'étincelle. Cette décharge est à l'origine de l'apparition d'un plasma et la compréhension des mécanismes impliqués dans le transfert d'énergie entre ce plasma et le gaz réactif environnant est essentielle. Ce travail s'intéresse à la modélisation de l'étincelle dans sa phase d'arc électrique afin de pouvoir prédire le comportement hydrodynamique de l'arc et la propagation de l'onde de choc. Les modèles transitoires bidimensionnels ou tridimensionnels utilisés sont basés sur le logiciel @ANSYS Fluent couplé à des fonctions utilisateurs développées au sein de l'équipe AEPPT. Ils s'appuient dans un premier temps sur la littérature afin de comprendre le comportement général de la décharge, puis sur des configurations expérimentales utilisées dans le cadre du projet ANR FAMAC. Les simulations sont dans un premier temps et en majorité réalisées dans l'air sur des configurations simplifiées de type pointe-pointe afin de valider le modèle. Ensuite, une étude est faite dans une configuration de réacteur où l'arc est généré entre les bornes d'une bougie d'allumage. Le modèle permet de démontrer le rôle de chacun des paramètres initiaux des simulations ainsi que leur impact sur l'écoulement du plasma. L'influence de la prise en compte du champ magnétique est montrée dans le cadre d'un arc impulsionnel nanoseconde. Enfin, le modèle a permis de montrer le rôle d'un écoulement laminaire latéral en direction d'une décharge de type conventionnelle générée par une bobine d'allumage Audi. L'ensemble de ces résultats pourront être le point de départ d'une étude énergétique sur les systèmes d'allumage ainsi que d'une réflexion concernant la compréhension de l'initiation de la combustion. / The economic/ecological context and the CO2 regulation by the "euro" standards lead the automotive industry to improve the spark ignited engines. A way of improvement is the admission of a lean mixture or of a diluted mixture by recirculation of exhaust gases in the combustion chamber. The main difficulty in these conditions is to start the combustion. To overcome this problem, the ignition systems are studied and more particularly the spark. This discharge leads to the apparition of plasma and the understanding of the energy transfer mechanisms between this plasma and the reactive mixture is essential. This work is focus on the modeling of a spark during its electrical arc phase in order to predict the hydrodynamic behavior of the arc and the shock wave propagation. The 2D and 3D transient models are based on ANSYS Fluent coupled with user defined functions developed by the AEPPT team. First, the simulation is based on data from literature review in order to understand the general behavior of the discharge. Then, the model uses experimental configuration developed during the ANR FAMAC project. Simulations are mainly realized in air using simplified configurations (pin-to-pin configurations) in order to valid the model. Then, a study is done in a vessel configuration using real sparkplug geometry. This model allows us to show the role of each initial parameter as well as their impact on the plasma flow. The magnetic field influence is also determined for a nanosecond arc discharge. Finally, the model is used in order to determine the role of a cross flow on a discharge generated by a conventional Audi ignition coil. All these results could be the beginning of an energetic study on ignition systems and could lead to a discussion on the understanding of initiation of the combustion process.

Le champ magnétique vertical joue un rôle prépondérant dans la dynamique des disques d'accrétion. L'émission de jet par un disque ainsi que la turbulence qu'on suppose y exister sont tous deux fortement contraints par l'intensité de ce champ vertical. Ce champ évolue lui même suivant les mécanismes d'advection par la matière et de diffusion par la turbulence. Depuis plus de vingt ans, la question de l'évolution d'un tel champ dans un disque fait l'objet de nombreuses études, mais une modélisation globale de disque prenant en compte tous ces ingrédients n'avait encore jamais été réalisée. Je propose ici un modèle, considérant le transport d'un champ magnétique vertical par le disque, mais également la rétroaction de ce champ sur la dynamique du disque. Une résolution analytique de configurations homogènes est réalisée. Elle confirme les résultats des études précédentes, à savoir qu'en l'état actuel des connaissances des processus de transport, un disque turbulent ne peut advecter significativement le champ vertical pour permettre l'émission d'un jet. Elle met cependant en avant une configuration nouvelle de disque, mixte, dans laquelle les conditions d'éjection sont réunies non pas à l'intérieur du disque mais dans ses régions externes. La stabilité des configurations homogènes calculée a été réalisée, et de nouvelles instabilités sont mises en avant. L'effectivité de ces instabilités dépend des dépendances fonctionnelles employées pour quantifier la dynamique du disque. Une caractérisation, via des simulation locales, des ces dépendances fonctionnelles, permettrait de savoir si ces instabilités peuvent être effectives dans un disque d'accrétion. Enfin, les outils numériques développé permettent d'étudier les configurations envisagées. Les configurations homogènes stationnaires sont récupérées, et une étude dynamique de la configuration mixte permet de caractériser les conditions d'advection de la limite disque éjectant/disque standard. / The vertical magnetic field plays a fundamental role in the dynamics of accretion discs. The jet launching, so as the turbulence that is supposed to exist in these discs are strongly constrained by the intensity of this field. This field evolves following the mechanisms of advection by the mater and diffusion by turbulence. The question of the evolution of such a field has been studied since more than 20 years, but a global modelisation, involving all these méchanisms wasn't done yet. I propose a model, taking into account the transport of a vertical magnetic field by the disc, and also the feedback of this field on the dynamics of the disc. Analytical solutions for standard configurations a calculated. It confirms previous studies in the sense that considering the state of the art, a turbulent disc can not advect a vertical field in order to allow a jet launching. However, a new configuration is rised, in wich the ejection conditions are realised in the outer radius of the disc. The stability of the standard configurations is calculated, and new instabilities are rised. The effectivity of such instabilities depends on the functionnal dependancies used to quantify the disc dynamics. A determination of such dependancies, via local simulations, would clarify if such instabilities could be effective in accretion discs. At last, the numerical tools developped allows to study the configurations. Standard one are found, and a dynamical study of the new configuration is done to determine the advection conditions for the limit ejecting disc/ standard disc.

La recherche actuelle dans le domaine des pompes à induction électromagnétique s’oriente sur la question de l'instabilité MagnétoHydroDynamique (MHD) avec un intérêt particulier pour les régimes à haut nombre de Reynolds magnétique de glissement ( ). Notre étude se focalise sur les pompes à induction linéaires annulaires (ALIP) fonctionnant avec du sodium liquide. La thèse s’inscrit dans le contexte du programme français de recherche et développement de réacteur rapide en sodium de la GEN IV. Pour le démonstrateur ASTRID, l'utilisation d’une ALIP à haut débit dans les boucles de refroidissement secondaires est identifiée. Le CEA, a conçu, réalisé et exploitera la boucle PEMDYN, représentative d’instabilités MHD à hauts débits.Dans cette étude, la stabilité d'une ALIP idéale est abordée du point de vue théorique en se focalisant sur l'analyse de la stabilité linéaire. L'analyse a révélé que la forte amplification de la perturbation est attendue lorsque le seuil de stabilité convective est atteint. La théorie est soutenue par les résultats numériques et des expériences rapportées dans la littérature. Le fonctionnement stable et les moyens de stabilisation jouant avec deux fréquences dans le cas d'une ALIP idéale est discuté et les conditions nécessaires obtenues.Des modèles numériques détaillés de pompe plate à induction linéaire (FLIP) en tenant compte des phénomènes d'une véritable pompe sont développés. Une nouvelle technique de mesures du champ magnétique est introduite et les résultats expérimentaux démontrent un accord qualitatif avec des modèles numériques permettant de capturer tous les phénomènes principaux tels que l'oscillation du champ magnétique et les profils de vitesse perturbée. Ces résultats précisent les phénomènes d'instabilité MHD qui peuvent être rencontrés et peuvent être utilisés en tant que référence dans des études ultérieures. / The research explores the issue of magnetohydrodynamic (MHD) instability in electromagnetic induction pumps with focus on the regimes of high slip Reynolds magnetic number ( ) in Annular Linear Induction Pumps (ALIP) operating with liquid sodium. The context of the thesis is French GEN IV Sodium Fast Reactor research and development program for ASTRID in a framework of which the use of high discharge ALIP in the secondary cooling loops is being studied. CEA has designed, realized and will exploit PEMDYN facility, able to represent MHD instability in high discharge ALIP.In the thesis stability of an ideal ALIP is elaborated theoretically using linear stability analysis. Analysis revealed that strong amplification of perturbation is expected after convective stability threshold is reached. Theory is supported with numerical results and experiments reported in literature. Stable operation and stabilization technique operating with two frequencies in case of an ideal ALIP is discussed and necessary conditions derived.Detailed numerical models of flat linear induction pump (FLIP) taking into account effects of a real pump are developed. New technique of magnetic field measurements has been introduced and experimental results demonstrate a qualitative agreement with numerical models capturing all principal phenomena such as oscillation of magnetic field and perturbed velocity profiles. These results give significantly more profound insight in the phenomenon of MHD instability and can be used as a reference in further studies.

In the present work, Current Reversal Equilibrium Configurations (CRECs) in the context of Magnetohydrodinamic (MHD) equilibrium are considered. The hamiltonian nature of the magnetic field lines is used to introduce the concept of magnetic surfaces and their relation to the Grad-Shafranov (G-S) equation. From a geometrical perspective and the Maxwell equations, it is shown that current reversal configurations in two-dimensional equilibrium do not generate the usual nested topology of the equilibrium magnetic surfaces. The concept of intersecting critical curves is introduced to describe the CRECs and recently published equilibria are shown to be compatible with such description. The equilibrium with a single magnetic island is constructed analytically, through a local successive approximations method, valid for any choice of the source functions of the G-S equation. From the local solution, an estimate of the island width in terms of simple quantities is deduced and verified to a good accuracy with recently published CRECs; the accuracy of this simple model suggests the existence of strong topological constraints in the formation of the equilibria. Lastly, an instability mechanism is conjectured to explain the lack of conclusive experimental evidence of reversed currents, in favor of the current clamp hypothesis. / No presente trabalho, as configurações de equilíbrio com corrente reversa (CRECs), são consideradas no contexto de Equilíbrio Magnetoidrodinâmico. A natureza hamiltoniana das linhas de campo magnético é usada para introduzir o conceito de superfícies magnéticas, e sua relação com a equação de Grad-Shafranov (G-S). Desde uma perspectiva geométrica e usando as equações de Maxwell, é demonstrado que as configurações de corrente reversa em equilíbrios bidimensionais não é compativel com as topologias aninhadas usuais para as superfícies magnéticas de equilíbrio. O conceito de curvas críticas é introduzido para descrever as CRECs e é observado que os equilíbrios recentemente publicados satisfazem esta descrição. O equilíbrio com uma única ilha magnética é construído analiticamente, por meio de aproximações sucessivas locais, este é válido para qualquer escolha das funções arbitrárias da equação G-S. A partir da solução local, se desenvolve uma estimativa do tamanho da ilha magnética em termos de quantidades simples. Esta estimativa concorda bem com as CRECs da literatura recente, sugerindo pela simplicidade do modelo, que existem fortes restrições topológicas no estabelecimento do equilíbrio. Finalmente, na forma de conjectura, introduzimos um mecanismo para instabilidades que tenta dar conta da falta de evidência experimental conclusiva em relação às CRECs em favor da hipótese de corrente unidirecional (current clamp).

Neste trabalho foram estudadas instabilidades magnetohidrodinâmicas (MHD) utilizando um novo sistema bolométrico que foi instalado no tokamak TCABR para medidas da evolução temporal da potência irradiada. Este novo sistema conta com 24 cordas verticais, capazes de mapear toda uma secção poloidal da coluna de plasma com resolução espacial de aproximadamente 2 cm e uma resolução temporal de 20 µs. Como se sabe, as instabilidades MHD degradam o connamento do plasma e modicam a topologia das superfícies magnéticas, causando a perda da energia do plasma. Por conta disso, compreender essas instabilidades é fundamental para o sucesso dos futuros reatores de fusão nuclear. As perturbações (oscilações) causadas pelas instabilidades MHD modulam diversos parâmetros macroscópicos do plasma como a densidade, a temperatura e a potência irradiada. Então, utilizando o diagnóstico bolométrico, é possível medir as oscilações no perl de potência irradiada e, a partir deles, extrair informações importantes para determinar a origem e as características de tais instabilidades. No tokamak TCABR, as instabilidades foram caracterizadas através da análise espectral dos 24 sinais provenientes do novo sistema bolométrico. Para auxiliar a caracterização das instabilidades, um programa foi desenvolvido em Matlab para simular as medidas das perturbações no perl de potência irradiada. Através do mesmo procedimento de análise espectral, os resultados simulados foram comparados aos experimentais de forma que os parâmetros simulados, como largura e posição das ilhas magnéticas, fossem ajustados aos experimentais. Através dessa metodologia de análise, que combina simulação e experimento, foi possível caracterizar diversas instabilidades como o precursor dos dentes de serra e ilhas magnéticas de modos m = 2 e m = 3. / In this dissertation, magnetohydrodynamic (MHD) instabilities were investigated using a new bolometric system that was installed in the TCABR tokamak for radiation power measurements. This diagnostic is composed by 24 vertical chords that provide a full view of the poloidal cross section of the plasma column and provides spatial and temporal proles with approximately 2 cm space and 20 µs time resolution. As it is well known, the MHD instabilities degrade the plasma connement and modify the magnetic topology, leading to energy loss from the plasma. Therefore, the understanding of these instabilities is essential for the success of the controlled thermonuclear fusion reactors. The MHD instabilities also cause perturbations (oscillations) in various macroscopic parameters, such as plasma density, temperature, and radiated power. Therefore, the oscillations in the radiated power prole measured by the bolometric diagnostic system provide a possibility to investigate the origin and features of the instabilities. In the TCABR tokamak, the instabilities were characterized by spectral analysis of the 24 vertical chords of the bolometric signals. In addition, a Matlab program was developed to simulate the integral characteristic of the oscillations in the radiated power measured by the bolometric system. The spectral analysis of the simulated signals is then compared with the spectral analysis of the bolometric signals. The simulated parameters, island width and radial position, were then adjusted to t the experimental spectrum results. Using this method of analysis, which combines experiment and simulation, it was possible to characterize various instabilities, such as sawtooth precursor and m = 2 and m = 3 magnetic islands.

La régulation du moment cinétique est l'une des questions les plus importantes dans la formation d'étoiles. Du nuage moléculaire à l'étoile finale, le système perd la grande majorité de son moment cinétique et plusieurs processus sont avancés pour l'expliquer. Nous nous concentrons sur la magneto-hydrodynamique (MHD) non-idéale, qui permet de décrire le couplage entre un champ magnétique et un fluide. Son efficacité pour réguler le moment cinétique dans des conditions réalistes a été montrée à plusieurs reprises. Dans un premier temps, nous développons un code qui calcule l'équilibre chimique d'éléments présents dans les premières étapes de la formation d'étoile. Ainsi, nous pouvons retrouver la valeur des coefficients définissant l'intensité de chaque processus de la MHD non-idéale. Nous nous intéressons ensuite à l'un d'entre eux, l'effet Hall, encore peu étudié dans ce contexte. Nous l'implémentons dans le code eulérien RAMSES, et l'utilisons pour quantifier son influence pendant un effondrement gravitationnel. Comme prévu par la théorie, l'effet Hall influence grandement la taille du disque protoplanétaire, dans lequel se forment les planètes, et crée des enveloppes de gas tournant en sens inverse du reste du système / The angular momentum regulation is a hot topic in star formation. From the molecular cloud to th final star, the system loses most of its angular momentum, and several processes are proposed to explain this phenomenon. We focus on non-ideal magnetohydrodynamics (MHD), which describes the coupling between a fluid and its magnetic field. Its efficiency to regulate the angular momentum in realistic conditions has been shown in several studies. First, we develop a code that computes the chemical equilibrium of elements present in the early stages of star formation. We can therefore obtain the values of coefficients defining the strength of the phyical processes associated with non-ideal MHD. We then take interest in one of them, the Hall effect, still poorly studied in this context. We implement it in the eulerian code RAMSES, and use it to quantify its influence during a gravitational collapse. As predicted by theory, the Hall effect greatly influences the size of the protoplanetary disk, in which planets form, and creates envelopes of gas rotating backward compared to the rest of the system