In highly conductive plasmas described by the ideal magnetohydrodynamics (MHD), magnetic field lines are frozen-in to the plasma. The contrary process takes place when the localized non-ideal and diffusive effects allow the field lines to break and reform, and therefore, called "magnetic reconnection" process. Magnetic reconnection is well recognized as an important plasma process capable of converting enormous amounts of stored magnetic energy to both thermal energy and bulk acceleration of the plasma. Single-fluid MHD model of this process can not explain the rate of magnetic reconnection observed in the space and laboratory plasmas, but the two-fluid model has raised the promises of explaining the magnetic reconnection satisfactorily. This thesis by employing the two-fluid MHD model of the magnetic reconnection studies theoretically this process.

Les modes de déchirement sont connus pour détériorer le confinement et limiter les performances dans les machines de fusion. Plusieurs études sur les modes de déchirements ont été menées, en incluant un degré croissant de complexité dans le modèle physique afin de mieux comprendre les observations expérimentales. Une de ces extensions est l'introduction d'une description du plasma comme un fluide à deux espèces, ions et électrons, dont les dynamiques sont fortement différentes. Un autre mécanisme physique connu pour être important est la courbure du champ magnétique non perturbé. Dans cette thèse, nous étudions les questions de la stabilité linéaire et de l'évolution non linéaire des îlots magnétiques, en présence de la courbure des lignes de champ et de la rotation diamagnétique, avec le code MHD non linéaire XTOR-2F, qui inclut le transport anisotrope de chaleur et les effets géométriques. Cette analyse est appliquée à une décharge entièrement non-inductive de Tore Supra. Ce mode d'opération est crucial pour démontrer la possibilité d'un fonctionnement continu sur un réacteur de type tokamak. Dans cette thèse, la possibilité d'une stabilisation complète des modes de déchirement par la rotation diamagnétique, en présence de la courbure toroidale des lignes de champ magnétique, est démontrée. Dans le domaine linéairement stable, le mode est métastable: le niveau de saturation dépend de la taille de l'îlot initial. Dans le domaine non linéaire, la saturation de l'îlot est fortement réduite par la rotation diamagnétique et par le nombre de Lundquist. La question de l'extrapolation des résultats obtenus vers la future generation de machines de fusion est également abordée / Tearing modes are known to deteriorate the confinement and limit plasma performance in fusion devices. Various studies of this mode have been performed lately including an increasing level of complexity in the physical description which is required for understanding of experimental observations. One of such extensions is the introduction of diamagnetic rotation into the system. Another physical mechanisms known to be important for tearing mode dynamics is the curvature of unperturbed magnetic field lines and neoclassical physics. In this thesis we investigate the issues of linear stability of the tearing modes in a presence of both curvature and diamagnetic rotation using the non linear full-MHD toroidal code XTOR-2F, which includes anisotropic heat transport, diamagnetic and geometrical effects. This analysis is applied to one of the fully non-inductive discharges on Tore-Supra. Such experiments are crucially important to demonstrate reactor scale steady state operation for the tokamak. In this thesis, the possibility of full linear stabilization of the tearing modes by diamagnetic rotation in the presence of toroidal curvature is shown. In the linearly stable domain, the mode is metastable: saturation level depends on the seed island size. In the non linear regime, the saturation of n=1, m=2 mode is found to be strongly reduced by diamagnetic rotation and by Lundquist number. The question of extrapolation of the obtained results towards future generation of fusion devices is also addressed. In particular, for ITER size machines, the toroidal curvature is expected to be more important due to higher performance factor β.

La stabilité des plasmas de fusion est un enjeu crucial dans le cadre du développement de nouvelles sources d'énergie. L'interaction entre le plasma et le champ magnétique peut en effet amener à la destruction du confinement : c'est une disruption. Le sujet de cette thèse porte sur les îlots magnétiques, une des causes des disruptions. Ces îlots magnétiques sont observés expérimentalement et analytiquement. Les théories peuvent prévoir la croissance d'un îlot magnétique et sa taille, mais les restrictions sur le domaine de validité de la théorie sont fortes et elles dé-corrèlent largement les domaines de validité théoriques et expérimentaux. Dans une première partie, nous montrons que, génériquement, les méthodes de contrôle dynamiques d'évolution des îlots magnétiques, basées notamment sur une relation entre la taille de l'îlot et la perturbation de flux magnétique à la résonance, devraient prendre en compte la modification du flux magnétique moyenné le long de la ligne de champ. Nous donnons aussi des limites quand au cadre de notre assertion (coalescence des îlots, effondrement du point X, ...). la seconde partie de la thèse aborde un nouvel effet dû au courant de part et d'autre de l'îlot magnétique. Il change la dynamique de l'îlot et la perception que l'on en a. Jusqu'à présent la dynamique de l'îlot était étudiée principalement au travers de mécanisme actifs au niveau de la résonance. Nous démontrons que la présence de courant aux abords de l'îlot peuvent jouer un rôle très important sur sa croissance et sur sa taille finale. La troisième partie détaille comment la turbulence aux abords d'un îlot magnétique peut affecter sa croissance. / The fusion plasma stability is a critical point for the developpement of newenergy source. The interaction between the plasma and the magnetic field can drive to the confinement descrution : it is a disruption. The topic of this thesis is the magnetic island, one of disruption causes. Those magnetic islands are observed theoretically and numerically. The theory can predict the growth and the final size of magnetic islands, but restrictions of its validity range are strong and they decorrelate the experimental and theoritical validity domain. In the first part, we show that the dynamic method of magnetic island control, based on the link between the island size and the perturbed magnetic flux at the resonance, should take in account the modification of the magnetic flux averaged along the field line. We show aswell the limitation of our assertion (magnetic island coalescence, X point collapse ...). The second part of the thesis address a new effet du to the current on sides of the magnetic island. This effect changes the magnetic island dynamics and the perception we got on it. Until now, the magnetic island dynamics have been studied through active mechanisms at the resonance. We show that the presence of current on sides can play an important role on the growth and saturation of the magnetic island. The last part of thesis details how the turbulence on the outskirts of a magnetic island can affect the island growth. We show that a turbulence generate by an interchange instability can penetrate into a stable zone concerning tearing mode and induce by a 3D mechanisme the growth of an magnetic island.

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Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(エネルギー科学) / 甲第19091号 / エネ博第315号 / 新制||エネ||64 / 32042 / 京都大学大学院エネルギー科学研究科エネルギー基礎科学専攻 / (主査)教授 岸本 泰明, 教授 前川 孝, 教授 中村 祐司 / 学位規則第4条第1項該当

京都大学 / 0048 / 新制・課程博士 / 博士(エネルギー科学) / 甲第19091号 / エネ博第315号 / 新制||エネ||64(附属図書館) / 32042 / 京都大学大学院エネルギー科学研究科エネルギー基礎科学専攻 / (主査)教授 岸本 泰明, 教授 前川 孝, 教授 中村 祐司 / 学位規則第4条第1項該当 / Doctor of Energy Science / Kyoto University / DFAM

In this thesis we investigate current sheets in the solar corona. The well known 1D model for the tearing mode instability is presented, before progressing to 2D where we introduce a non-uniform resistivity. The effect this has on growth rates is investigated and we find that the inclusion of the non-uniform term in η cause a decrease in the growth rate of the dominant mode. Analytical approximations and numerical simulations are then used to model current sheet formation by considering two distinct experiments. First, a magnetic field is sheared in two directions, perpendicular to each other. A twisted current layer is formed and we find that as we increase grid resolution, the maximum current increases, the width of the current layer decreases and the total current in the layer is approximately constant. This, together with the residual Lorentz force calculated, suggests that a current sheet is trying to form. The current layer then starts to fragment. By considering the parallel electric field and calculating the perpendicular vorticity, we find evidence of reconnection. The resulting temperatures easily reach the required coronal values. The second set of simulations carried out model an initially straight magnetic field which is stressed by elliptical boundary motions. A highly twisted current layer is formed and analysis of the energetics, current structures, magnetic field and the resulting temperatures is carried out. Results are similar in nature to that of the shearing experiment.

The tearing mode (TM) is a resistive instability that can arise in magnetically confined plasmas. The TM can be driven unstable by the gradient of the plasma current. When the mode grows it destroys the magnetic field symmetry and reconnects the magnetic field in the form of a so-called magnetic island. The TMs are inherent to a type of device called the reversed-field pinch (RFP), which is a device for toroidal magnetic confinement of fusion plasmas. In the RFP, TMs arise at several resonant surfaces, i.e. where the field lines and the perturbation have the same pitch angle. These surfaces are closely spaced in the RFP and the neighboring TM islands can overlap. Due to the island overlap, the magnetic field lines become tangled resulting in a stochastic magnetic field, i.e. the field lines fill a volume instead of lying on toroidal surfaces. Consequently, a stochastic field results in an anomalously fast transport in the radial direction. Stochastic fields can also arise in other plasmas, for example, the tokamak edge when a resonant magnetic perturbation (RMP) is applied by external coils. This stochastization is intentional to mitigate the edge-localized modes. The RMPs are also used for control of other instabilities. Due to the finite number of RMP coils, however, the RMP fields can contain sidebands that decelerate and lock the TMs via electromagnetic torques. The locking causes an increased plasma-wall interaction. And in the tokamak, the TM locking can cause a plasma disruption which is disastrous for future high-energy devices like the ITER. In this thesis, the TM locking was studied in two RFPs (EXTRAP T2R and Madison Symmetric Torus) by applying RMPs. The experiments were compared with modern mode-locking theory. To determine the viscosity in different magnetic configurations where the field is stochastic, we perturbed the momentum via an RMP and an insertable biased electrode. In the TM locking experiments, we found qualitative agreement with the mode-locking theory. In the model, the kinematic viscosity was chosen to match the experimental locking instant. The model then predicts the braking curve, the short timescale dynamics, and the mode unlocking. To unlock a mode, the RMP amplitude had to decrease by a factor ten from the locking amplitude. These results show that mode-locking theory, including the relevant electromagnetic torques and the viscous plasma response, can explain the experimental features. The model required viscosity agreed with another independent estimation of the viscosity. This showed that the RMP technique can be utilized for estimations of the viscosity. In the momentum perturbation experiments, it was found that the viscosity increased 100-fold when the magnetic fluctuation amplitude increased 10-fold. Thus, the experimental viscosity exhibits the same scaling as predicted by transport in a stochastic magnetic field. The magnitude of the viscosity agreed with a model that assumes that transport occurs at the sound speed -- the first detailed test of this model. The result can, for example, lead to a clearer comparison between experiment and visco-resistive magnetohydrodynamics (MHD) modeling of plasmas with a stochastic magnetic field. These comparisons had been complicated due to the large uncertainty in the experimental viscosity. Now, the viscosity can be better constrained, improving the predictive capability of fusion science. / <p>QC 20171122</p>

Magnetically confined fusion (MCF) plasmas are typically subject to several unstable modes. The growth of one mode can limit the plasma energy confinement and might cause a termination of the plasma. Externally applied resonant magnetic perturbations (RMPs) are used to control and to mitigate some of the unstable modes. Examples are, mitigation of edge localized modes and steering of neoclassical tearing mode position for stabilization by electron cyclotron current drive. Consequently, use of RMPs are considered necessary in planned future fusion machines. There are however negative consequences, the RMP interaction with a tearing mode (TM) of the same resonance can cause deceleration of the TM and possibly wall-locking. If a TM is non-rotating relative the machine-wall, it can grow and degrade fusion plasma performance and lead to a plasma disruption. Thus, all fusion confinement machines want to avoid wall-locked modes. Resonant magnetic fields can also be present in the form of machine-error-fields, which can produce the same effects. Clearly, it is of importance to understand the TM-RMP interaction. Typically, the modes with long wavelength are described by magnetohydrodynamic (MHD) theory. Considering the finite plasma resistivity, MHD predicts a mode that tears and reconnects magnetic field lines, called a tearing mode (TM). TMs occur at surfaces where the magnetic field lines close on themselves after a number of (m) toroidal and (n)poloidal turns. These surfaces are resonant in the sense that magnetic field and helical current perturbation has the same helicity, which minimize stabilizing effect of magnetic field line bending. In this thesis, the mechanisms of TM locking and unlocking due to external resonant magnetic perturbations (RMPs) are experimentally studied. The studies are conducted in two MCF machines of the type reversed-field pinch (RFP): EXTRAP T2R and Madison Symmetric Torus (MST). The studied machines exhibit multiple rotating TMs under normal operation. In EXTRAP T2R TM locking and unlocking are studied by application of a single harmonic RMP. Observations show that after the TM is locked, RMP amplitude has to be reduced significantly in order to unlock the TM. In similar studies in MST unlocking is not observed at all after turn-off of the RMP. Hence, in both machines, there is hysteresis in the locking and subsequent unlocking of a tearing mode. Results show qualitative agreement with a theoretical model of the TM evolution when subjected to an RMP. It is shown that the RMP cause a reduction of TM and plasma rotation at the resonant surface. The velocity reduction is opposed by a viscous torque from surrounding plasma. After TM locking, relaxation of the whole plasma rotation is observed, due to the transfer of velocity reduction via viscosity. This results in a reduced viscous resorting torque, which explains the observed hysteresis. The hysteresis is further deepened by the increase in amplitude of a locked mode. / <p>QC 20160111</p>