MODELING OF MHD INSTABILITIES IN EXISTING AND FUTURE FUSION DEVICES IN VIEW OF CONTROL

In questo lavoro viene presentata una versione migliorata del codice CarMa, chiamato CarMa-D, per lo studio di Resistive Wall Modes (RWMs) nei reattori a fusione termonucleare. Tale codice \ue8 in grado di rappresentare accuratamente le strutture conduttrici tridimensionali della macchina, e considerare simultaneamente nel modello gli effetti dovuti alla dinamica del plasma, alla toroidal rotation e agli effetti drift-cinetici. CarMa-D \ue8 il risultato dell\u2019accoppiamento dei codici CARIDDI, per lo studio delle correnti indotte nelle strutture conduttrici, e MARS-K per analisi di stabilit\ue0 MHD nel plasma. Punto di forza della strategia di accoppiamento alla base di CarMa-D \ue8 che non si basa sulle ipotesi semplificative su cui si basa la versione statica di CarMa, ovvero non vengono trascurati la massa del plasma, toroidal rotation e l\u2019effetto del damping cinetico. In questo modo la risposta del plasma a perturbazioni esterne dipende dall\u2019andamento temporale della perturbazione stessa: questo andamento viene approssimato per mezzo di funzioni razionali di Pad\ue9 a coefficienti matriciali. Il passo successivo \ue8 dato dalla combinazione della risposta di plasma approssimata con l\u2019equazione delle correnti indotte nelle strutture passive, per ottenere un modello matematico desctitto come un sistema di equazioni differenziali lineari formalmente uguale alla versione statica di CarMa, ma con un numero maggiori di gradi di libert\ue0 per tener conto della dinamica di plasma. La nuova versione del codice supera le principali limitazioni del modello originale, in particolare: (i) considerando la massa del plasma \ue8 possibile modellare modi con dinamiche molto veloci, come l\u2019external-kink ideale, (ii) il modello \ue8 in grado di tener conto rigorosamente di toroidal rotation e damping cinetico. Questi vantaggi rendono CarMa-D uno strumento potente, in grado di studiare fenomeni macroscopici in cui sia la dinamica del plasma, che gli effetti 3-D delle strutture, sono marcati. Inoltre, il modello matematico risultate \ue8 stato generalizzato per tener conto della simulazione pi\uf9 armoniche toroidali simultaneamente (multi-modal CarMa-D). Il codice \ue8 stato poi testato con successo su un equilibrio di riferimento dato da un plasma a sezione circolare, e successivamente per lo studio di stabilit\ue0 per i modi n = 1 e n = 2 su JT-60SA, Scenario 5. Infine, si \ue8 dimostrato come il modello matematico di CarMa-D possa essere scritto in una formulazione state-space, in vista di un successivo impiego nella progettazione di un controllo in retoazione per la stabilizzazione attiva dei RWMs

Fast growing double tearing modes in a tokamak plasma

Configurations with nearby multiple resonant surfaces have broad spectra of linearly unstable coupled tearing modes with dominant high poloidal mode numbers m. This was recently shown for the case of multiple q = 1 resonances [Bierwage et al., Phys. Rev. Lett. 94 (6), 65001 (2005)]. In the present work, similar behavior is found for double tearing modes (DTM) on resonant surfaces with q >= 1. A detailed analysis of linear instability characteristics of DTMs with various mode numbers m is performed using numerical simulations. The mode structures and dispersion relations for linearly unstable modes are calculated. Comparisons between low- and higher-m modes are carried out, and the roles of the inter-resonance distance and of the magnetic Reynolds number S_Hp are investigated. High-m modes are found to be destabilized when the distance between the resonant surfaces is small. They dominate over low-m modes in a wide range of S_Hp, including regimes relevant for tokamak operation. These results may be readily applied to configurations with more than two resonant surfaces.Comment: 11 pages, 15 figure

An upgrade of the magnetic diagnostic system of the DIII-D tokamak for non-axisymmetric measurements

The DIII-D tokamak magnetic diagnostic system [E. J. Strait, Rev. Sci. Instrum. 77, 023502 (2006)] has been upgraded to significantly expand the measurement of the plasma response to intrinsic and applied non-axisymmetric "3D" fields. The placement and design of 101 additional sensors allow resolution of toroidal mode numbers 1 ≤ n ≤ 3, and poloidal wavelengths smaller than MARS-F, IPEC, and VMEC magnetohydrodynamic model predictions. Small 3D perturbations, relative to the equilibrium field (10(-5) < δB/B0 < 10(-4)), require sub-millimeter fabrication and installation tolerances. This high precision is achieved using electrical discharge machined components, and alignment techniques employing rotary laser levels and a coordinate measurement machine. A 16-bit data acquisition system is used in conjunction with analog signal-processing to recover non-axisymmetric perturbations. Co-located radial and poloidal field measurements allow up to 14.2 cm spatial resolution of poloidal structures (plasma poloidal circumference is ~500 cm). The function of the new system is verified by comparing the rotating tearing mode structure, measured by 14 BP fluctuation sensors, with that measured by the upgraded B(R) saddle loop sensors after the mode locks to the vessel wall. The result is a nearly identical 2/1 helical eigenstructure in both cases.S. R. Haskey wishes to thank AINSE Ltd. for providing financial assistance

An active feedback recovery technique from disruption events induced by m=2 n=1 tearing modes in ohmically heated tokamak plasmas

We present experimental results of magnetic feedback control on the m=2, n=1 tearing mode in RFX-mod operated as a circular ohmically heated tokamak. The feedback suppression of the non-resonant m=2, n=1 Resistive Wall Mode (RWM) in q(a)<2 plasmas is a well-established result of RFX-mod. The control of the tearing counterpart, which develops in q(a)>2 equilibrium, is instead a more difficult issue. In fact, the disruption induced by a growing amplitude m=2, n=1 tearing mode can be prevented by feedback only when the resonant surface q=2 is close to the plasma edge, namely 2<q(a)<2.5, and the electron density does not exceed approximately half of the Greenwald limit. A combined technique of tearing mode and q(a) control has been therefore developed to recover the discharge from the most critical conditions: the potentially disruptive tearing mode is converted into the relatively benign RWM by suddenly decreasing q(a) below 2. The experiments demonstrate the concept with 100% of successful cases. The q(a) control has been performed through the plasma current, given the capability of the toroidal loop-voltage power supply of RFX-mod. We also propose a path for controlling q(a) by acting on the plasma shape, which could be applied to medium size elongated tokamaks

High-Resolution MHD Spectroscopy of External Kinks in a Tokamak Plasma

This thesis describes the first results of passive and active MHD spectroscopy experiments on the High Beta Tokamak-Extended Pulse (HBT-EP) device using a new array of magnetic diagnostics and coils. The capabilities of the HBT-EP experiment are significantly extended with the installation of a new adjustable conducting wall, high-power modular control coil arrays, and an extensive set of 216 magnetic sensors that allow simultaneous high-resolution detection of multimode MHD phenomena. The design, construction, and calibration of this system are described. The capability of this new magnetic diagnostic set is demonstrated by biorthogonal decomposition analysis of passive measurements of rotating resistive wall modes (RWMs). A strong multimode effect is detected for the first time in HBT-EP plasmas consisting of the simultaneous existence of m/n=3/1 and 6/2 RWMs which cause the plasma to evolve in a non-rigid multimode manner. Additional mode numbers as high as n=3 are also observed. Active MHD spectroscopy experiments using a "phase-flip" resonant magnetic perturbation (RMP) are able to excite a clear three-dimensional response. By adjusting the helicity of the magnetic field applied by the control coils, the driven plasma response is shown to be predominantly resonant field amplification. When the amplitude of the applied field is not too large, the driven resonant response appears linear, independent of the presence of background MHD phenomena and consistent with the predictions of single-helicity modeling of kink mode dynamics. The spatial structures of both the naturally rotating kink mode and the externally driven response are observed to be identical, while the temporal evolutions are approximately independent. The phase-flip driven plasma response is measured as a function of edge safety factor, plasma rotation, and the amplitude of the applied magnetic perturbation. As the RMP amplitude increases, the plasma response is shown to be linear, saturated, and ultimately, disruptive

Fast-ion transport induced by externally applied Resonant Magnetic Perturbations in the ASDEX Upgrade tokamak

In magnetically con ned fusion plasmas, MHD instabilities such as the Edge Localized Modes (ELMs), present in current devices, need to be kept under control in order to avoid too high heat uxes on plasma facing components. Therefore, substantial e orts have been focused on developing techniques to mitigate these instabilities. Among these methods, one of the most promising techniques is the application of external Magnetic Perturbations (MPs), which have been observed to e ectively mitigate or even suppress ELM instabilities. However, the inclusion of a 3D perturbative eld has a strong impact on the plasma stability and con nement. Fast-ions (i.e. supra-thermal ions) resulting from the fusion device plasma heating systems and fusion reactions require a good con nement to preserve the device performance and integrity. Therefore, the study of the impact that perturbative elds have on energetic particles is crucial to assess and design the MPs systems in future machines like ITER. In this thesis, dedicated experiments in AUG have been carried out to analyse the fast-ion transport dependence on the poloidal spectra of the perturbation, showing that the amplitude of the observed fast-ion losses depends strongly on the energetic particle phase space and poloidal mode spectra of the external perturbation. The transport mechanism underlying these experimental results has been analysed through realistic numerical simulations using the ASCOT code. The results of these simulations have been combined with an analytical theory of nonlinear wave-particle resonances. This has shown that the combination of multiple linear and nonlinear resonances with the applied perturbative elds create a region where resonant transport is maximised. This transport occurs at the plasma edge and depends on the perturbation poloidal and toroidal spectra, as well as the magnetic equilibrium and particle orbit topology. The impact of the collisionality and the radial electric elds on these resonances has also been assessed throughout this work. This analysis contributes to the ability to control the resonant transport at the plasma edge, which opens new avenues for the control of the energetic particle population and associated MHD uctuations in future burning plasmas

Alfvén modes and wave-particle interaction in a tokamak

This work is motivated by the nonlinear wave-particle interaction problems. To build a self-consistent theory, we consider eigenmodes of the bulk plasma as well as the dynamics of the energetic particles. The modes of our particular interest are the Alfvén Cascades and the Toroidicity Alfven Eigenmodes (TAE), which we describe using Magnetohydrodynamic(MHD) analysis and the AEGIS codes. We investigate the stabilizing effect for the Alfvenic waves from continuum damping, especially near the TAE gap. For the kinetic description of the energetic particles, we propose new canonical straight field line coordinates to model the guiding center motion. We then formulate wave-particle interaction problem using the action-angle variables. In Chapter 2, we interpret Alfvén Cascades observed in Madison Symmetric Torus (MST). We do linear MHD calculations and find the mode frequency, structure, and stability boundary. We then perform MHD simulation using the AEGIS code, with the equilibrium reconstructed from experiment. The result is discussed and compared with the experimentally observed features. In Chapter 3, we analyze continuum damping for Alfvénic waves, especially in the extreme situation near the TAE gap. We find that the continuum tip absorption feature is actually related to the existing of TAEs in the gap. On the technical level, we improve the numerical scheme of AEGIS and resolve two closely-spaced singularities. As a result, the absorption features observed in the simulation show good agreement with our analytical calculation. In order to simulate the energetic particle guiding center motion in the Hamiltonian form, we propose a new set of straight magnetic field line coordinates. The new coordinates exist for general tokamak devices and facilitate both MHD calculations and energetic particles. The new coordinate system makes it very convenient to take the advantage of the Hamiltionian structure of the guiding center motion. We use a canonical transformation to action-angle variables to formulate the interaction model for particles. The action-angle variables allow us to resolve wave-particle resonances and describe the conserved quantities for resonance particles. The model can give us a complete picture for nonlinear stage of wave-particle interaction.Physic