This thesis presents the first systematic study of multimode external kink structure and dynamics in a tokamak using a high-resolution magnetic sensor set. Multimode effects are directly measured, rather than inferred from anomalies in single-mode behavior. In order to accomplish this, an extensive set of 216 poloidal and radial magnetic field sensors has been installed in the High Beta Tokamak -- Extended Pulse (HBT-EP) device for high-resolution measurements of three-dimensional mode activity. An analysis technique known as biorthogonal decomposition (BD) is described, and simulations are presented to justify its use for studying kink mode dynamics in HBT-EP data. Coherent activity of multiple simultaneous modes is observed using the BD without needing to define a mode structure basis beforehand. Poloidal mode numbers up to m=8 are observed via sensor arrays with full 360 degree coverage. Higher poloidal mode numbers are suggested by the data, but cannot be well-resolved with the available diagnostics. Toroidal mode numbers up to n=4 are observed. Non-rigid, multimode activity is observed for coexisting external kinks having m/n=3/1 and 6/2 structures. Despite sharing the same helicity and same resonant surface, rotation of 6/2 modes is independent of 3/1 mode rotation -- the n=2 mode does not simply rotate with double the frequency of the n=1 mode. During periods of 3/1-dominated activity, the 6/2 mode is observed to modulate the 3/1 amplitude, and in brief instances can overpower the 3/1. Statistical analysis over many shots reveals the multimode nature of the 3/1 kink to be more significant when the resonant q=3 surface begins internal, then is ejected from the plasma. This inference is based on the relative amplitudes of secondary modes during 3/1-dominated activity, as well as spectral content of the modes. Conformal conducting wall segments were also retracted away from the plasma surface using low-order poloidal and toroidal asymmetries to excite measurable differences in low m- and n-number modes. Kink mode amplitudes increase as the wall segments are withdrawn, and non-symmetric wall configurations modulate the amplitude and frequency of the rotating modes depending upon their toroidal orientation with respect to the non-symmetric wall. Modulations of mode amplitude and rotation are larger for the toroidal wall asymmetry than for the poloidal wall asymmetry.

The application of electrostatic bias to both low density plasma with coherent fluctuations and high density plasma with turbulent fluctuations confined by a magnetic dipole are investigated. Previously, electrostatic biasing of low density plasma was symmetric, drove rapid plasma rotation, and excited the centrifugal interchange instability. This research investigates the application of non-symmetric bias and the influence of broken symmetry on strongly turbulent plasmas. Non- symmetric bias is applied through either point biasing or an equatorial array spanning the device. In both cases, the spatial symmetry of applied bias dramatically effects the plasma fluctuations. With bias applied, the plasma achieves a new equilibrium characterized by amplified low order modes and diminished amplitude of higher order modes. Although the turbulent spectrum changes, the RMS fluctuation level is unchanged by the bias. Bias also causes the turbulent electrostatic fluctuations to coalesce into a quasi-coherent mode and the appearance of increased coherence. The effect of bias configuration is also seen to change the measured levels of nonlinear coupling. Non-symmetric biasing increases nonlinear coupling while symmetric biasing leaves the coupling unchanged. These results represent the first experimental demonstration of symmetry breaking driving the inverse energy cascade in a quasi-two dimensional plasma system. The application of dynamic and rotating electrostatic bias as well as plans for applying turbulent feedback are discussed.

Understanding the maintenance and stability of plasma pressure confined by a strong magnetic field is a fundamental challenge in both laboratory and space plasma physics. Using magnetic and X-ray measurements on the Levitated Dipole Experiment (LDX), the equilibrium plasma pressure has been reconstructed, and variations of the plasma pressure for different plasma conditions have been examined. The relationship of these profiles to the magnetohydrodynamic (MHD) stability limit, and to the enhanced stability limit that results from a fraction of energetic trapped electrons, has been analyzed. In each case, the measured pressure profiles and the estimated fractional densities of energetic electrons were qualitatively consistent with expectations of plasma stability. LDX confines high temperature and high pressure plasma in the field of a superconducting dipole magnet. The strong dipole magnet can be either mechanically supported or magnetically levitated. When the dipole was mechanically supported, the plasma density profile was generally uniform while the plasma pressure was highly peaked. The uniform density was attributed to the thermal plasma being rapidly lost along the field to the mechanical supports. In contrast, the strongly peaked plasma pressure resulted from a fraction of energetic, mirror trapped electrons created by microwave heating at the electron cyclotron resonance (ECRH). These hot electrons are known to be gyrokinetically stabilized by the background plasma and can adopt pressure profiles steeper than the MHD limit. X-ray measurements indicated that this hot electron population could be described by an energy distribution in the range 50-100 keV. Combining information from the magnetic reconstruction of the pressure profile, multi-chord interferometer measurements of the electron density profile, and X-ray measurements of the hot electron energy distribution, the fraction of energetic electrons at the pressure peak was estimated to be about 35% of the total electron population. When the dipole was magnetically levitated the plasma density increased substantially because particle losses to the mechanical supports were eliminated so particles could only be lost via slower cross-field transport processes. The pressure profile was observed to be broader during levitated operation than it was during supported operation, and the pressure appeared to be contained in both a thermal population and an energetic electron population. X-ray spectra indicated that the X-rays came from a similar hot electron population during levitated and supported operation; however, the hot electron fraction was an order of magnitude smaller during levitated operation (<3% of the total electron population). Pressure gradients for both supported and levitated plasmas were compared to the MHD limit. Levitated plasmas had pressure profiles that were (i) steeper than, (ii) shallower than, or (iii) near the MHD limit dependent on plasma conditions. However, those profiles that exceeded the MHD limit were observed to have larger fractions of energetic electrons. When the dipole magnet was supported, high pressure plasmas always had profiles that exceeded the MHD interchange stability limit, but the high pressure in these plasmas appeared to arise entirely from a population of energetic trapped electrons.

This thesis presents the systematic study of the multimode external kink mode structure and dynamics in the High-Beta Tokamak Extended-Pulse experiment (HBT-EP) when the plasma rotation is externally controlled using a source of toroidal momentum input. The capabilities of the HBT-EP tokamak to study rotation physics was greatly extended during a 2009-2010 major upgrade, when a new adjustable conducting wall, a high-power modular control coil array system, and an extensive set of 216 poloidal and radial magnetic sensors were installed on the machine. HBT-EP was additionally equipped with a biased edge electrode which made it possible to adjust the plasma ion and plasma magnetohydrodynamics (MHD) mode rotation frequencies by imparting an electromagnetic torque on the plasma. The design of this biased edge electrode, and its capability to torque the plasma is described. The rotation frequency of the helical kink modes was directly inferred from analysis of the magnetics dataset. To directly measure the plasma ion acceleration as the plasma was torqued by the biased electrode, a novel high-throughput and fast-response spectroscopic rotation diagnostic was installed on HBT-EP. This spectroscopic rotation diagnostic was designed to measure the velocity of He ions, therefore when conducting experiments using the spectroscopic rotation diagnostic a gas mixture of 90%D and 10%He was used. With its current power supplies the bias probe is capable of accelerating the primary m/n=3/1 helical kink mode (which has a natural rotation frequency between +7-+9kHz) to somewhere between -50kHz-+25kHz depending on the probe bias. At a probe voltage of +175V the He impurity ions were seen to accelerate by 3km/sec. Biorthogonal decomposition (BD) analysis was applied to the large magnetics dataset and used to determine the multimode m/n spectrum of the helical kink modes present in HBT-EP. The dominant helicities present as revealed by the BD are the m/n=3/1 and m/n=6/2 modes, which represent about 85% and 8% of the total MHD activity respectively. This percentages remain consistent across the entire range of 3/1 mode rotation frequencies obtainable from the bias probe, (-50kHz-25kHz). The Hilbert transform technique was also applied to magnetic sensor data to determine the instantaneous amplitude and frequency of the total MHD activity. The total MHD amplitude was seen to decrease with increasing plasma rotation, a 35% reduction as the 3/1 mode was accelerated from +6-+24kHz. Active MHD spectroscopy experiments using a resonant magnetic perturbation (RMP) are able to excite a clear three-dimensional plasma response. Plasma rotation is theoretically expected to increase plasma stability to external resonant error elds, and in HBT-EP the plasma amplitude response to a m/n=3/1 RMP increases by a factor of 2.7 when the plasma rotation is decreased from +25kHz to +-2kHz. As the RMP amplitude increases, slower plasmas are seen to disrupt at a lower perturbation amplitude than unperturbed or rapidly rotating modes. The 6/2 helical kink mode also shows an amplitude and phase response to the 3/1 RMP, and like the 3/1 mode the amplitude response is largest when the plasma is slowly rotating. The ratio between the plasma 6/2 amplication and the 3/1 amplication to a 3/1 RMP is nearly constant, regardless of the plasma rotation or the RMP amplitude.

In this thesis, I present measurements from a high-speed video camera diagnostic on the High Beta Tokamak - Extended Pulse (HBT-EP). This work represents the first use of video data to analyze and understand the behavior of long wavelength kink perturbations in a wall-stabilized tokamak. A Phantom v7.3 camera was installed to capture the plasma's global behavior using visible light emissions and it operates at frame rates from 63 to 125 kfps. A USB2000 spectrometer was used to identify the dominant wavelength of light emitted in HBT-EP. At 656 nm, it is consistent with the D-alpha light expected from interactions between neutral deuterium and plasma electrons. The fast camera in combination with an Acktar vacuum black background produced images which were inverted using Abel techniques to determine the average radial emissivity profiles. These profiles were found to be hollow with a radial scale length of approximately 4 cm at the plasma edge. As a result, the behavior measured and analyzed using visible light videography is limited to the edge region. Using difference subtraction, biorthogonal decomposition and Fourier analysis, the structures of the observed edge fluctuations are computed. By comparing forward modelling results to measurements, the plasma is found to have an m/n = 3/1 helical shape that rotates in the electron drift direction with a lab-frame frequency between 5 and 10 kHz. The fast camera was also used to measure the plasma's response to applied helical magnetic perturbations which resonate with the equilibrium magnetic field at the plasma's edge. The static plasma response to non-rotating resonant magnetic perturbations (RMPs) is measured by comparing changes in the recorded image following a fast reversal, or phase flip, of the applied RMP. The programmed toroidal angle of the RMP is directly inferred from the resulting images of the plasma response. The plasma response and the intensityof the RMP are compared under different conditions. I found the resulting amplitude correlations to be consistent with previous measurements of the static response using an array of magnetic sensors. My work has shown that high-speed videography can be an extremely useful diagnostic for measuring edge perturbations in a tokamak. Future measurements, such as those using multiple cameras with different views, are expected to improve our understanding of plasma behavior and to detect edge fluctuations with higher temporal and spatial resolution. Supplementary Videos: Video 1 - This is an example of the video data from Shot 77324, an unforced plasma shot taken with the shells inserted. Video 2 - The strongest naturally-rotating mode has been extracted from a subset of the raw data shown in Video 1 using a biorthogonal decomposition. Long striations can be seen which are common in shots that have the shells inserted. Video 3 - In this video of the raw data from Shot 77537, the shells are retracted. The smooth non-reflective Acktar black background can be seen between the shells. Video 4 - The dominant BD mode from Shot 77537 shows pinwheel-like behavior. With the shells retracted, the plasma encounters fewer physical structures for neutral recycling and this affects the light emissions. Video 5 - This video shows the dominant BD modes from Shot 78029 during which a phase-flip RMP was used to influence the plasma. The mode seems to slow in its rotation as it resonates with the externally-applied field.

Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged fields generated by beam-plasma instabilities can be responsible for defocusing and distorting beams propagating in background plasma. This can be problematic in inertial fusion applications where the beam is intended to propagate ballistically as the background plasma neutralizes the beam space charge and current. We used particle-in-cell (PIC) code LSP to numerically investigate the defocusing effects in an ion beam propagating in background plasma experiences as it is exposed to the non-linear fields generated by Two-Stream instability between beam ions and plasma electrons. Supported by theory and benchmarked by the numerical solutions of governing E&M equations, the simulations were used to find and check scaling laws for the defocusing forces in the parameter space of beam and plasma density as well as the beam ion mass. A transition region where the defocusing fields peak has been identified, which should be avoided in the design of experimental devices. We further proposed a diagnostic tool to identify the presence of the two-stream instability in a system with parameters similar to the National Drift Compression Experiment II (NDCX-II) and conducted proof-of concept simulations. In the case of electron beam propagating in background plasma instability driven collisionless scattering and plasma heating is observed. 1-D simulations conducted in EDIPIC were benchmarked in LSP to study the excitation and time-evolution of electron-electron Two-Stream instability. Coupling of electron dynamics via non-linear ponderomotive force created by instability generated fields with ion cavities and Ion-Acoustic mode excitation was observed. Furthermore 2-D simulations of an electron-beam in a background plasma was performed. Many of the effects in observed in 1-D simulations were replicated. Morever generation of oblique modes with transverse wave numbers were observed in the simulations, which resulted in significant transverse scattering of beam electrons and the time evolution of the turbulent spectrum was studied via Fourier techniques. It is plausible that the modes excited might be interacting non-linearly via mode-coupling, however further theoretical and numerical investigation of the turbulent spectrum is needed. The study of the more realistic 2-D system and the spectrum is important for the understanding of collisionless heating of plasmas by beams and the underlying energy delivery which can have important applications in especially low temperature plasma systems used primarily in etching and materials processing.

This thesis investigates the behavior of electron temperature gradient (ETG) driven instabilities in the Columbia Linear Machine (CLM). Building on prior work in CLM, the primary goal of this research is to produce, identify, and illuminate the basic physics of these instabilities, and explore the behavior of these instabilities under the presence of trapping and curved magnetic field lines. The first part of this thesis is focused on studying the saturated ETG mode, and the general behavior of the mode under varying levels of magnetic curvature. Measuring ETG modes can be problematic since they have large real frequencies, fast growth rates (~MHz) and small spatial scales, but carefully designed probe diagnostics can overcome these limits. In order to produce curved magnetic field lines, we modified CLM to operate with an internal movable mirror coil. We determined the temperature and density profiles under varying curvature, and measured changes in the mode structure and frequency. We found small changes in the azimuthal/poloidal structure and frequency, characterized by an increase in the m-number (m_slab~10-13 and Δ m~1), along with small changes in the axial/toroidal structure (k_ǁcurvature<k_ǁslab) and frequency. We also present one of the first experimental scaling of ETG mode amplitude as a function (ω _curvature<ω_slab). Our key finding was a that overall levels of saturated ETG mode amplitude had a modest increase (~1.5x) which is slightly larger than existing theory and simulations would predict, and that the power density and amplitude of individual mode peaks can increase more dramatically (~2-3x amplitude). The second part of this thesis studies the radial transport for saturated ETG modes in CLM. ETG modes are believed to be a significant source of anomalous electron energy transport in plasmas, and a better understanding of these modes and the transport they drive across magnetic field lines is of particular interest for advanced tokamaks and future fusion reactors, where these is a continued push for energy efficiency. A specially designed triple probe has been developed, which can measure fluctuations in temperature and potential simultaneously, with a high frequency and special resolution suitable for ETG studies. We present an experimental scaling of radial transport as a function of magnetic field curvature, again one of the first of its kind. Our findings indicate a modest increase in radial transport (~2x) with increased curvature, but unlike saturated mode amplitudes, we find that radial transport saturates for higher levels of curvature in CLM.

Turbulence in plasma confined by a magnetic dipole is dominated by interchange fluctuations with complex dynamics and short spatial coherence. We report the first use of local current-collection feedback to modify, amplify, and suppress these fluctuations. The spatial extent of turbulence regulation is limited to a correlation length near the collector. Changing the gain and phase of collection results in power either extracted from or injected into the turbulence. This mechanism is analogous to the magnetospheric-ionospheric coupling by field-aligned currents. The measured plasma response shows some agreement with calculations of the linear response of global interchange-like MHD and entropy modes to current-collection feedback.

Dissertação (Mestrado em Engenharia Mecânica) - Centro Universitário da FEI, São Bernardo do Campo, 2014

Tese de mestrado integrado. Engenharia Química. Faculdade de Engenharia. Universidade do Porto. 2010