Fractional Order Modeling and Control: Development of Analog Strategies for Plasma Position Control of the Stor-1M Tokamak

This work revolves around the use of fractional order calculus in control science. Techniques such as fractional order universal adaptive stabilization (FO-UAS), and the fascinating results of their application to real-world systems, are presented initially. A major portion of this work deals with fractional order modeling and control of real-life systems like heat flow, fan and plate, and coupled tank systems. The fractional order models and controllers are not only simulated, they are also emulated using analog hardware. The main aim of all the above experimentation is to develop a fractional order controller for plasma position control of the Saskatchewan torus-1, modified (STOR-1M) tokamak at the Utah State University (USU) campus. A new method for plasma position estimation has been formulated. The results of hardware emulation of plasma position and its control are also presented. This work performs a small scale test measuring controller performance, so that it serves as a platform for future research efforts leading to real-life implementation of a plasma position controller for the tokamak

Diamagnetic flux measurements on the STOR-M tokamak

Diamagnetic measurements of poloidal beta have been performed in the STOR-M tokamak by a flux loop placed exterior to the vacuum chamber. Poloidal beta is defined as the ratio of plasma kinetic pressure to poloidal magentic field pressure. Compensation for the vacuum toroidal field has been performed using a non-enclosing co-planar coil, and vibrational compensation from auxiliary coils. It was found that in STOR-M conditions (20% toroidal magnetic field decay over discharge) there is significant influence on the diamagnetic flux measurements from strong residual signals, presumably from image currents being induced by the toroidal field coils, requiring further compensation. A blank (non-plasma) shot is used specifically to eliminate the residual component which is not proportional to the toroidal magnetic field. Data from normal ohmic discharge operation is presented and calculations of poloidal beta from coil data (βθ ≃ 0.5) is found to be in reasonable agreement with the values of poloidal beta obtained from measurements of electron density and Spitzer temperature with neoclassical corrections for trapped electrons. Contributions present in the blank shot (residual) signal and the limitations of this method are discussed. A pulse with Compact Toroid Injection was examined and compared to a normal ohmic discharge, and one where the Compact Toroid Injector was used to supply the tokamak with neutral gas. Soft X-Ray (SXR) measurements were taken and compared. There is a strong agreement between the profiles of the poloidal beta and the SXR measurements. The bulk plasma thermal energy was measured and found to increase by 5.6 J following the injection of a CT. The diamagnetic measurements appear to be affected by image currents induced in the chamber walls by the plasma current, and also by plasma position fluctuations. Future work outlining the possibilty of compensating these currents and improving the measurements is presented

Effects of edge safety factor on the toroidal flow velocity of the STOR-M plasma.

The effect of changing edge safety factor on the toroidal flow of the STOR-M plasma has been investigated during the application of both resonant magnetic perturbation (RMP) and compact torus injection (CTI). The edge safety factor was varied by varying the plasma current while keeping the toroidal field constant. A Czyner-Turner spectrometer was used to collect the spectral data from which the velocity of specific impurity ions was diagnosed. Time resolved velocity measurements were inferred from the Doppler wavelength shift of the emission lines. Impurity emission lines at different ionization stages are located at different radial locations within the STOR-M plasma. Properties of these impurity ions are assumed to be closely related the hydrogen ion (main working gas) due to the strong interaction among the ion species. Changing the edge safety factor has a similar effect on the toroidal flow of STOR-M plasma during discharges with both RMP and CTI. A velocity shear was discovered for different impurity ions. The toroidal flow is enhanced for edge ions while a reversal of flow is observed for core ions. As the edge safety factor reduces, the emission location for the core ions is located with q=2 surface and RMP has a significant impact on their toroidal flow velocity. It was also observed that CT injection has a significant effect on the toroidal velocity of the core ions compared to that of the edge ions. In addition, high plasma current (low safety factor) induced large change in the toroidal flow velocity of the STOR-M plasma

Visible and near-infrared divertor spectroscopy on the MAST and JET-ILW tokamaks

Passive spectroscopy diagnostics play a key role in advancing the physics of plasma exhaust in the edge and divertor regions of tokamaks. Information obtained from spectral line intensities and profile shapes is crucial for estimating plasma parameters, particularly for studies of cold and dense detached plasmas. This work aims to characterise the visible and near-infrared spectral regions with emphasis on the Balmer and Paschen hydrogen series lines, their diagnostic applications and interpretation techniques. Whereas the Balmer series lines are measured routinely, few observations of the Paschen series lines have been carried out in the fusion plasma context. Extending observations to the near-infrared region for more detailed studies of the Paschen series is addressed through diagnostic development with the aim of providing coverage of the visible to near-infrared spectral range (350-1900 nm) along the same optical line-of-sight. An initial spectral survey on MAST using a purpose built diagnostic provides new insight into the spectral features in the near-infrared and confirms the viability of Paschen line observations. Following the proof of concept measurements on MAST, diagnostic development on the JET ITER-like wall mirror-linked divertor spectroscopy system facilitated more refined measurements. The main outputs include first of its kind measurements of the Pa-alpha line and spatially resolved spectral line profile measurements of the Pa-beta line. In the visible range ELM-resolved Balmer and impurity emission profile measurements at high spatial resolution were obtained using a new filtered camera system. A detailed assessment of the diagnostic scope for parameter estimation from both high-n and low-n Balmer and Paschen series lines is presented, underpinned by a parametrised line profile model which captures the relevant broadening and splitting mechanisms, including the Zeeman, Stark and Doppler processes. Interpretation of JET divertor plasma measurements, in combination with synthetic data simulation results, highlights the importance of complementary Balmer and Paschen series measurements for refining parameter estimates in divertor plasmas

Pedestal Characteristics and MHD Stability of H-Mode Plasmas in TCV

The tokamak à configuration variable (TCV) is unique in its ability to create a variety of plasma shapes and to heat the electron population in high density regimes using microwave power at the third harmonic of the electron cyclotron frequency. In the frame of this thesis, the impact of plasma shaping and heating on the properties of the edge transport barrier (ETB) in the high confinement mode (H-mode) was studied. This mode of operation is foreseen as one of the reference scenarios for ITER, the International Tokamak Experimental Reactor, which is being built to demonstrate the feasibility of thermonuclear fusion using magnetic confinement. A feature of H-mode regime operation are edge localized modes (ELMs), instabilities driven by the steep pressure gradients that form in the plasma edge region due to a transport barrier. During an ELM event, energy and particles are expelled from the plasma in a short burst. This will cause serious problems with respect to the heat load on plasma facing components in a tokamak of the size of ITER. Understanding of the phenomena associated with ELMs is thus required and dedicated investigations of their theory and experimental observations are carried out in many laboratories worldwide. This thesis presents several experimental and numerical investigations of tokamak behavior for configurations where the plasma edge plays an important role. From the experimental viewpoint, studies of transport barriers are challenging, as plasma parameters change strongly within a narrow spatial region. As part of the work presented here, the TCV Thomson scattering system was upgraded to meet the requirements for diagnosing electron temperature and density with high spatial resolution in the region of internal and external transport barriers. Simultaneously, the data analysis was significantly improved to cope with statistical uncertainties and alleviate eventual systematic errors. For measurements of the time evolution of density and temperature profile during the ELM cycle, the low repetition rate of the lasers used for Thomson scattering is a limiting. Although the system on TCV comprises 3 laser units that may be triggered in sequence with time separations down to 1 ms, time evolution over longer periods can only be reconstructed from repetitive events. In this context, an adjustment of the laser trigger to improve the synchronization with the ELM event is an advantage. A method was developed and implemented to generate a synchronizing trigger sequence, by a real-time monitoring of the D-alpha emission, which provides a marker for the ELM event. Recently, a "snowflake" (SF) divertor configuration, proposed as a possible solution to reduce the plasma-wall interaction by changing the divertor's poloidal magnetic field topology, was generated, for the first time, in TCV. A numerical code (KINX), based on a magnetohydrodynamic model (ideal MHD), was used to investigate the stability limits of this configuration under H-mode conditions and compare them with a similar standard single-null equilibrium. In a series of experiments, improved energy confinement was found and explained by improved stability of the edge region in the SF configuration. The influence of the pedestal structure in ELMy H-mode plasmas on the energy confinement and on ELM energy losses was investigated. The different ELM regimes found in TCV were analyzed, in particular the transition between type-III to type-I ELMs. The operational boundary of each ELM regime was characterized and verified by ideal MHD stability simulations for the ETB region. Recent studies on the scaling of the pedestal width with normalized poloidal pressure were confirmed. Using the capabilities of TCV, the influence of plasma shaping on pedestal parameters and MHD stability limits was investigated. In the past, models were developed to describe the onset of type-I ELMs, which are associated with modes in the ETB region arising from a coupling of pressure- and current-driven instabilities (coupled kink-ballooning modes). Experimental studies were performed to trace the temporal evolution of pedestal parameters characterizing the ETB during an ELM cycle. The results of these experiments were analyzed using information from MHD stability calculations. It is concluded that these models are capable of predicting limits as necessary conditions for ELM activity, but are not sufficient to fully explain ELM triggering