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Onset and Saturation of a Non-resonant Internal Mode in NSTX and Implications For AT Modes in ITER

Description: Motivated by experimental observations of apparently triggerless tearing modes, we have performed linear and nonlinear MHD analysis showing that a non-resonant mode with toroidal mode number n = 1 can develop in the National Spherical Torus eXperiment (NSTX) at moderate normalized βN when the shear is low and the central safety factor q0 is close to but greater than one. This mode, which is related to previously identified ‘infernal’ modes, will saturate and persist, and can develop poloidal mode number m = 2 magnetic islands in agreement with experiments. We have also extended this analysis by performing a free-boundary transport simulation of an entire discharge and showing that, with reasonable assumptions, we can predict the time of mode onset. __________________________________________________
Date: August 1, 2011
Creator: J.A. Breslau, M.S. Chance, J. Chen, G.Y. Fu, S,. Gerhardt, N. Gorelenkov, S.C. Jardin and J. Manickam
Partner: UNT Libraries Government Documents Department

Microtearing Instability In The ITER Pedestal

Description: Unstable microtearing modes are discovered by the GS2 gyrokinetic siimulation code, in the pedestal region of a simulated ITER H-mode plasma with approximately 400 WM DT fusion power. Existing nonlinear theory indicates that these instabilities should produce stochastic magnetic fields and broaden the pedestal. The resulted electron thermal conductivity is estimated and the implications of these findings are discussed.
Date: December 1, 2010
Creator: Wong, K. L.; Mikkelsen, D. R.; Rewoldt, G. M. & Budny, R.
Partner: UNT Libraries Government Documents Department

Nonlinear tearing mode interactions and mode locking in reversed field pinches

Description: The nonlinear interaction of a set of tearing instabilities and plasma flow is studied in a cylindrical plasma. An analytic theory of mode locking is developed which includes the effects of the localized electromagnetic torques, plasma inertia and cross-field viscosity. The calculation is specialized for the case of mode locking on the Madison Symmetric Torus (MST) reversed field pinch. In MST plasmas, a set of m = 1 tearing instabilities become phase locked and form a toroidally localized, rotating magnetic disturbance. An evolution equation for the phase velocity of this magnetic disturbance is derived which accounts for two types of electromagnetic torques. The external torques describe the interaction of the tearing modes with static magnetic perturbations located outside the plasma region. The interior torques describe the nonlinear interaction of three tearing modes which satisfy a wave number resonance condition. For conditions typical of MST, the internal torques dominate the external torques, which suggest the nonlinear interaction of tearing instabilities play a prominent role in the momentum degradation and mode locking.
Date: June 1, 1996
Creator: Hegna, C.C.
Partner: UNT Libraries Government Documents Department

Neoclassical Tearing Modes in Tokamak Fusion Test Reactor Experiments Part I. Measurements of Magnetic Islands and Delta Prime

Description: Tearing type modes are observed in most high-confinement operation regimes in TFTR. Three different methods are used to measure the magnetic island widths: external magnetic coils, internal temperature fluctuation from electron cyclotron emission (ECE) diagnostic and an experiment where the plasma major radius is rapidly shifted (`Jog` experiments). A good agreement between the three methods is observed. Numerical and analytic calculations of delta prime (the tearing instability index) are compared with an experimental measurement of delta prime using the tearing mode eigenfunction mapped from the Jog data. The obtained negative delta prime indicates that the observed tearing modes cannot be explained by the classical current-gradient-driven tearing theory.
Date: November 3, 1997
Creator: Chang, Z.; Fredrickson, E.D. & Batha, S.H.
Partner: UNT Libraries Government Documents Department

A study of tearing modes via electron cyclotron emission from tokamak plasmas

Description: This thesis studies several tearing mode problems from both theoretical and experimental points of view. A major part of this thesis is to demonstrate that Electron Cyclotron Emission (ECE) is an excellent diagnostic for studying an MHD mode structure and its properties in a tokamak plasma. It is shown that an MHD mode can be detected from the electron temperature fluctuations measured by ECE. The amplitude and phase profiles of the fluctuations contain detailed information about the mode structure. The ECE fluctuation phase profile indicates the magnetic island deformation due to the combination of sheared flow and viscosity. A model is presented to relate qualitatively the observed phase gradient to the local magnetic field, flow velocity shear and viscosity in a 2D slab geometry, using an ideal Ohm`s law and the plasma momentum equation including flow and viscosity. Numerical solution of the resultant Grad-Shafranov-like equation describing the deformed island shows that the experimentally observed value of the phase gradient can be obtained under realistic parameters for the shear in the flow velocity and viscosity. A new approach to the tearing mode stability boundary and saturation level is also presented.
Date: July 1, 1998
Creator: Ren, C.
Partner: UNT Libraries Government Documents Department

Stability of tearing modes in tokamak plasmas

Description: The stability properties of m {ge} 2 tearing instabilities in tokamak plasmas are analyzed. A boundary layer theory is used to find asymptotic solutions to the ideal external kink equation which are used to obtain a simple analytic expression for the tearing instability parameter {Delta}{prime}. This calculation generalizes previous work on this topic by considering more general toroidal equilibria (however, toroidal coupling effects are ignored). Constructions of {Delta}{prime} are obtained for plasmas with finite beta and for islands that have nonzero width. A simple heuristic estimate is given for the value of the saturated island width when the instability criterion is violated. A connection is made between the calculation of the asymptotic matching parameter in the finite beta and island width case to the nonlinear analog of the Glasser effect.
Date: February 1, 1994
Creator: Hegna, C.C. & Callen, J.D.
Partner: UNT Libraries Government Documents Department

Magnetohydrodynamic calculations with a nonmonotonic q profile and equilibrium, sheared toroidal flow

Description: The linear and nonlinear stability of a nonmonotonic q profile is examined using a reduced set of magnetohydrodynamic (MHD) equations with an equilibrium, sheared toroidal flow. The reversed shear profile is shown to be unstable to a rich variety of resistive MHD modes including pressure-driven instabilities and tearing instabilities possessing a tearing/interchange character at low Lundquist number, S, and taking on a double/triple tearing structure at high S. Linear calculations show that the destabilizing effect of toroidal velocity shear on tearing modes is enhanced at finite pressure seen previously for tearing modes at high S. Nonlinear calculations show the generation of a large, m = 1, n = 0, Reynolds-stress-driven poloidal flow in the absence of significant flow damping. Calculations in which the poloidal flow was heavily damped show that sub-Alfvenic, sheared toroidal flows have a minimal effect on weakly-coupled, localized instabilities.
Date: July 1, 1998
Creator: Held, E.D.; Leboeuf, J.N. & Carreras, B.A.
Partner: UNT Libraries Government Documents Department

Off-axis sawteeth and double-tearing reconnection in reversed magnetic shear plasmas in TFTR

Description: Off-axis sawteeth are often observed in reversed magnetic shear plasmas when the minimum safety factor q is near or below 2. Fluctuations with m/n = 2/1 (m and n are the poloidal and toroidal mode numbers) appear before and after the crashes. Detailed comparison has been made between the measured T{sub e} profile evolution during the crash and a nonlinear numerical magnetohydrodynamics (MHD) simulation. The good agreement between the observation and simulation indicates that the off-axis sawteeth are due to a double-tearing magnetic reconnection process.
Date: June 1, 1996
Creator: Chang, Z.; Park, W. & Fredrickson, E.D.
Partner: UNT Libraries Government Documents Department

Computational modeling of neoclassical and resistive MHD tearing modes in tokamaks

Description: Numerical studies of the nonlinear evolution of MHD-type tearing modes in three-dimensional toroidal geometry with neoclassical effects are presented. The inclusion of neoclassical physics introduces an additional free-energy source for the nonlinear formation of magnetic islands through the effects of a bootstrap current in Ohm`s law. The neoclassical tearing mode is demonstrated to be destabilized in plasmas which are otherwise {Delta}` stable, albeit once an island width threshold is exceeded. The plasma pressure dynamics and neoclassical tearing growth is shown to be sensitive to the choice of the ratio of the parallel to perpendicular diffusivity ({Chi}{parallel}/{Chi}{perpendicular}). The study is completed with a demonstration and theoretical comparison of the threshold for single helicity neoclassical MHD tearing modes, which is described based on parameter scans of the local pressure gradient, the ratio of perpendicular to parallel pressure diffusivities {Chi}{perpendicular}/{Chi}{parallel}, and the magnitude of an initial seed magnetic perturbation.
Date: June 24, 1996
Creator: Gianakon, T.A.; Hegna, C.C. & Callen, J.D.
Partner: UNT Libraries Government Documents Department

Dynamics of seed magnetic island formation due to geometrically coupled perturbations

Description: Seed magnetic island formation due to a dynamically growing external source in toroidal confinement devices is modeled as an initial value forced reconnection problem. For an external source whose amplitude grows on a time scale quickly compared to the Sweet-Parker time of resistive magnetohydrodynamics, the induced reconnection is characterized by a current sheet and a reconnected flux amplitude which lags in time the source amplitude. This suggests that neoclassical tearing modes, whose excitation requires a seed magnetic island, are more difficult to cause in high Lundquist number plasmas.
Date: June 1, 1998
Creator: Hegna, C.C.; Callen, J.D. & LaHaye, R.J.
Partner: UNT Libraries Government Documents Department

Operational limits in the National Spherical Torus Experiment

Description: The National Spherical Torus Experiment (NSTX) is a proof-of-principle scale device whose mission is to establish the physics basis of low aspect configurations most notably in the areas of plasma stability, transport and non-inductive current drive. The first series of physics experiments was conducted during the period from Sept. 1999 through Jan. 2000. Among the first experiments was a study to map out and characterize the operational density and q-limits. Density limits have typically been associated with enhanced radiated power due to overfuelling or impurity influx, although ion neoclassical transport may impose a density limit at very high densities in ohmic, gas-fueled plasmas. q-limits have typically been manifestations of destabilization of m=2/n=1 kink or tearing modes that lead to a sudden discharge termination.
Date: June 12, 2000
Creator: Kaye, S.M.; Bell, M. G.; Bell, R. E.; Gates, D.; Maingi, R.; Mazzucato, E. et al.
Partner: UNT Libraries Government Documents Department

Observation of Spontaneous Neoclassical Tearing Modes

Description: We present data in this paper from the Tokamak Fusion Test Reactor (TFTR) which challenges the commonly held belief that extrinsic MHD events such as sawteeth or ELMs [edge localized modes] are required to provide the seed islands that trigger Neoclassical Tearing Modes (NTMs). While sawteeth are reported to provide the trigger for most of the NTMs on DIII-D [at General Atomics in San Diego, California] and ASDEX-U [at Max-Planck-Institut fuer Plasmaphysik in Garching, Germany], the majority of NTMs seen in TFTR occur in plasmas without sawteeth, that is which are above the beta threshold for sawtooth stabilization. Examples of NTMs appearing in the absence of any detectable extrinsic MHD activity will be shown. Conversely, large n=1 modes in plasmas above the NTM beta threshold generally do not trigger NTMs. An alternative mechanism for generating seed islands will be discussed.
Date: October 3, 2001
Creator: Fredrickson, E.D.
Partner: UNT Libraries Government Documents Department

Non-linear evolution of double tearing modes in tokamaks

Description: The delta prime formalism with neoclassical modifications has proven to be a useful tool in the study of tearing modes in high beta, collisionless plasmas. In this paper the formalism developed for the inclusion of neoclassical effects on tearing modes in monotonic q-profile plasmas is extended to plasmas with hollow current profiles and double rational surfaces. First, the classical formalism of tearing modes in the Rutherford regime in low beta plasmas is extended to q profiles with two rational surfaces. Then it is shown that this formalism is readily extended to include neoclassical effects.
Date: December 17, 1999
Creator: Fredrickson, E.; Bell, M.; Budny, R.V. & Synakowski, E.
Partner: UNT Libraries Government Documents Department

Tearing mode analysis in tokamaks, revisited

Description: A new {Delta}{prime} shooting code has been developed to investigate tokamak plasma tearing mode stability in a cylinder and large aspect ratio ({epsilon} {le} 0.25) toroidal geometries, neglecting toroidal mode coupling. A different computational algorithm is used (shooting out from the singular surface instead of into it) to resolve the strong singularities at the mode rational surface, particularly in the presence of finite pressure term. Numerical results compare favorably with Furth et al. results. The effects of finite pressure, which are shown to decrease {Delta}{prime}, are discussed. It is shown that the distortion of the flux surfaces by the Shafranov shift, which modifies the geometry metric element stabilizes the tearing mode significantly, even in a low {beta} regime before the toroidal magnetic curvature effects come into play. Double tearing modes in toroidal geometries are examined as well. Furthermore, m {ge} 2 tearing mode stability criteria are compared with three dimensional initial value MHD simulation by the FAR code.
Date: December 1, 1997
Creator: Nishimura, Y.; Callen, J.D. & Hegna, C.C.
Partner: UNT Libraries Government Documents Department

Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

Description: In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
Date: June 1, 1998
Creator: Mirus, K.A.
Partner: UNT Libraries Government Documents Department

Stability of short wavelength tearing and twisting modes

Description: The stability and mutual interaction of tearing and twisting modes in a torus is governed by matrices that generalize the well-known {Delta}{prime} stability index. The diagonal elements of these matrices determine the intrinsic stability of modes that reconnect the magnetic field at a single resonant surface. The off-diagonal elements indicate the strength of the coupling between the different modes. The author shows how the elements of these matrices can be evaluated, in the limit of short wavelength, from the free energy driving radially extended ballooning modes. The author applies the results by calculating the tearing and twisting {Delta}{prime} for a model high-beta equilibrium with circular flux surfaces.
Date: September 22, 1998
Creator: Waelbroeck, F.L.
Partner: UNT Libraries Government Documents Department

Threshold condition for nonlinear tearing modes in tokamaks

Description: Low-mode-number tearing, mode nonlinear evolution is analyzed emphasizing the need for a threshold condition, to account for observations in tokamaks. The discussion is illustrated by two models recently introduced in the literature. The models can be compared with the available data and/or serve as a basis for planning some experiments in order to either test theory (by means of beta-limit scaling laws, as proposed in this paper) or attempt to control undesirable tearing modes. Introducing a threshold condition in the tearing mode stability analysis is found to reveal some bifurcation points and thus domains of intrinsic stability in the island dynamics operational space.
Date: March 1, 1996
Creator: Zabiego, M.F. & Callen, J.D.
Partner: UNT Libraries Government Documents Department

Stabilization of global MHD instabilities by toroidal plasma rotation

Description: Theoretical study and experimental observations suggest that rotation can play a crucial role in determining plasma stability. Since conventional magnetohydrodynamic (MHD) analysis ignores rotation, more advanced computational tools are being developed to confirm the theoretical understanding and to perform comparison between theory and experiment. In a previous work, the authors reported on the formulation and computation of MHD modes in plasmas with a small (subsonic) toroidal rotation. R.otation is found to have a substantial stabilizing effect under many circumstances. In this work, they extend the formulation in Ref. 4 to include an arbitrary (large) toroidal plasma rotation. It is the purpose of this work to examine the difference between these two formulations and report on results from computations using these formulations.
Date: July 1, 1995
Creator: Chu, M.S.; Miller, R.L.; Bondeson, A.; Luetjens, H.; DeRidder, G. & Sauter, O.
Partner: UNT Libraries Government Documents Department

Mode coupling trigger of neoclassical magnetohydrodynamic tearing modes in tokamaks

Description: Numerical studies of the nonlinear evolution of coupled magnetohydrodynamic - type tearing modes in three-dimensional toroidal geometry with neoclassical effects are presented. The inclusion of neoclassical physics introduces an additional free-energy source for the nonlinear formation of magnetic islands through the effects of a bootstrap current in Ohm`s law. The neoclassical tearing mode is demonstrated to be destabilized in plasmas which are otherwise {Delta}{prime} stable, albeit once a threshold island width is exceeded. A possible mechanism for exceeding or eliminating this threshold condition is demonstrated based on mode coupling due to toroidicity with a pre-existing instability at the q = 1 surface.
Date: May 1, 1997
Creator: Gianakon, T.A.; Hegna, C.C. & Callen, J.D.
Partner: UNT Libraries Government Documents Department

Measurement of magnetic turbulence structure and nonlinear mode coupling of tearing fluctuations in the Madison Symmetric Torus reversed field pinch edge

Description: Linear and nonlinear magnetohydrodynamic (MHD) stability of current-driven modes are studied in the MST reversed field pinch. Measured low frequency (f < 35 kHz) magnetic fluctuations are consistent with the global resistive tearing instabilities predicted by 3-D MHD simulations. At frequencies above 35 kHz, the magnetic fluctuations were detected to be localized and externally resonant. Discrete dynamo events, ``sawtooth oscillations,`` have been observed in the experimental RFP plasmas. This phenomenon causes the plasma to become unstable to m = 1 tearing modes. The modes that may be important in different phases of these oscillations are identified. These results then assist in nonlinear studies and also help to interpret the spectral broadening of the measured data during a discrete dynamo event. Three-wave nonlinear coupling of spectral Fourier modes is measured in the MST by applying bispectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 poloidal and 32 toroidal modes. Comparison to bispectra predicted by resistive MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomitant with a broadened k-spectrum. During the sawtooth formation the plasma is undergoing a pure diffusive process. The dynamo only occurs during the sawtooth crash. High frequency activity prior to a sawtooth crash is caused by nonlinear frequency (small-scale) mode coupling. Growth rate and coupling coefficients of toroidal mode spectra are calculated by statistical modeling. Temporal evolution of edge toroidal mode spectra has been predicted by transfer function analysis. The driving sources of electrostatic fields are different than for the magnetic fields. The characteristics of tearing modes can be altered by external field errors and addition of impurities to the plasma.
Date: January 1, 1994
Creator: Assadi, S.
Partner: UNT Libraries Government Documents Department

Nonlinear growth of strongly unstable tearing modes

Description: Rutherford`s theory of the tearing instability is extended to cases where current nonlinearities are important, such as long wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect-ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded.
Date: November 1, 1993
Creator: Waelbroeck, F. L.
Partner: UNT Libraries Government Documents Department

Effect of a static external magnetic perturbation on resistive mode stability in tokamaks

Description: The influence of a general static external magnetic perturbation on the stability of resistive modes in a tokamak plasma is examined. There are three main parts to this investigation. Firstly, the vacuum perturbation is expanded as a set of well-behaved toroidal ring functions and is, thereafter, specified by the coefficients of this expansion. Secondly, a dispersion relation is derived for resistive plasma instabilities in the presence of a general external perturbation and finally, this dispersion relation is solved for the amplitudes of the tearing and twisting modes driven in the plasma by a specific perturbation. It is found that the amplitudes of driven tearing and twisting modes are negligible until a certain critical perturbation strength is exceeded. Only tearing modes are driven in low-{beta} plasmas with {epsilon}{beta}{sub p} << 1. However, twisting modes may also be driven if {epsilon}{beta}{sub p}{approx}>1. For error-field perturbations made up of a large number of different poloidal and toroidal harmonics the critical strength to drive locked modes has a {open_quote}staircase{close_quote} variation with edge-q, characterized by strong discontinuities as coupled rational surfaces enter or leave the plasma. For single harmonic perturbations the variation with edge-q is far smoother. Both types of behaviour have been observed experimentally. The critical perturbation strength is found to decrease strongly close to an ideal external kink stability boundary. This is also in agreement with experimental observations.
Date: March 1, 1994
Creator: Fitzpatrick, R. & Hender, T. C.
Partner: UNT Libraries Government Documents Department

Stability of Coupled Tearing and Twisting Modes in Tokamaks

Description: A dispersion relation is derived for resistive modes of arbitrary parity in a tokamak plasma. At low mode amplitude, tearing and twisting modes which have nonideal MHD behavior at only one rational surface at a time in the plasma are decoupled via sheared rotation and diamagnetic flows. At higher amplitude, more unstable {open_quote}compound{close_quote} modes develop which have nonideal behavior simultaneously at many surfaces. Such modes possess tearing parity layers at some of the nonideal surfaces, and twisting parity layers at others, but mixed parity layers are generally disallowed. At low mode number, {open_quote}compound{close_quote} modes are likely to have tearing parity layers at all of the nonideal surfaces in a very low-{beta} plasma, but twisting parity layers become more probable as the plasma {beta} is increased. At high mode number, unstable twisting modes which exceed a critical amplitude drive conventional magnetic island chains on alternate rational surfaces, to form an interlocking structure in which the O-points and X-points of neighboring chains line up.
Date: March 1, 1994
Creator: Fitzpatrick, R.
Partner: UNT Libraries Government Documents Department

Heat loss by helicity injection in spheromaks

Description: A model is presented for spheromak buildup and decay including thermal diffusivity associated with magnetic turbulence during helicity injection. It is shown that heat loss by magnetic turbulence scales more favorably than gyroBohm transport. Thus gyroBohm scaling for the proposed ignition experiment would be the conservative choice, though present experiments may be dominated by magnetic turbulence. Because of a change in boundary conditions when the gun is turned off, the model may account for the observed increase in electron temperature in CTX after turnoff.
Date: March 17, 1994
Creator: Fowler, T. K.
Partner: UNT Libraries Government Documents Department