Dana Harold Edgell

Resistive wall mode stabilization with internal feedback coils in DIII-D

A set of twelve coils for stability control has recently been installed inside the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] vacuum vessel, offering faster time response and a wider range of applied mode spectra than the previous external coils. Stabilization of the n=1 ideal kink mode is crucial to many high beta, steady-state tokamak scenarios. A resistive wall converts the kink to a slowly growing resistive wall mode (RWM). With feedback-controlled error field correction, rotational stabilization of the RWM has been sustained for more than 2.5 s. Using the internal coils, the required correction field is smaller than with the external coils, consistent with a better match to the mode spectrum of the error field. Initial experiments in direct feedback control have stabilized the RWMs at higher beta and lower rotation than could be achieved by the external coils in similar plasmas, in qualitative agreement with numerical modeling. The new coils have also allowed wall stabilization in plasmas with...

Resistive wall stabilization of high-beta plasmas in DIII?D

Recent DIII?D experiments show that ideal kink-modes can be stabilized at high beta by a resistive wall, with sufficient plasma rotation. However, the resonant response to static magnetic field asymmetries by a marginally stable resistive wall mode can lead to strong damping of the rotation. Careful reduction of such asymmetries has allowed plasmas with beta well above the ideal MHD no-wall limit, and approaching the ideal-wall limit, to be sustained for durations exceeding 1?s. Feedback control can improve plasma stability by direct stabilization of the resistive wall mode or by reducing magnetic field asymmetry. Assisted by plasma rotation, direct feedback control of resistive wall modes with growth rates more than five times faster than the characteristic wall time has been observed. These results open a new regime of tokamak operation above the free-boundary stability limit, accessible by a combination of plasma rotation and feedback control.

Model-based dynamic resistive wall mode identification and feedback control in the DIII-D tokamak

A new model-based dynamic resistive wall mode (RWM) identification and feedback control algorithm has been developed. While the overall RWM structure can be detected by a model-based matched filter in a similar manner to a conventional sensor-based scheme, it is significantly influenced by edge-localized-modes (ELMs). A recent study suggested that such ELM noise might cause the RWM control system to respond in an undesirable way. Thus, an advanced algorithm to discriminate ELMs from RWM has been incorporated into this model-based control scheme, dynamic Kalman filter. Specifically, the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] resistive vessel wall was modeled in two ways: picture frame model or eigenmode treatment. Based on the picture frame model, the first real-time, closed-loop test results of the Kalman filter algorithms during DIII-D experimental operation are presented. The Kalman filtering scheme was experimentally confirmed to be effective in discriminating ELMs from RWM. As a result, the...

Modelling of feedback and rotation stabilization of the resistive wall mode in tokamaks

This paper describes the modelling of the feedback control and rotational stabilization of the resistive wall mode (RWM) in tokamaks. A normal mode theory for the feedback stabilization of the RWM has been developed for an ideal plasma with no toroidal rotation. This theory has been numerically implemented for general tokamak geometry and applied to the DIII-D tokamak. A general formulation is further developed for the feedback stabilization of a tokamak with toroidal rotation and plasma dissipation. It has been used to understand the role of the external resonant field in affecting the plasma stability and compared with the resonant field amplification phenomenon observed in DIII-D. The effectiveness of a differentially rotating resistive wall in stabilizing the RWM has also been studied numerically. It is found that for a non-circular tokamak, a wide range of flow patterns are all effective. The structure of the RWM predicted from ideal MHD theory has been compared with signals from various diagnostics. It is also projected that based on DIII-D results scaled up to the ITER-FEAT, 33 MW of 1 MeV negative neutral beam injection will be able to sustain plasma rotation sufficient to stabilize the RWM without relying on feedback.

Magnetohydrodynamic mode identification from magnetic probe signals via a matched filter method

A matched filter analysis has been developed to identify the amplitude and phase of magnetohydrodynamic modes in DIII-D tokamak plasmas using magnetic probe signals (δB p ). As opposed to conventional Fourier spatial analysis of toroidally spaced probes, this analysis includes data from both toroidally and poloidally spaced magnetic probe arrays. Using additional probes both improves the statistics of the analysis and more importantly incorporates poloidal information into the mode analysis. The matched filter is a numeric filter that matches signals from the magnetic probes with numerically predicted signals for the mode. The numerical predictions are developed using EFIT equilibrium reconstruction data as input to the stability code GATO and the vacuum field code VACUUM. Changes is the plasma equilibrium that occur on the same time scale as the mode are taken into account by modeling simple matched filter vectors corresponding to changes in total plasma current, plus vertical and horizontal plasma shifts. The matched filter method works well when there is good understanding of a mode and good modeling of its structure. Matched filter analysis results for a fast growing ideal kink mode, where equilibrium change effects are minimal, show the effectiveness of this method. A slow growing resistive-wall mode (RWM) is also analyzed using the matched filter method. The method gives good results for identifying the amplitude and phase of the RWM but the simple equilibrium vectors are insufficient for complete elimination of equilibrium changes on this time scale. An analysis of the computational requirements of the scheme indicates that real-time application of the matched filter for RWM identification will be possible.

Electron cyclotron resonance ion source one-dimensional fluid modeling

A one-dimensional (1D) fluid computer model for multiple ion species in an electron cyclotron resonance ion source (ECRIS) plasma has been developed. The ions species are assumed to be highly collisionally coupled and are treated using 1D fluid equations. The non-Maxwellian anisotropic electron distribution function is modeled by a 1D bounce-averaged Fokker–Planck code. ECR heating is included in the model as a quasilinear rf-diffusion term including relativistic detuning, rf pitch-angle scattering, and multiple resonance frequencies/locations. In a typical ECRIS, the electrons are very noncollisional and confined magnetically. The ions follow this electron confinement via the electrostatic potential. The 1D axial electrostatic potential profile predicted by the model shows an ion confining core electrostatic well as expected in ECRIS plasmas. Modeling results for the Argonne National Laboratory ECR-I ECRIS configuration are presented along with a discussion of the difficulties in benchmarking the model w...

A one-dimensional axial electron cyclotron resonance source model

A conventional zero-dimensional (uniform plasma parameters with no spatial variations) fluid model will provide a good match with an experimental electron cyclotron resonance ion source (ECRIS) charge-state distribution (CSD) if provided with a judicious set of user inputs. However, this arbitrarily chosen set of inputs is not necessarily unique. To be truly predictive, an ECRIS model should rely on experimental parameters as inputs. A multi-species model for an ECRIS plasma using experimental parameters as inputs is under development. The model eliminates electron temperature as a user input by employing a 2 V(v,θ) Fokker–Planck code with an ECR heating term to calculate the non-Maxwellian anisotropic electron distribution function. Further arbitrary user inputs are eliminated in favor of controlled parameters by bounce averaging the Fokker–Planck coefficients for a one-dimensional (1D)/2 V axial model. The neutral gas modeling has been extended to 1D using axially coupled particle balance equations. The...

Techniques for the measurement of ionization times in ECR ion sources using a fast sputter sample and fast gas valve

Two techniques for the discrete injection of material into an Electron Cyclotron Resonance ion source (ECRIS) have been developed for the purpose of measuring the ionization and confinement times of ion species. Previously only solid materials in conjunction with a pulsed laser were used in these studies due to the discrete material introduction produced by this configuration. The first method replaces the pulsed laser with a fast high voltage pulse applied to a sputter sample. The high voltage pulse has a rise time of 100 ns, fall time of 80.0 μs, and variable pulse duration. The second method utilizes a fast-pulsed gas valve capable of producing a gas pulse 160 μs in width. These pulse widths are well below the ionization times of the lower charge states and thus allows for time measurements to be made of all charge states. Both of these techniques can be employed to study the effects of rf power, coil configuration, biased disk, and gas mixing on ionization and confinement times. Rise times for neon, a...

Resistive wall mode identification by contrast enhancing technique of soft x-ray measurements on DIII-D

A contrast enhancing technique (CET) for soft x-ray (SXR) measurements has been developed and tested for the early identification of the low amplitude resistive wall mode (RWM) on the DIII-D tokamak. The technique is simple and fast. It utilizes the chord-by-chord difference of low-pass digitally filtered time derivatives of the signals from the twelve-chord fan-shape soft x-ray arrays located at toroidal angles of 195° and 45°. The two arrays allow a demonstration of the CET method principle, although they cannot completely resolve the RWM structure. The time derivative of the x-ray signal amplifies the effect of the temperature perturbation convected by the RWM, while naturally incorporating the equilibrium evolution effect. The correlation with the parameters measured by other diagnostics, such as the radial magnetic field δBr from the magnetic probes, the radial profiles of plasma current density j, pressure p, and safety factor q from the motional Stark effect, the radial profile of the temperature p...

Argon ionization cross sections for charge state distribution modeling in electron cyclotron resonance ion source

An updated and more accurate database for single- and double-ionization cross sections for almost all argon ions has been developed for the modeling of the charge state distribution (CSD) within an electron cyclotron resonance ion source. When the highly non-Maxwellian anisotropic electron-distribution function, is modeled by a Fokker–Planck code, one has to use the ionization cross sections instead of the Maxwellian rate coefficients. Most of the fitting coefficients used within the well-established semi-empirical formulas for direct ionization and double ionization have been recalculated using more accurate crossed-beam experimental data available. The shift of the CSD to higher-charge states due to the contribution of excitation autoionization and double ionization is presented by comparing the GEM code modeling using the Lotz formula and the cross sections with updated fitting coefficients.