Control of the resistive wall mode with internal coils in the DIIID tokamak

Abstract. New coils were installed inside the vacuum vessel of the DIII-D device for producing nonaxisymmetric magnetic fields. These " Internal-Coils" are predicted to stabilize the Resistive Wall Mode (RWM) branch of the long-wavelength external kink mode with plasma beta close to the ideal wall limit. Feedback using these new Internal-Coils was found to be more effective when compared with using the External-Coils located outside the vacuum vessel, because the location inside the vessel allows faster response and their geometry also couples better to the helical mode structure. A proper choice of feedback gain increased the plasma beta above the no-wall limit to C β ≥ 0.9, where C β is a measure of achievable beta above no-wall limit defined as (β-β nowall.limit )/(β ideal.wall.limit -β no.wall.limit ). The feedback system with Internal-Coils can suppress the RWM up to the normalized growth rate γτ w ~ 10 (τ w is the resistive flux penetration time of the wall). The feedback-driven dynamic error field correction helps to stabilize the RWM by reducing the rotational drag for Ω rot > Ω crit , where Ω rot is the angular rotation frequency of plasma and Ω crit is the critical value for the rotational stabilization. When Ω rot < Ω crit /2, the feedback system must stabilize the RWM mainly through direct magnetic control of the mode. The estimated Ω crit /Ω A is ≈ 2.5% by the MARS-F code analysis with experimentally observed profiles, where Ω A is the Alfvén angular rotational frequency at q = 2 surface. The MARS-F code also predicts that for successful RWM magnetic feedback control the power supply characteristic time should be a fraction of the growth time of the targeted RWM

Soft x-ray virtual diagnostics for tokamak simulations

The numerical toolset, FAR-TECH Virtual Diagnostic Utility, for generating virtual experimental data based on theoretical models and comparing it with experimental data, has been developed for soft x-ray diagnostics on DIII-D. The virtual (or synthetic) soft x-ray signals for a sample DIII-D discharge are compared with the experimental data. The plasma density and temperature radial profiles needed in the soft x-ray signal modeling are obtained from experimental data, i.e., from Thomson scattering and electron cyclotron emission. The virtual soft x-ray diagnostics for the equilibriums have a good agreement with the experimental data. The virtual diagnostics based on an ideal linear instability also agree reasonably well with the experimental data. The agreements are good enough to justify the methodology presented here for utilizing virtual diagnostics for routine comparison of experimental data. The agreements also motivate further detailed simulations with improved physical models such as the nonideal magnetohydrodynamics contributions (resistivity, viscosity, nonaxisymmetric error fields, etc.) and other nonlinear effects, which can be tested by virtual diagnostics with various stability modeling

On the roles of direct feedback and error field correction in stabilizing resistive-wall modes

Active feedback control in the DIII-D tokamak has fully stabilized the current-driven ideal kink resistive-wall mode (RWM). While complete stabilization is known to require both low frequency error field correction (EFC) and high frequency feedback, unambiguous identification has been made about the distinctive role of each in a fully feedback-stabilized discharge. Specifically, the role of direct RWM feedback, which nullifies the RWM perturbation in a time scale faster than the mode growth time, cannot be replaced by low frequency EFC, which minimizes the lack of axisymmetry of external magnetic fields

On the roles of direct feedback and error field correction in stabilizing resistive-wall modes

Active feedback control in the DIII-D tokamak has fully stabilized the current-driven ideal kink resistive-wall mode (RWM). While complete stabilization is known to require both low frequency error field correction (EFC) and high frequency feedback, unambiguous identification has been made about the distinctive role of each in a fully feedback-stabilized discharge. Specifically, the role of direct RWM feedback, which nullifies the RWM perturbation in a time scale faster than the mode growth time, cannot be replaced by low frequency EFC, which minimizes the lack of axisymmetry of external magnetic fields

Measurement and modeling of three-dimensional equilibria in DIII-D

A detailed experiment-theory comparison reveals that linear ideal MHD theory is in quantitative agreement with external magnetic and internal soft x-ray measurements of the plasma response to externally applied non-axisymmetric fields over a broad range of beta and rotation. This result represents a significant step toward the goal of advancing the understanding of three-dimensional tokamak equilibria. Both the magnetic and soft x-ray measurements show the driven plasma perturbation increases linearly with the applied perturbation, suggesting the relevance of linear plasma response models. The magnetic and soft x-ray measurements are made at multiple toroidal and poloidal locations, allowing well resolved measurements of the global structure. The comparison also highlights the need to include kinetic effects in the MHD model once beta exceeds 80% of the kink mode limit without a conducting wall. Two distinct types of response fields are identified by the linear ideal MHD model: one that consists of localized currents at the rational surfaces that cancel the applied resonant field and another that is excited by the components of the external field that couple to the kink mode. Numerical simulations show these two fields have similar amplitudes in ITER-shaped DIII-D discharges where n = 3 fields are used to suppress edge localized modes

Comprehensive control of resistive wall modes in DIII-D advanced tokamak plasmas

The resistive wall mode (RWM) and neoclassical tearing mode (NTM) have been simultaneously suppressed in the DIII-D for durations of over 2s at beta values 20% above the no-wall limit with modest electron cyclotron current drive and very low plasma rotation. The achieved plasma rotation was significantly lower than reported previously. However, in this regime where stable operation is obtained, it is not unconditionally guaranteed. Various MHD activities, such as edge localized modes (ELMs) and fishbones, begin to couple to the RWM branch near the no-wall limit; feedback has been useful in improving the discharge stability to such perturbations. Simultaneous operation of slow dynamic error field correction and fast feedback suppressed the pile-up of ELM-induced RWM at a series of ELM events. This result implies that successful feedback operation requires not only direct feedback against unstable RWM but also careful control of MHD-induced RWM aftermath, which is the dynamical response to a small-uncorrected error field near the no-wall beta limit. These findings are extremely useful in defining the challenge of control of the RWM and NTM in the unexplored physics territory of burning plasmas in ITER

Comprehensive control of resistive wall modes in DIII-D advanced tokamak plasmas

The resistive wall mode (RWM) and neoclassical tearing mode (NTM) have been simultaneously suppressed in the DIII-D for durations of over 2 s at beta values 20% above the no-wall limit with modest electron cyclotron current drive and very low plasma rotation. The achieved plasma rotation was significantly lower than reported previously. However, in this regime where stable operation is obtained, it is not unconditionally guaranteed. Various MHD activities, such as edge localized modes (ELMs) and fishbones, begin to couple to the RWM branch near the no-wall limit; feedback has been useful in improving the discharge stability to such perturbations. Simultaneous operation of slow dynamic error field correction and fast feedback suppressed the pile-up of ELM-induced RWM at a series of ELM events. This result implies that successful feedback operation requires not only direct feedback against unstable RWM but also careful control of MHD-induced RWM aftermath, which is the dynamical response to a small-uncorrected error field near the no-wall beta limit. These findings are extremely useful in defining the challenge of control of the RWM and NTM in the unexplored physics territory of burning plasmas in ITER