Session GI2: Stability and Pedestal Physics

Progress Toward Stabilization of Low Internal Inductance Spherical Torus Plasmas in NSTX

Steady-state spherical torus plasmas for fusion applications, such as a component test facility or demonstration power plant, target operation with high non-inductive current fraction. These broad current profile targets have low values of plasma internal inductance, li, less than 0.4, near to the lower end of present NSTX operation. A key significance of this operation is that it approaches the purely current-driven ideal kink limit, which by definition exceeds the no-wall stability limit for all values of plasma normalized pressure (beta). In this regime, passive or active kink and resistive wall mode (RWM) stabilization is critical. Experiments on NSTX have recently approached this condition, evidenced by a significant reduction of the n = 1 no-wall stability limit computed by DCON. This limit drops from normalized beta of 4.2 -- 4.6 at li $\sim $ 0.6, to 3.4 at li $\sim $ 0.5, to below 2.8 for li $\sim $ 0.4. Nevertheless, passive and active RWM control has produced high toroidal beta up to 28 percent, and normalized beta up to 6.5 (nearly double the no-wall limit), closely following a record normalized beta to li ratio of 13 between li = 0.4 - 0.5. Non-inductive current fraction reaches 0.5 in these high normalized current plasmas. However, the disruption probability of these plasmas increases significantly, with about half of the discharges suffering terminating instabilities. Alteration of n = 1 RWM control system parameters, plasma rotation profile, and the role of beta feedback is examined to potentially improve mode stability. Ion precession drift and bounce frequency resonance stabilization is examined for these plasmas and compared to the identified stabilization reduction at intermediate plasma rotation and higher li.\footnote{J.W. Berkery, et al., Phys. Rev. Lett. 104, 035003 (2010).}   

Electron Cyclotron Emission Imaging of MHD Activity on the DIII-D, TEXTOR, ASDEX-U, and KSTAR Tokamaks

Recently developed electron cyclotron emission imaging (ECEI) diagnostics on DIII-D, ASDEX-U, and TEXTOR have provided unprecedented 2-D time-resolved images (e.g., movies) of MHD modes present in tokamak plasmas, proving to be uniquely capable of characterizing phenomena over a broad range of plasma parameters, tokamak operating scenarios, and fluctuation regimes. On DIII-D, dual independently configurable detector arrays provide simultaneous 2-D images of $T_{e}$ fluctuations with a total of 320 (20 vertical x 16 radial) channels. Similar systems at TEXTOR and ASDEX-U consist of 128 (16 vertical x 8 radial) channels in a single array. Receiver electronics provide a bandwidth of 400 kHz for fluctuations up to 3 cm$^{-1}$. First data from this diagnostic demonstrates sensitivity to coherent electron temperature fluctuations as low as 0.1{\%}, providing excellent resolution of precursor oscillations and low-level MHD. 2-D images of Alfv\'{e}n eigenmodes provide unambiguous measurement of poloidal mode structure and mode evolution in excellent agreement with ideal MHD theory. During experiments on both DIII-D and ASDEX-U, the imaged mode structure reveals poloidal asymmetries that are consistent with predicted non-ideal MHD effects. New features of the sawtooth instability have been observed on DIII-D and TEXTOR. Precursor oscillations and intermediate relaxation events have been imaged and analyzed using biorthogonal decomposition to reveal long-lived co- and counter-rotating modes which exhibit kink and tearing-like attributes. The presence of strong harmonic content in these modes reveals toroidal structure with n$>$1. This is compared to the results of similar analyses performed on slowly rotating tearing modes imaged at DIII-D with ECEI.   

Nonlinear Evolution of Edge Localized MHD Instabilities: A Comparison of Peeling and Ballooning-Dominated Equilibria

Analytic and numerical techniques are employed to describe the nonlinear evolution properties of edge localized ideal MHD instabilities. It is shown that the nonlinear dynamics of these instabilities depend upon the nature of the linear ideal MHD instability drive. Edge-localized ideal MHD modes for two shifted-circle tokamak equilibria are examined nonlinearly using the extended-MHD code NIMROD. The equilibria have H-mode-like profiles with differing edge currents and pressure gradients to produce linear stability spectra that peak at low-$n $(peeling-like) and high-$n $(ballooning-like). Numerical simulations characterize the evolution from the linear to the intermediate nonlinear regime, which is characterized by an ideal MHD displacement amplitude comparable to the mode width. For the peeling-like plasma, an edge-localized, $n $= 0, sheared cross-field plasma flow arises. As the instability enters the intermediate nonlinear regime the flow-shearing rate becomes comparable to the linear growth rate and nonlinearly slows the mode growth. This result is in sharp contrast to the ballooning-like equilibria where a smaller shear rate is generated and the mode grows exponentially with the linear growth rate well into the intermediate nonlinear regime [1]. The numerical results are consistent with an analytic theory derived to describe the nonlinear evolution properties of edge localized ideal MHD modes. A set of nonlinear evolution equations for the intermediate nonlinear phase of peeling mode instability is derived using the ratio of the radial mode width to the minor radius as an asymptotic expansion parameter. This differs from previous work on the nonlinear ballooning instability where a conventional ballooning order is used to derive the nonlinear evolution equations [1]. \\[4pt] [1] P. Zhu, C.C. Hegna, and C.R. Sovinec, \textit{Phys. Rev. Lett.} 102, 235003 (2009).   

Pressure-Gradient-Limiting Instability Dynamics in the H-mode Pedestal on DIII-D

Detailed 2D measurements of long-wavelength density fluctuations in the pedestal region with beam emission spectroscopy during the inter-ELM phase indicate two distinct bands of fluctuations propagating in opposite poloidal directions in the plasma frame: one lower frequency band (20-150~kHz) advects in the ion-diamagnetic drift direction (ion mode), and a higher frequency band (200-400~kHz) advects in the electron diamagnetic drift direction (electron mode). Interestingly, the mode amplitudes are modulated with the ELM cycle with the ion mode having some features qualitatively similar to those predicted for kinetic ballooning modes (KBM). Experiments have focused on determining the role of current and pressure gradient-driven instabilities in determining the H-mode pedestal structure. Detailed analysis of the temporal evolution reveals complex dynamics. The ion mode amplitude increases rapidly after an ELM and then saturates, consistent with the dynamics of the pedestal electron pressure, while the electron mode is quasi-stationary between ELMs. The decorrelation time of the ion mode is $<$5$\,\mu$s ($\tau_c\times c_s/a\le 1$), the radial correlation length is of order 10\,$\rho_i$ and the poloidal wave-number $k_\theta\rho_i \sim 0.1$. The mode velocity is comparable to the diamagnetic velocity. In related Quiescent H-mode experiments, pedestals with high electron pressure and high $E\times B$ shearing rates exhibit a set of high-frequency coherent modes propagating in the ion diamagnetic direction. These modes also exhibit KBM-like characteristics, but do not develop into fully turbulent structures. Numerical simulations are in progress to help identify the underlying instabilities and nature of these modes, and ultimately help validate nonlinear models of the H-mode pedestal structure.   

H-Mode Pedestal Scaling in DIII-D, AUG and JET

In H-modes the edge pedestal width determines the height of the pressure pedestal if the pedestal gradient is limited by MHD stability. This study separately compares the temperature and density pedestal widths $w_{T}$ and $w_{n}$ from high spatial resolution measurements on DIII-D, AUG, and JET, with theory based models. The ExB velocity shear turbulence suppression predict $w_{T}$\textit{/a$\propto \rho *$}$^{1/2}$ to w$_{T}$\textit{/a$\propto \rho *$ }(\textit{$\rho *$}$^{ }$\textit{$\propto \quad \surd $T}$_{i}$\textit{/aB}$_{T})$, however, a combination of JET and DIII-D discharges indicated $w_{T}$\textit{/a $\propto $ ($\rho $*)}$^{-0.17\pm 0.08}$, inconsistent with these theories. EPED1 couples kinetic-ballooning and peeling-ballooning constraints to set pedestal height and width giving $w_{T ,n}^{ }$\textit{$\propto \quad \beta $}$_{p}^{1/2}$, \textit{$\beta $}$_{p}=p_{ped}/($<$B_{p}^{2}$\textit{$>$/2$\mu $}$_{0})$. DIII-D data shows a strong correlation with $w_{T ,n}^{ }$\textit{$\propto \quad \beta $}$_{p}^{1/2}$, while JET data shows no strong\textit{ $\beta $}$_{p}$ dependence. AUG data cannot exclude $w^{ }$\textit{$\propto \quad \beta $}$_{p}^{1/2}$ for $w_{T}$ but does for $w_{n}$. The experimental scaling found in this study is beneficial for future fusion devices as the weak \textit{$\rho $*} scaling of $w/a$ implies a scaling with machine size.   

Role of plasma edge region in global stability on NSTX

Kinetic resonances have recently been identified to play an important role in the stability of the resistive wall mode (RWM) in NSTX and other tokamaks. Agreement between measured and predicted RWM stability thresholds has improved substantially, but differences are still sometimes observed. Key to this physics is the ExB drift frequency which is typically calculated by computing the radial electric field from radial force-balance from measured impurity density, temperature, and velocity. In the limit of large toroidal velocity and small poloidal velocity, the ExB rotation frequency is well approximated by the carbon impurity toroidal frequency. However, in the limit of reduced toroidal rotation typical of magnetic braking or reduced torque input, the toroidal and neoclassical poloidal velocities become comparable near the plasma edge. Recently, in NSTX and MAST the measured poloidal velocity has been shown to be consistent with neoclassical predictions enabling more accurate calculations of the ExB frequency. Importantly, for NSTX plasmas in which error-field correction has been employed to increase the toroidal rotation in the plasma edge region (r/a $>$ 0.8), the poloidal rotation can modify the inferred ExB rotation frequency (normalized to the Alfven frequency) by 0.2-0.5{\%} which is the same order of magnitude as the toroidal rotation frequency. Thus, edge poloidal rotation is sufficiently high to play a role in RWM marginal stability. The H-mode pedestal structure and the resistivity in the edge region can also influence stability. Previous modeling has shown that self-consistent calculations of the mode eigenfunction can modify RWM stability compared to perturbative methods - especially near the plasma edge. Comparisons between the measured marginal stability and predictions from the MARS-F and MARS-K codes including these effects will be presented.