Session TI2: Stability Limits and Transport

Marshall N. Rosenbluth Outstanding Doctoral Thesis Award Talk: Control of Non-Axisymmetric Fields With Static and Dynamic Boundary Conditions

Small deformations of the otherwise axisymmetric field, known as ``error fields" (EFs), lead to large changes in global MHD stability. This talk will compare results from both 1)~a line-tied screw-pinch with rotating conducting walls and 2)~the DIII-D tokamak to illustrate that in both devices the EF has greatest effect where it overlaps with the spatial structure of its global kink mode. In both configurations the kink structure in the symmetry direction is well described by a single mode number (azimuthal $m=1$, toroidal $n=1$, respectively) and EF ordering is clear. In the asymmetric direction (axial and poloidal, respectively) the harmonics of the kink are coupled (by line-tying and toroidicity, respectively) and thus EF ordering is not straightforward. In the pinch, the kink is axially localized to the anode region and consequently the anode EF dominates the MHD stability. In DIII-D, the poloidal harmonics of the $n=1$ EF whose pitch is smaller than the local field-line pitch are empirically shown to be dominant across a wide breadth of EF optimization experiments. In analogy with the pinch, these harmonics are also where overlap with the kink is greatest and thus where the largest plasma kink response is found. The robustness of the kink structure further enables vacuum-field cost-function minimization techniques to accurately predict optimal EF correction coil currents by strongly weighting the kink-like poloidal harmonics in the minimization. To test the limits of this paradigm recent experiments in DIII-D imposed field structures that lack kink-overlapping harmonics, yielding $\approx$10X less sensitivity. The very different plasmas of the pinch and tokamak thus both demonstrate the dominance of the kink mode in determining optimal EF correction.   

Measured Improvement of Global MHD Mode Stability at High-beta, and in Reduced Collisionality Spherical Torus Plasmas

Global mode stability is studied in high-beta National Spherical Torus Experiment (NSTX) plasmas to avoid disruptions that must be kept to low probability in ITER and future tokamaks. Dedicated experiments using low frequency active magnetohydrodynamic (MHD) spectroscopy of applied, rotating $n =$ 1 magnetic fields, which provides an experimental measurement of plasma stability, revealed key dependencies of stability on plasma parameters. Stability\textit{ increases} at the highest values of $\beta_{\mathrm{N}}$/l$_{\mathrm{i}}$ in high $\beta_{\mathrm{N}}$ plasmas, consistent with other resistive wall mode (RWM) active control experiments and the wider database. This behavior is shown to correlate with kinetic stabilization [1]. Kinetic theory stipulates that when the trapped thermal ion precession and ExB motions are in resonance, energy is most efficiently transferred between the mode and the particles. The measurements also indicate that plasma stability can benefit from reduced collisionality, in agreement with the expectation from kinetic theory that reduced collisionality can allow resonant effects to be stronger, and in contrast to collisional stabilization models. Full kinetic RWM stability calculations with the MISK code generally agree with the experimental results. Calculations support the understanding that RWM stability can be increased by kinetic effects at low rotation by precession drift resonance and at high rotation by bounce and transit resonances. A simplified kinetic resonance criterion is evaluated, and the related stable range of measured ExB frequency is identified. The results are being analyzed for use in real-time instability determination to guide future rotation profile control and to supplement active RWM control for disruption avoidance.\\[4pt] [1] J.W. Berkery, et al., Phys. Rev. Lett. \textbf{104}, 035003 (2010).   

Feedback-Assisted Extension of the Tokamak Operating Space to Low Safety Factor

Recent DIII-D experiments have demonstrated stable operation at very low edge safety factor, $q_{95} \la 2$ through the use of magnetic feedback to control the $n=1$ resistive wall mode (RWM) instability. The performance of tokamak fusion devices may benefit from increased plasma current, and thus, decreased $q$. However, disruptive stability limits are commonly encountered in experiments at $q_{edge}\approx 2$ (limited plasmas) and $q_{95}\approx2$ (diverted plasmas), limiting exploration of low $q$ regimes. In the recent DIII-D experiments, the impact and control of key disruptive instabilities was studied. Locked $n=1$ modes with exponential growth times on the order of the wall eddy current decay timescale $\tau_w$ preceded disruptions at $q_{95}=2$. The instabilities have a poloidal structure that is consistent with VALEN simulations of the RWM mode structure at $q_{95}=2$. Applying proportional gain magnetic feedback control of the $n=1$ mode resulted in stabilized operation with $q_{95}$ reaching 1.9, and an extension of the discharge lifetime for $>100\,\tau_w$. Loss of feedback control was accompanied by power supply saturation, followed by a rapidly growing $n=1$ mode and disruption. Comparisons of the feedback dynamics with VALEN simulations will be presented. The DIII-D results complement and will be discussed alongside recent RFX-MOD demonstrations of RWM control using magnetic feedback in limited tokamak discharges with $q_{edge} < 2$ [1]. These results call attention to the utility of magnetic feedback in significantly extending the tokamak operational space and potentially opening a new route to economical fusion power production.\par \vskip3pt \noindent [1]~P.~Martin, et al., Proc.\ 24th IAEA Fusion Energy Conf.\ (San Diego, USA), paper OV/5-2Rb, 2012).   

On the non-stiffness of edge transport in L-modes

Transport analyses using first principle turbulence codes with 1$^{1}$/$_{2}$-D transport codes often study transport properties in a region between the plasma axis and a normalized radius around 0.8. Here, heat transport shows significant stiffness properties with R/L$_{\mathrm{Te}}$ values relatively independent of the auxiliary input power. We present experimental studies, in the TCV tokamak, of the transport properties in the edge region, close to the last closed flux surface, namely between $\rho_{\mathrm{V}}=$0.8 and 1 ($\rho_{\mathrm{\psi }}\ge $0.9), where $\rho_{\mathrm{V}}$ relates to the square root of the normalized volume inside the flux surface. We show that electron transport is not stiff in this region and extremely high R/L$_{\mathrm{Te}}$ values can be attained even with L-mode confinement. This result brings a new perspective to several ``accepted'' understandings. In particular, a specific study related to the Ip scaling of ohmic and ECH L-mode discharges shows that the strong Ip scaling is, in reality, strongly related with this non-stiff edge region. The Te scale length is shown to be proportional to Ip in the edge region and constant (independent of Ip) in the core. The relation with L-H transition and the I-modes will also be discussed, as the edge gradient can now be continuously increased, by increasing the input power, even during the L-mode phase. It is proposed that the pedestal width is related to the width over which the transport is non-stiff, and that this can already be studied, in detail, in L-mode. This study explains the large increase in confinement obtained with negative triangularity and a new model is proposed, including non-stiff edge local transport, which recovers the experimental observations.   

Landau-Fluid Closures for Edge Plasma Simulation: Models and Implementation

Two issues key to the development of practical gyro-Landau-fluid (GLF) simulation capability for magnetic fusion edge plasmas, and of interest for any situation with both strong spatial nonuniformity and a combination of collisionless and collisional regimes, are addressed. A highly efficient non-Fourier method for the computation of Landau-fluid (LF) closure operators [1] is introduced, based on an approximation by a sum of Helmholtz-equation solves (SHS) in configuration space. This method has fast-Fourier-like scaling of the computational cost, and results in large savings compared with direct application of ``delocalization'' kernels [2]. It also gives a very compact data representation of these operators in a nonuniform plasma. Systematic procedures have been developed to optimize the resulting operators for accuracy and computational cost. A GLF model [1] has been implemented in the BOUT$++$ code using the SHS method for both the parallel and toroidal-drift resonance closures, and first-order Pade' approximations for the closures associated with gyroaveraging. Excellent agreement has been obtained with gyrokinetic results [3] for linear toroidal ion-temperature-gradient (ITG) mode growth rates. Results from nonlinear simulations including closures for zonal flow and nonlinear phase mixing will be presented. LF closures are extended using the dynamic heat-flux equation to include strong spatial inhomogeneity, flows, collisions, and collisionless phase-mixing. Comparisons of the resulting model with detailed Fokker-Planck calculations will be presented. \\[4pt] [1] M. A. Beer and G. W. Hammett, Phys. Plasmas \textbf{3}, 4046 (1996), and references therein.\\[0pt] [2] G. P. Schurtz, Ph. D. Nicola\"{\i}, and M. Busquet, Phys. Plasmas \textbf{7}, 4238 (2000).\\[0pt] [3] A. M. Dimits, et. al., Phys. Plasmas \textbf{7}, 969 (2000).   

The Dynamics of Turbulence and Shear Flow Across the L-H Transition on DIII-D

Comprehensive 2D turbulence and flow measurements demonstrate that a rapidly increasing turbulence-driven shear flow is generated $\sim$100 microseconds prior to the L-H transition and appears to trigger the transition. Understanding the details of this L-H transition triggering mechanism and the physics behind the power threshold scaling is critical for fusion research, since burning plasmas will require H-mode operation to achieve their performance goals. Using 2D turbulence imaging data acquired with Beam Emission Spectroscopy and applying velocimetry analysis techniques to quantify turbulent flow patterns, a rapid evolution of turbulence and flow shear is observed 1-2 cm inside the separatrix immediately before the L-H transition. Measurements show that in plasmas with injected power just above the L-H power threshold, the inferred turbulent Reynolds stress increases rapidly, as does the poloidal flow shearing rate. The energy transfer rate from turbulence to the flow peaks during this rapid evolution prior to the transition and exceeds the effective turbulence recovery rate. Visualizations of turbulence demonstrate a strong shearing of the turbulent eddies during this final phase. In plasmas with injected power below the L-H power threshold, the measured Reynolds stress, shear flow and energy transfer are lower and the shearing rates are below the decorrelation rate. These observations suggest that increasing power flux leads to increased turbulence, turbulent Reynolds stress, shear flow development and a rapidly increasing poloidal flow that triggers the transition. Similar analysis is applied to measurements at different toroidal fields and densities to help understand the underlying physics behind the empirical L-H transition power threshold.