Enhanced Transport at High Plasma Pressure and Subthreshold Kinetic Ballooning Modes in Wendelstein 7-X.

High-performance fusion plasmas, requiring high pressure ß, are not well understood in stellarator-type experiments. Here, the effect of ß on ion-temperature-gradient-driven (ITG) turbulence is studied in Wendelstein 7-X (W7-X), showing that subdominant kinetic ballooning modes (KBMs) are unstable well below the ideal MHD threshold and get strongly excited in the turbulence. By zonal-flow erosion, these subthreshold KBMs (stKBMs) affect ITG saturation and enable higher heat fluxes. Controlling stKBMs will be essential to allow W7-X and future stellarators to achieve maximum performance.

Field-Line Localized Destabilization of Ballooning Modes in Three-Dimensional Tokamaks.

Field-line localized ballooning modes have been observed at the edge of high confinement mode plasmas in ASDEX Upgrade with rotating 3D perturbations induced by an externally applied n=2 error field and during a moderate level of edge localized mode mitigation. The observed ballooning modes are localized to the field lines which experience one of the two zero crossings of the radial flux surface displacement during one rotation period. The localization of the ballooning modes agrees very well with the localization of the largest growth rates from infinite-n ideal ballooning stability calculations using a realistic 3D ideal magnetohydrodynamic equilibrium. This analysis predicts a lower stability with respect to the axisymmetric case. The primary mechanism for the local lower stability is the 3D distortion of the local magnetic shear.

Stellarator Turbulence: Subdominant Eigenmodes and Quasilinear Modeling.

Owing to complex geometry, gyrokinetic simulations in stellarator geometry produce large numbers of subdominant unstable and stable, near-orthogonal eigenmodes. Here, results based on the full eigenmode spectrum in stellarator geometry are presented for the first time. In the nonlinear state of a low-magnetic-shear ion-temperature-gradient-driven case, a multitude of these modes are active and imprint the system. Turbulent frequency spectra are broadband as a consequence, in addition to a nonlinear, narrow signature at electron frequencies. It is shown that successful quasilinear, mixing-length transport modeling is possible in stellarators, where it is essential to account for all subdominant unstable modes.

Pedestal bifurcation and resonant field penetration at the threshold of edge-localized mode suppression in the DIII-D Tokamak.

Rapid bifurcations in the plasma response to slowly varying n=2 magnetic fields are observed as the plasma transitions into and out of edge-localized mode (ELM) suppression. The rapid transition to ELM suppression is characterized by an increase in the toroidal rotation and a reduction in the electron pressure gradient at the top of the pedestal that reduces the perpendicular electron flow there to near zero. These events occur simultaneously with an increase in the inner-wall magnetic response. These observations are consistent with strong resonant field penetration of n=2 fields at the onset of ELM suppression, based on extended MHD simulations using measured plasma profiles. Spontaneous transitions into (and out of) ELM suppression with a static applied n=2 field indicate competing mechanisms of screening and penetration of resonant fields near threshold conditions. Magnetic measurements reveal evidence for the unlocking and rotation of tearinglike structures as the plasma transitions out of ELM suppression.

Measurement of peeling mode edge current profile dynamics.

Peeling modes, an instability mechanism underlying deleterious edge localized mode (ELM) activity in fusion-grade plasmas, are observed at the edge of limited plasmas in a low aspect ratio tokamak under conditions of high edge current density (J(edge) ∼ 0.1 MA/m2) and low magnetic field (B ∼ 0.1 T). They generate edge-localized, electromagnetic activity with low toroidal mode numbers n≤3 and amplitudes that scale strongly with measured J(edge)/B instability drive, consistent with theory. ELM-like field-aligned, current-carrying filaments form from an initial current-hole J(edge) perturbation that detach and propagate outward.

Observation of peak neoclassical toroidal viscous force in the DIII-D tokamak.

Observation of a theoretically predicted peak in the neoclassical toroidal viscosity (NTV) force as a function of toroidal plasma rotation rate Ω is reported. The NTV was generated by applying n=3 magnetic fields from internal coils to low Ω plasmas produced with nearly balanced neutral beam injection. Locally, the peak corresponds to a toroidal rotation rate Ω(0) where the radial electric field E(r) is near zero as determined by radial ion force balance.

Stabilization of the resistive wall mode by a rotating solid conductor.

Stabilization of the resistive wall mode (RWM) by high-speed differentially rotating conducting walls is demonstrated in the laboratory. To observe stabilization intrinsic azimuthal plasma rotation must be braked with error fields. Above a critical error field the RWM frequency discontinuously slows (locks) and fast growth subsequently occurs. Wall rotation is found to reduce the locked RWM saturated amplitude and growth rate, with both static (vacuum vessel) wall locked and slowly rotating RWMs observed depending on the alignment of wall to plasma rotation. At high wall rotation RWM onset is found to occur at larger plasma currents, thus increasing the RWM-stable operation window.

Exponential growth of nonlinear ballooning instability.

Recent ideal magnetohydrodynamic (MHD) theory predicts that a perturbation evolving from a linear ballooning instability will continue to grow exponentially in the intermediate nonlinear phase at the same linear growth rate. This prediction is confirmed in ideal MHD simulations. When the Lagrangian compression, a measure of the ballooning nonlinearity, becomes of the order of unity, the intermediate nonlinear phase is entered, during which the maximum plasma displacement amplitude as well as the total kinetic energy continues to grow exponentially at the rate of the corresponding linear phase.

Instability-enhanced collisional effects and Langmuir's paradox.

Anomalously fast equilibration of the electron distribution function to a Maxwellian in gas-discharge plasmas with low temperature and pressure, i.e., Langmuir's paradox, may be explained by electron scattering via an instability-enhanced collective response and hence fluctuations arising from convective ion-acoustic instabilities near the discharge boundaries.

Instability-enhanced collisional friction can determine the Bohm criterion in multiple-ion-species plasmas.

A generalized Lenard-Balescu theory that accounts for instability-enhanced collective responses is used to calculate the collisional friction between ion species in the plasma-boundary transition region (presheath). Ion-ion streaming instabilities are shown to cause such a strong frictional force that the relative flow speed between ion species cannot significantly exceed the critical threshold value (DeltaV(c)) at which instability onset occurs. When combined with the Bohm criterion, this condition uniquely determines the flow speed of each ion species at the plasma-sheath boundary. For cold ions, DeltaV(c) --> 0 and each ion species leaves the plasma at a common system sound speed c(s).

Observation of resistive and ferritic wall modes in a line-tied pinch.

The resistive wall mode is experimentally identified and characterized in a line-tied, cylindrical screw pinch when the edge safety factor is less than a critical value. Different wall materials have been used to change the wall time and show that the growth rates for the RWM scale with wall time and safety factor as expected by theory. The addition of a ferritic wall material outside the conducting shell leads to growth rates larger than the observed RWM and larger than theoretical predictions for the ferritic wall mode.

Absence of complete finite-Larmor-radius stabilization in extended MHD.

The dominant finite-Larmour-radius (FLR) stabilization effects on interchange instability can be retained by taking into account the ion gyroviscosity or the generalized Ohm's law in an extended MHD model. However, recent simulations and theoretical calculations indicate that complete FLR stabilization of the interchange mode may not be attainable by ion gyroviscosity or the two-fluid effect alone in the framework of extended MHD. For a class of plasma equilibria in certain finite-beta or nonisentropic regimes, the critical wave number for complete FLR stabilization tends toward infinity.

Effect of neoclassical toroidal viscosity on error-field penetration thresholds in tokamak plasmas.

A model for field-error penetration is developed that includes nonresonant as well as the usual resonant field-error effects. The nonresonant components cause a neoclassical toroidal viscous torque that keeps the plasma rotating at a rate comparable to the ion diamagnetic frequency. The new theory is used to examine resonant error-field penetration threshold scaling in Ohmic tokamak plasmas. Compared to previous theoretical results, we find the plasma is less susceptible to error-field penetration and locking, by a factor that depends on the nonresonant error-field amplitude.

Loss of second-ballooning stability in three-dimensional equilibria.

The effect of three-dimensional geometry on the stability boundaries of ideal ballooning modes is investigated. In particular, the relationship between the symmetry properties of the local shear and the magnetic curvature is addressed for quasisymmetric configurations. The presence of symmetry breaking terms in the local shear can produce localized ballooning instabilities in regions of small average magnetic shear which lower first-ballooning stability thresholds and can potentially eliminate the second stability regime.