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

High-performance fusion plasmas, requiring high pressure β, are not well understood in stellarator-type experiments. Here, the effect of β 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.

Threshold Heat-Flux Reduction by Near-Resonant Energy Transfer

Near-resonant energy transfer to large-scale stable modes is shown to reduce transport above the linear critical gradient, contributing to the onset of transport at higher gradients. This is demonstrated for a threshold fluid theory of ion temperature gradient turbulence based on zonal-flow-catalyzed transfer. The heat flux is suppressed above the critical gradient by resonance in the triplet correlation time, a condition enforced by the wave numbers of the interaction of the unstable mode, zonal flow, and stable mode.

Turbulence Mechanisms of Enhanced Performance Stellarator Plasmas

We theoretically assess two mechanisms thought to be responsible for the enhanced performance observed in plasma discharges of the Wendelstein 7-X stellarator experiment fueled by pellet injection. The effects of the ambipolar radial electric field and the electron density peaking on the turbulent ion heat transport are separately evaluated using large-scale gyrokinetic simulations. The essential role of the stellarator magnetic geometry is demonstrated, by comparison with a tokamak.

Direct Measurement of a Toroidally Directed Zonal Flow in a Toroidal Plasma

Zonal flow appears in toroidal, magnetically confined plasmas as part of the self-regulated interaction of turbulence and transport processes. For toroidal plasmas having a strong toroidal magnetic field, the zonal flow is predominately poloidally directed. This Letter reports the first observation of a zonal flow that is toroidally directed. The measurements are made just inside the last closed flux surface of reversed field pinch plasmas that have a dominant poloidal magnetic field. A limit cycle oscillation between the strength of the zonal flow and the amplitude of plasma potential fluctuations is observed, which provides evidence for the self-regulation characteristic of drift-wave-type plasma turbulence. The measurements help advance understanding and gyrokinetic modeling of toroidal plasmas in the pursuit of fusion energy.

Nonlinear Electromagnetic Stabilization of Plasma Microturbulence

The physical causes for the strong stabilizing effect of finite plasma β on ion-temperature-gradient-driven turbulence, which far exceeds quasilinear estimates, are identified from nonlinear gyrokinetic simulations. The primary contribution stems from a resonance of frequencies in the dominant nonlinear interaction between the unstable mode, the stable mode, and zonal flows, which maximizes the triplet correlation time and therefore the energy transfer efficiency. A modification to mixing-length transport estimates is constructed, which reproduces nonlinear heat fluxes throughout the examined β range.

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.

Subdominant modes in zonal-flow-regulated turbulence

From numerical solutions of a gyrokinetic model for ion temperature gradient turbulence it is shown that nonlinear coupling is dominated by three-wave interactions that include spectral components of the zonal flow and damped subdominant modes. Zonal flows dissipate very little energy injected by the instability, but facilitate its transfer from the unstable mode to dissipative subdominant modes, in part due to the small frequency sum of such triplets. Although energy is transferred to higher wave numbers, consistent with shearing, a large fraction is transferred to damped subdominant modes within the instability range. This is a new aspect of regulation of turbulence by zonal flows.

Nonlinear stabilization of tokamak microturbulence by fast ions

Nonlinear electromagnetic stabilization by suprathermal pressure gradients found in specific regimes is shown to be a key factor in reducing tokamak microturbulence, augmenting significantly the thermal pressure electromagnetic stabilization. Based on nonlinear gyrokinetic simulations investigating a set of ion heat transport experiments on the JET tokamak, described by Mantica et al. [Phys. Rev. Lett. 107, 135004 (2011)], this result explains the experimentally observed ion heat flux and stiffness reduction. These findings are expected to improve the extrapolation of advanced tokamak scenarios to reactor relevant regimes.

Extreme heat fluxes in gyrokinetic simulations: a new critical β

A hitherto unexplained feature of electromagnetic simulations of ion temperature gradient turbulence is the apparent failure of the transport levels to saturate for certain parameters; this effect, termed here nonzonal transition, has been referred to as the high-β runaway. The resulting large heat fluxes are shown to be a consequence of reduced zonal flow activity, brought on by magnetic field perturbations shorting out flux surfaces.

Origin of magnetic stochasticity and transport in plasma microturbulence

Nonlinear excitation of linearly stable microtearing modes--with zonal modes acting as a catalyst--is shown to be responsible for the near-ubiquitous magnetic stochasticity and associated electromagnetic electron heat transport in electromagnetic gyrokinetic simulations of plasma microturbulence.

Gyrokinetic microtearing turbulence

The nonlinear dynamics of microtearing modes in standard tokamak plasmas are investigated by means of ab initio gyrokinetic simulations. The saturation levels of the magnetic field fluctuations can be understood in the framework of a balance between (small poloidal wave number) linear drive and small-scale dissipation. The resulting heat transport is dominated by the electron magnetic component, and the transport levels are found to be experimentally relevant. Microtearing modes thus constitute another candidate for explaining turbulent transport in such toroidal systems.

Electrostatic and magnetic transport of energetic ions in turbulent plasmas

Analytical and numerical work is used in tandem to address the problem of turbulent transport of energetic ions in magnetized plasmas. It is shown that orbit averaging is not valid under rather generic conditions, and that perpendicular decorrelation effects lead to a slow 1/E decay of the electrostatic particle diffusivity of beam ions, while the respective magnetic quantity is even independent of the particle energy E.