Considerations of ion‐temperature‐gradient‐driven turbulence

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.

Theory of coupled resistive drift and resistive drift ballooning instabilities in fusion plasma

Drift wave instabilities (DWI) associated with the two-fluid dynamics seems to be responsible for anomalous transport in modern day tokamaks. Ballooning instabilities tend to exchange flux tubes of different pressure, resulting in convective transport. The micro-level turbulence (drift wave) is coupled with the macro-level (ballooning mode) dynamics in fusion experiments. The co-existence of DWI and drift ballooning instabilities (DBI) is discussed in this work using a four-field plasma model. The formulation preserves both the microscopic and macroscopic dynamics of plasma. To demonstrate the coupling, a new dispersion relation is derived to analyze stability of the coupled modes in a non-uniform magnetized plasma. Linear stability of coupled drift-ballooning and drift-acoustic modes have been explored. The two-fluid effect (micro-level influence) through diamagnetic drift frequency for electrons and curvature drift frequency on unstable modes are demonstrated.

Stellarators Resist Turbulent Transport on the Electron Larmor Scale

Electron temperature gradient (ETG)-driven turbulence, despite its ultrafine scale, is thought to drive significant thermal losses in magnetic fusion devices-but what role does it play in stellarators? The first numerical simulations of ETG turbulence for the Wendelstein 7-X stellarator, together with power balance analysis from its initial experimental operation phase, suggest that the associated transport should be negligible compared to other channels. The effect, we argue, originates essentially from the geometric constraint of multiple field periods, a generic feature of stellarators.

Distinct Turbulence Saturation Regimes in Stellarators

In the complex 3D magnetic fields of stellarators, ion-temperature-gradient turbulence is shown to have two distinct saturation regimes, as revealed by petascale numerical simulations and explained by a simple turbulence theory. The first regime is marked by strong zonal flows and matches previous observations in tokamaks. The newly observed second regime, in contrast, exhibits small-scale quasi-two-dimensional turbulence, negligible zonal flows, and, surprisingly, a weaker heat flux scaling. Our findings suggest that key details of the magnetic geometry control turbulence in stellarators.

Experimental signatures of critically balanced turbulence in MAST

Beam emission spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field, and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as ν(*i)(-0.8 ± 0.1), where ν(*i) = ion  collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding those of the drift waves by ∼ ν(*i)(-0.8).

Critically balanced ion temperature gradient turbulence in fusion plasmas

Scaling laws for ion temperature gradient driven turbulence in magnetized toroidal plasmas are derived and compared with direct numerical simulations. Predicted dependences of turbulence fluctuation amplitudes, spatial scales, and resulting heat fluxes on temperature gradient and magnetic field line pitch are found to agree with numerical results in both the driving and inertial ranges. Evidence is provided to support the critical balance conjecture that parallel streaming and nonlinear perpendicular decorrelation times are comparable at all spatial scales, leading to a scaling relationship between parallel and perpendicular spatial scales. This indicates that even strongly magnetized plasma turbulence is intrinsically three dimensional.

Dimits shift in realistic gyrokinetic plasma-turbulence simulations

In simulations of turbulent plasma transport due to long wavelength (k perpendicular rhoi < or = 1) electrostatic drift-type instabilities, we find a persistent nonlinear up-shift of the effective threshold. Next-generation tokamaks will likely benefit from the higher effective threshold for turbulent transport, and transport models should incorporate suitable corrections to linear thresholds. The gyrokinetic simulations reported here are more realistic than previous reports of a Dimits shift because they include nonadiabatic electron dynamics, strong collisional damping of zonal flows, and finite electron and ion collisionality together with realistic shaped magnetic geometry. Reversing previously reported results based on idealized adiabatic electrons, we find that increasing collisionality reduces the heat flux because collisionality reduces the nonadiabatic electron microinstability drive.

Prediction of significant tokamak turbulence at electron gyroradius scales

The experimental conditions under which tokamak turbulence at hyperfine (electron gyroradius) scales is predicted to be significant and observable are described. The first quantitative predictions of fluctuation amplitudes, spectral features, and the associated electron energy transport are presented. A novel theoretical model which quantitatively describes the boundaries of the high-amplitude streamer transport regime is presented and shown to explain the gyrokinetic simulation results. This model uniquely includes consideration of two distinct secondary instabilities.

Electron temperature gradient turbulence

The first toroidal, gyrokinetic, electromagnetic simulations of small scale plasma turbulence are presented. The turbulence considered is driven by gradients in the electron temperature. It is found that electron temperature gradient (ETG) turbulence can induce experimentally relevant thermal losses in magnetic confinement fusion devices. For typical tokamak parameters, the transport is essentially electrostatic in character. The simulation results are qualitatively consistent with a model that balances linear and secondary mode growth rates. Significant streamer-dominated transport at long wavelengths occurs because the secondary modes that produce saturation become weak in the ETG limit.

Magnetic reconnection in toroidal eta(i) mode turbulence

Based on three-dimensional simulations of the Braginskii equations we show that for typical plasma-edge parameters the saturation of electromagnetic toroidal eta(i) mode turbulence is controlled by the self-generation and subsequent annihilation of radial magnetic field perturbations. This should be contrasted with the electrostatic limit, where the growth of the linear eta(i) mode is terminated by the onset of sheared flow modes driven by the radial plasma streams. The impact of the saturation amplitude on the transport level is substantial and is not in accord with simple mixing length arguments, suggesting that electromagnetic effects should generally be included in simulations of eta(i) mode turbulence.