Ion-gyroradius-scale microinstabilities typically have a frequency comparable to the ion transit frequency. Due to the small electron-to-ion mass ratio and the large electron transit frequency, it is conventionally assumed that passing electrons respond adiabatically in ion-gyroradius-scale modes. However, in gyrokinetic simulations of ion-gyroradius-scale modes in axisymmetric toroidal magnetic fields, the nonadiabatic response of passing electrons can drive the mode, and generate fluctuations with narrow radial layers, which may have consequences for turbulent transport in a variety of circumstances. In flux tube simulations, in the ballooning representation, these instabilities reveal themselves as modes with extended tails. The small electron-to-ion mass ratio limit of linear gyrokinetics for electrostatic instabilities is presented, in axisymmetric toroidal magnetic geometry, including the nonadiabatic response of passing electrons and associated narrow radial layers. This theory reveals the existence of ion-gyroradius-scale modes driven solely by the nonadiabatic passing electron response, and recovers the usual ion-gyroradius-scale modes driven by the response of ions and trapped electrons, where the nonadiabatic response of passing electrons is small. The collisionless and collisional limits of the theory are considered, demonstrating parallels in structure and physical processes to neoclassical transport theory. By examining initial-value simulations of fastest-growing eigenmodes, the predictions for mass-ratio scaling are tested and verified numerically for a range of collision frequencies. Insights from the small electron-to-ion mass ratio theory may lead to a computationally efficient treatment of extended modes.

Multiple space and time scales arise in plasma turbulence in magnetic confinement fusion devices because of the smallness of the square root of the electron-to-ion mass ratio (m e /m i ) 1/2 and the consequent disparity of the ion and electron thermal gyroradii and thermal speeds. Direct simulations of this turbulence that include both ion and electron space-time scales indicate that there can be significant interactions between the two scales. The extreme computational expense and complexity of these direct simulations motivates the desire for reduced treatment. By exploiting the scale separation between ion and electron scales, and expanding the gyrokinetic equations for the turbulence in (m e /m i ) 1/2 , we derive such a reduced system of gyrokinetic equations that describes cross-scale interactions. The coupled gyrokinetic equations contain novel terms which provide candidate mechanisms for the observed cross-scale interaction. The electron scale turbulence experiences a modified drive due to gradients in the ion scale distribution function, and is advected by the ion scale E ×B drift, which varies in the direction parallel to the magnetic field line. The largest possible crossscale term in the ion scale equations is sub-dominant in our (m e /m i ) 1/2 expansion.Hence, in our model the ion scale turbulence evolves independently of the electron scale turbulence. To complete the scale-separated approach, we provide and justify a parallel boundary condition for the coupled gyrokinetic equations in axisymmetric equilibria based on the standard "twist-and-shift" boundary condition. This approach allows one to simulate multi-scale turbulence using electron scale flux tubes nested within an ion scale flux tube.Scale-Separated Turbulence otherwise questionable. Examples may be found in [11][12][13][14][15][16][17]. Nonetheless, it is known that electron scale turbulence can drive experimentally relevant levels of transport in some cases [13]. Electron scale transport has been observed on NSTX [18], and is a candidate for anomalous transport on MAST [14,17].Without directly simulating or observing the full multi-scale turbulence, it is difficult to assess to what extent there are cross scale interactions in the turbulence, and whether or not all scales will contribute significantly to the transport. Unfortunately, studying multi-scale turbulence through direct simulation is made very challenging by the size of (m e /m i ) 1/2 for a realistic deuterium plasma, (m e /m i ) 1/2 ∼ 1/60, which determines the separation of ρ th,e /ρ th,i ∼ (m e /m i ) 1/2 and v th,i /v th,e ∼ (m e /m i ) 1/2 . For example, if one wanted to extend the resolution of a well-resolved ion scale simulation to capture both the a/v th,i and a/v th,e time scales then one must increase the resolution in time by approximately v th,e /v th,i ∼ (m i /m e ) 1/2 . To resolve length scales perpendicular to the magnetic field line comparable to both ρ th,i and ρ th,e one must increase the resolution in both the perpendicular directions by ρ th,i /ρ th,e ∼ ...

In magnetic confinement fusion devices, the ratio of the plasma pressure to the magnetic field energy, β, can become sufficiently large that electromagnetic microinstabilities become unstable, driving turbulence that distorts or reconnects the equilibrium magnetic field. In this paper, a theory is proposed for electromagnetic, electron-driven linear instabilities that have current layers localised to mode-rational surfaces and binormal wavelengths comparable to the ion gyroradius. The model retains axisymmetric toroidal geometry with arbitrary shaping, and consists of orbit-averaged equations for the mode-rational surface layer, with a ballooning space kinetic matching condition for passing electrons. The matching condition connects the current layer to the large scale electromagnetic fluctuations, and is derived in the limit that β is comparable to the square root of the electron-to-ion-mass ratio. Electromagnetic fluctuations only enter through the matching condition, allowing for the identification of an effective β that includes the effects of equilibrium flux surface shaping. The scaling predictions made by the asymptotic theory are tested with comparisons to results from linear simulations of micro-tearing and electrostatic microinstabilities in MAST discharge #6252, showing excellent agreement. In particular, it is demonstrated that the effective β can explain the dependence of the local micro-tearing mode (MTM) growth rate on the ballooning parameter θ0 – possibly providing a route to optimise local flux surfaces for reduced MTM-driven transport.

Nonlinear multiscale gyrokinetic simulations of a Joint European Torus edge pedestal are used to show that electron-temperature-gradient (ETG) turbulence has a rich three-dimensional structure, varying strongly according to the local magnetic-field configuration. In the plane normal to the magnetic field, the steep pedestal electron temperature gradient gives rise to anisotropic turbulence with a radial (normal) wavelength much shorter than in the binormal direction. In the parallel direction, the location and parallel extent of the turbulence are determined by the variation in the magnetic drifts and finite-Larmor-radius (FLR) effects. The magnetic drift and FLR topographies have a perpendicular-wavelength dependence, which permits turbulence intensity maxima near the flux-surface top and bottom at longer binormal scales, but constrains turbulence to the outboard midplane at shorter electron-gyroradius binormal scales. Our simulations show that long-wavelength ETG turbulence does not transport heat efficiently, and significantly decreases overall ETG transport -- in our case by $\sim$40 \% -- through multiscale interactions.

Magnetised plasma turbulence can have a multiscale character: instabilities driven by mean temperature gradients drive turbulence at the disparate scales of the ion and the electron gyroradii. Simulations of multiscale turbulence, using equations valid in the limit of infinite scale separation, reveal novel cross-scale interaction mechanisms in these plasmas. In the case that both long-wavelength (ion-gyroradius-scale) and short-wavelength (electron-gyroradius-scale) linear instabilities are driven far from marginal stability, we show that the short-wavelength instabilities are suppressed by interactions with long-wavelength turbulence. Two novel effects contributed to the suppression: parallel-to-the-field-line shearing by the long-wavelength ${{\boldsymbol {E}} \times \boldsymbol {B}}$ flows, and the modification of the background density gradient by the piece of the long-wavelength electron adiabatic response with parallel-to-the-field-line variation. In contrast, simulations of multiscale turbulence where instabilities at both scales are driven near marginal stability demonstrate that when the long-wavelength turbulence is sufficiently collisional and zonally dominated the effect of cross-scale interaction can be parameterised solely in terms of the local modifications to the mean density and temperature gradients. We discuss physical arguments that qualitatively explain how a change in equilibrium drive leads to the observed transition in the impact of the cross-scale interactions.