Dimits transition in three-dimensional ion-temperature-gradient turbulence

Abstract

We extend our previous work on the two-dimensional (2-D) Dimits transition in ion-scale turbulence (Ivanov et al., J. Plasma Phys., vol. 86, 2020, 855860502) to include variations along the magnetic field. We consider a three-field fluid model for the perturbations of electrostatic potential, ion temperature, and ion parallel flow in a constant-magnetic-curvature geometry without magnetic shear. It is derived in the cold-ion, long-wavelength asymptotic limit of the gyrokinetic theory. Just as in the 2-D model, a low-transport (Dimits) regime exists and is found to be dominated by a quasistatic staircase-like arrangement of strong zonal flows and zonal temperature. This zonal staircase is formed and maintained by a negative turbulent viscosity for the zonal flows. Unlike the 2-D model, the three-dimensional (3-D) one does not suffer from an unphysical blow up beyond the Dimits threshold where the staircase becomes nonlinearly unstable. Instead, a well-defined finite-amplitude saturated state is established. This qualitative difference between the 2-D and 3-D models is due to the appearance of small-scale ‘parasitic’ modes that exist only if we allow perturbations to vary along the magnetic field lines. These modes extract energy from the large-scale perturbations and provide an effective enhancement of large-scale thermal diffusion, thus aiding the energy transfer from large injection scales to small dissipative ones. We show that in our model, the parasitic modes always favour a zonal-flow-dominated state. In fact, a Dimits state with a zonal staircase is achieved regardless of the strength of the linear drive, provided the system is sufficiently extended along the magnetic field and sufficient parallel resolution is provided.

Gyrokinetic simulations of plasma turbulence in a Z-pinch using a moment-based approach and advanced collision operators

“…under the tertiary KHI instability threshold, transport regimes characterized by bursts rising from the competition between ZF collisional damping and quenching of the primary instability are identified and modelled with a predator-prey cycle by Kobayashi, Gürcan & Diamond (2015). In order to explore the mechanisms behind the ZF formation and damping, Ivanov et al (2020) use a fluid-diffusive collision operator obtained by integration of the linearized Coulomb collision operator and derive a three-field, two-dimensional fluid model directly from the GK equation in a Z-pinch geometry, later extended to three dimensions (Ivanov, Schekochihin & Dorland 2022). This model includes first-order finite Larmor radius (FLR) effects in the long-wavelength, cold-ion limit and allows exploration of the ZF dynamics within an analytical framework.…”

“…In order to explore the mechanisms behind the ZF formation and damping, Ivanov et al. (2020) use a fluid-diffusive collision operator obtained by integration of the linearized Coulomb collision operator and derive a three-field, two-dimensional fluid model directly from the GK equation in a Z-pinch geometry, later extended to three dimensions (Ivanov, Schekochihin & Dorland 2022). This model includes first-order finite Larmor radius (FLR) effects in the long-wavelength, cold-ion limit and allows exploration of the ZF dynamics within an analytical framework.…”

Scale invariance and critical balance in electrostatic drift-kinetic turbulence

“…1991; Newton, Cowley & Loureiro 2010; Ivanov et al. 2020; Ivanov, Schekochihin & Dorland 2022). The ITG and ETG instabilities in tokamaks rely on destabilisation mechanisms that are fundamentally fluid (i.e.…”

An analytical form of the dispersion function for local linear gyrokinetics in a curved magnetic field

“…2020; Adkins et al. 2022; Ivanov, Schekochihin & Dorland 2022) due to the assumption of constant magnetic curvature and lack of magnetic shear, which we have implicitly assumed. Under these assumptions, the system of (2.3), (2.8)–(2.10) is homogeneous in space, allowing us to impose periodic boundary conditions in all three spatial dimensions.…”

“…Newton, Cowley & Loureiro 2010 or the cold-ion fluid model of Ivanov et al. 2022 but with additional terms). Figure 9 shows a comparison between the kinetic and fluid growth rates at a fixed value of and varying .…”