Coupled ion temperature gradient and trapped electron mode to electron temperature gradient mode gyrokinetic simulations

Abstract

Electron temperature gradient (ETG) transport is conventionally defined as the electron energy transport at high wave number (high-k) where ions are adiabatic and there can be no ion energy or plasma transport. Previous gyrokinetic simulations have assumed adiabatic ions (ETG-ai) and work on the small electron gyroradius scale. However such ETG-ai simulations with trapped electrons often do not have well behaved nonlinear saturation unless fully kinetic ions (ki) and proper ion scale zonal flow modes are included. Electron energy transport is separated into ETG-ki at high-k and ion temperature gradient-trapped electron mode (ITG/TEM) at low-k. Expensive (more computer-intensive), high-resolution, large-ion-scale flux-tube simulations coupling ITG/TEM and ETG-ki turbulence are presented. These require a high effective Reynolds number R≡[k(max)∕k(min)]2=μ2, where μ=[ρsi∕ρsi] is the ratio of ion to electron gyroradii. Compute times scale faster than μ3. By comparing the coupled expensive simulations with (1) much cheaper (less compute-intensive), uncoupled, high-resolution, small, flux-tube ETG-ki and with (2) uncoupled low-resolution, large, flux-tube ITG/TEM simulations, and also by artificially turning “off” the low-k or high-k drives, it appears that ITG/TEM and ETG-ki transport are not strongly coupled so long as ETG-ki can access some nonadiabatic ion scale zonal flows and both high-k and low-k are linearly unstable. However expensive coupled simulations are required for physically accurate k-spectra of the transport and turbulence. Simulations with μ⩾30 appear to represent the physical range μ>40. ETG-ki transport measured in ion gyro-Bohm units is weakly dependent on μ. For the mid-radius core tokamak plasma parameters studied, ETG-ki is about 10% of the electron energy transport, which in turn is about 30% of the total energy transport (with negligible E×B shear). However at large E×B shear sufficient to quench the low-k ITG/TEM transport, the high-k tail of the ETG-ki transport survives. Decreasing the trapping to minimize the TEM opens a stability gap between ITG and ETG. High-k ETG transport driven by low-k ITG instability in an ETG linearly stable plasma is demonstrated.

Parallel filtering in global gyrokinetic simulations

“…It peaks at around within this range. This is fortunately the case as nonlinear couplings trigger an energy cascade towards longer wavelengths [39]. In the previous section, it was demonstrated that the filtering procedure did not affect the fluxes.…”

Characterizing turbulent transport in ASDEX Upgrade L-mode plasmas via nonlinear gyrokinetic simulations

“…In reality, however, turbulence at larger scales (neglected here) would generate a fluctuating background, which may act in a stabilizing way on the smaller ETG structures and thus limit their radial extent. 52,71,72 In order to model this stabilizing effect, we add a weakly sheared background flow, as discussed already in Sec. III C, where MTMs caused saturation problems for the case D simulations.…”

Validation metrics for turbulent plasma transport

“…To address this question, one would extend the validation methodology discussed so far to calculation of a local sensitivity map in which both R=L Ti and R=L Te are varied, from which a fluxmatching fractional gradient error vectorẼ z ¼ ðE LT i ; E LT e Þ could be calculated by determining the simultaneous values of R=L Ti and R=L Te which when input into the microturbulence model yield predictions of Q i and Q e that simultaneously match the power balance Q i and Q e results. While the computational resources needed to perform such an analysis using long-wavelength gyrokinetic simulations (to say, nothing of multiscale simulations which incorporate electron-scale ETG dynamics that likely contribute to Q e in many cases [65][66][67][68][140][141][142][143][144][145][146] ) over many conditions or discharges remain prohibitive for current-day computing platforms, such approaches will likely be feasible on next-generation exascale platforms. Moreover, such an approach, or even further generalizations to include matching of particle and momentum fluxes via additional variations of density and rotation gradients, is readily feasible now for most reduced turbulent transport models with fairly modest computing resources, and should be pursued further.…”

“…A third, even more computationally expensive avenue of approach would be to investigate the impact of multiscale simulations which self-consistently incorporate q e -scale ETG fluctuations into these q i -scale simulations. [65][66][67][68][140][141][142][143][144][145][146] Other research avenues are possible as well. However, for the goals of this paper, it should be clear how utilizing a variety of local validation metrics for multiple predicted quantities can be employed to test model fidelity and our physical understanding at a level not possible by earlier global metrics.…”