M. J. Pueschel

Small-scale turbulence originating from microinstabilities limits the energy confinement time in magnetic confinement fusion. Here we develop a semi-analytical dispersion relation based on lowest-order solutions to the gyrokinetic equations in an asymptotic expansion in the ratio of transit (bounce) frequency to the mode frequency for ions (electrons), capable of describing two common instabilities: the ion temperature gradient (ITG) mode and trapped-electron mode (TEM), in the electrostatic limit. The dispersion relation, which is valid in arbitrary toroidal geometry, takes into account resonances with the magnetic ion and bounce-averaged electron drifts, incorporates non-local effects along the magnetic field line, is valid for arbitrary sign of the growth rate and magnetic curvature, and is shown to satisfy a variational property. Several common approximation models are introduced for both the magnetic drift and finite Larmor radius (FLR) damping, with the Padé approximation for FLR effect in particular resulting in remarkable agreement with the baseline dispersion relation model at significantly reduced costs. The baseline model is verified by comparing solutions of the dispersion relation model to high-fidelity linear gyrokinetic simulations, where the exact eigenfunction of the electrostatic potential from simulations is used as a trial function, showing good quantitative agreement for ITGs and TEMs in (shaped) tokamaks as well as low-magnetic-shear stellarators.

Linear instability characterization of seven JET discharges just prior to the L-H transition is performed at $ρ_{\text{tor}} \in [0.85,0.9,0.95]$ with the gyrokinetic GENE code. The discharges cover both the low- and high-density branches of the L-H transition at two different triangularities. Sensitivities to driving gradients, normalized electron collisonality $ν_e^*$, hydrogen isotope mass, magnetic geometry and finite-$β$ effects are all characterized. At $ρ_{\text{tor}}=0.85$ and $0.9$, trapped-electron modes (TEMs) propagating in both the electron- or ion-drift direction are observed at the lowest densities. At higher density ion-temperature-gradient (ITG) modes are dominant, some of which exhibit trapped-ion drive and unconventional ballooning structures. At $ρ_{\text{tor}}=0.95$, the low-density cases are similar to inner radii, while at higher densities subdominant modes are destabilized by higher collisionalities. The electron collisonality $ν_e^*$ is scanned around the experimental values at all three radii and for the seven discharges studied. The experimental collisionality range corresponds to a region of minimum linear drive between ITG-TEM mode branches at lower collisionalities and resistive mode branches at higher collisionalities. Moreover, the quasilinear particle flux is directed inward only in the collisionality domain where the linear drive is minimized at $ρ_{\text{tor}}=0.85$ for all densities and $0.9$ only for the highest densities. Model fidelity reduction is performed on the GENE simulations to evaluate the impact of various assumptions and simplifications made by the state-of-the-art quasilinear models QuaLiKiz and TGLF. QuaLiKiz is found to be inadequate beyond $ρ_{\text{tor}}=0.85$, while TGLF-SAT2 agrees well with linear spectra and the quasilinear heat fluxes from GENE up to and including $ρ_{\text{tor}}=0.9$.