arXiv subjects

M. C. L. Morren

Publications and source records attributed to M. C. L. Morren.

3 recordsLinked to original sources

arXiv2025

Fast electrostatic microinstability evaluation in arbitrary toroidal magnetic geometry using a variational approach

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.

physics.plasm-ph↗

arXiv2025

Resonant theory of kinetic ballooning modes in general toroidal geometry

The linear theory of the kinetic-ballooning-mode (KBM) instability is extended to capture a weakly-driven regime in general toroidal geometry where the destabilization is caused by the magnetic-drift resonance of the ions. Such resonantly-destabilized KBMs are characterized by broad eigenfunctions along the magnetic field line and near-marginal positive growth rates, even well below the beta threshold of their non-resonant counterparts. This unconventional (or sub-threshold) KBM, when destabilized, has been shown to catalyze an enhancement of turbulent transport in the Wendelstein 7-X (W7-X) stellarator [1, 2]. Simplifying the energy dependence of key resonant quantities allows for an analytical treatment of this KBM using the physics-based ordering from the more general equations of Tang, Connor, and Hastie [3]. Results are then compared with high-fidelity gyrokinetic simulations for the (st)KBM in W7-X and the conventional KBM in a circular tokamak at both high and low magnetic shear, where good agreement is obtained in all cases. This reduced KBM model provides deeper insight into (sub-threshold) KBMs and their relationship with geometry, and shows promise for aiding in transport model development and geometry-based turbulence optimization efforts going forward.

physics.plasm-ph↗

arXiv2024

Influence of collisions on trapped-electron modes in tokamaks and low-shear stellarators

The influence of collisions on the growth rate of trapped-electron modes (TEMs) in core plasmas is assessed through both analytical linear gyrokinetics and linear gyrokinetic simulations. Both methods are applied to the magnetic geometry of the DIII-D tokamak, as well as the Helically Symmetric eXperiment (HSX) and Wendelstein 7-X (W7-X) stellarators, in the absence of temperature gradients. Here we analytically investigate the influence of collisions on the TEM eigenmode frequency by a perturbative approach in the response of trapped particles to the mode, using an energy-dependent Krook operator to model collisions. Although the resulting growth rates exceed perturbative thresholds, they reveal important qualitative dependencies: a geometry-dependent stabilization rate occurs for all wavenumbers at high collisionality, while at low collisionality, a geometry-sensitive mixture of collisionless, resonantly driven, and collisionally destabilized modes is found. Additionally, linear gyrokinetic simulations have been performed with a rigorous pitch-angle scattering operator for the same geometries. In the case of DIII-D and large wavenumber modes in HSX, the trends predicted by analytical theory are reproduced. Dissimilarities are, however, obtained in W7-X geometry and for low wavenumber modes in HSX, which are shown to be due to a collision-induced transition to the Universal Instability as the dominant instability at marginal collisionality.

physics.plasm-ph↗