Moahan Murugappan

In this work, we explore the effects of collisions on turbulent transport, focusing on two different TCV magnetic equilibria featuring positive and negative triangularity. The investigation is conducted using gyrokinetic modeling. Both gradient-driven and flux-driven approaches are employed using the global code ORB5, and a comparison with GENE flux-tube modeling is also carried out. Linear and nonlinear simulations show that negative triangularity retains its beneficial effect on turbulent transport in both collisionless and collisional regimes. However, flux tube and global nonlinear simulations show contrasting trends on the impact of collisions on ion transport. Flux-driven simulations confirm that edge stiffness is significantly reduced in negative compared to positive triangularity, and a spontaneous pedestal-like logarithmic gradient develops for negative triangularity in the collisionless setup. However, without proper realistic profiles and physical boundary conditions, it is not possible to fully replicate the experimental differences observed in the temperature profiles between positive and negative triangularity. A collisionality scan reveals that the ion and electron transport coefficients do not change monotonically with collisionality, stressing how deep the interplay is between turbulent features and collisions. The general picture of collisions stabilizing TEM and damping zonal flows is confirmed, but it is shown that the effects on transport cannot be predicted without a numerical assessment.

Internal transport barriers (ITB) form through turbulence suppression, often observed when the safety factor profile exhibits an off-axis minimum. This work aims at improving our understanding of the conditions enabling the development of an ITB, using a more comprehensive physical model, including low-β electromagnetic flux-driven simulations. Our key findings are that electron dynamics is crucial for ITB formation even in an ITG scenario and that having q _min close to a lowest order rational value (2 in our simulations) to allow for eddies self-interaction is a necessary ingredient. Electron dynamics has two critical effects. First, it leads to a structure formation characterized by strong zonal flows shearing rate, quench of turbulence (i.e. reduction of transport coefficients and fluctuation correlation) and profile corrugation. Second, it leads to zonal current sheets that result in a broadening of the minimum-q region, qualitatively consistent with the flux-tube simulations of Volčokas et al (2024 arXiv:2412.01913). Flux-driven simulations performed with q min = 2 reveal the development of the transport barrier in the ion channel, forming at inner and outer radial positions with respect to the q _min position. The ITB formation in flux-driven setup is not recovered if q min = 2.03 . Additionally, a simulation at higher ρ ∗ indicates that the extent of the flattened region of the q-profile due to turbulent self-interaction does not change proportionally to ρ ∗ or to ρ _i , but somewhere in between. On the other hand, the input power required to achieve similar on-axis temperatures appears to exhibit almost gyro-Bohm scaling (for the two considered ρ ∗ values). Furthermore, considering an initial q-profile with q min = 2.01 , flux-driven simulations show that partial self-interaction can evolve to complete self-interaction. This occurs due to turbulent-driven zonal currents that lower and flatten the q-profile down to q min = 2.0 , in line with what is reported in Volčokas et al (2024 arXiv:2412.01913).

In the context of global gyrokinetic simulations of turbulence using a particle-in-cell framework, verifying the delta-f assumption with a fixed background distribution becomes challenging when determining quasi-steady state profiles corresponding to given sources over long time scales, where plasma profiles can evolve significantly. The advantage of low relative sampling noise afforded by the delta-f scheme is shown to be retained by considering the background as a time-evolving Maxwellian with time-dependent density and temperature profiles. Implementation of this adaptive scheme to simulate electrostatic collisionless flux-driven turbulence in tokamak plasmas show small and nonincreasing sampling noise levels, which would otherwise increase indefinitely with a stationary background scheme. The adaptive scheme furthermore allows one to reach numerically converged results of quasi-steady state with much lower marker numbers.

In this work, we explore the triangularity effects on turbulent transport employing global gyrokinetic simulations performed with the ORB5 code. Numerous experiments on the Tokamak á Configuration Variable (TCV) and, more recently, on the DIII-D machine, have demonstrated superior confinement properties in L-mode of negative triangularity (NT) over positive triangularity (PT) configuration. This presents a particularly attractive scenario, as L-mode operation eliminates or significantly mitigates the presence of hazardous edge-localized modes (ELMs). However, a full theoretical understanding of all these observations remains elusive. Specifically, questions remain about how NT improvements can extend to the core where triangularity is very small, and whether these improvements can scale to larger devices. This paper addresses these two questions. Our analysis is divided into two parts: we first demonstrate that the confinement enhancement in NT configurations arises from the interdependent edge-core dynamics, and then we present the results of a system size scan. Crucially, we find that the relative turbulent transport reduction of NT over PT appears not to be contingent on machine dimensions or fluctuation scales and is moreover robust with respect to variations in plasma profiles. This insight underscores the fundamental nature of the NT confinement advantage and paves the way for its potential application in future fusion devices, regardless of their size.

Long global gyrokinetic turbulence simulations are particularly challenging in situations where the system deviates strongly from its initial state and when fluctuation levels are high, for example, in strong gradient regions. For particle-in-cell simulations, statistical sampling noise accumulation from large marker weights due to large deviations from the control variate of a delta-f scheme makes such simulations often impractical. An adaptive control variate in the form of a flux-surface-averaged Maxwellian with a time-dependent temperature profile is introduced in an attempt to alleviate the former problem. Under simplified collisionless physics, this adaptive delta-f scheme is shown to reduce noise accumulation in the zonal flows and the simulated heat flux in a quasi-steady turbulent state. The method also avoids the collapse of the signal-to-noise ratio, which occurs in the standard non-adaptive scheme, and, therefore, allows one to reach numerically converged results even with lower marker numbers.

Long global gyrokinetic turbulence simulations are particularly challenging in situations where the system deviates strongly from its initial state and when fluctuation level are high e.g. in strong gradient regions. For Particle-in-Cell simulations, statistical sampling noise accumulation from large marker weights due to large deviations from the control variate of a delta-f scheme make such simulations often impractical. An adaptive control variate in the form of a flux-surface-averaged Maxwellian with a time-dependent temperature profile is introduced in an attempt to alleviate the former problem. Under simplified collisionless physics, this adaptive delta-f scheme is shown to reduce noise accumulation in the zonal flows and the simulated heat flux in a quasi-steady turbulent state. The method also avoids the collapse of the signal-to-noise ratio which occurs in the standard non-adaptive scheme, and therefore, allows one to reach numerically converged results even with lower marker numbers.

The gyrokinetic delta-f particle-in-cell (PIC) approach is known to be successful for simulating turbulence in the core of magnetic fusion plasmas, where fluctuations are relatively small and therefore the unperturbed particle distribution function, usually represented by a stationary Maxwellian f ₀, remains a good choice of a control variate for reducing statistical sampling noise. However, towards the plasma edge, characterized by low density and temperature and strong gradients, relative deviation amplitudes typically become large, so that the essential assumption of |δf/f ₀| << 1 underlying the delta-f PIC approach will not be valid, where δf is the fluctuating part of distribution. This motivates the study of the limits of the delta-f approach in a simplified system mimicking the plasma edge. To this end, simulations are run using GK-engine, which is a delta-f PIC code that solves the nonlinear gyrokinetic equation in a sheared slab geometry, using B-spline finite elements to represent the self-consistent electrostatic field. Initial radial density and ion temperature profiles exhibiting high logarithmic gradients representing plasma edge conditions are used. In order to avoid practical problems of particles exiting the simulation domain as the ion temperature profile relaxes, all profiles are mirrored at domain-centre and periodic boundary conditions are imposed. The validity of the delta-f approach is measured by statistical noise estimates, while monitoring relative deviation levels of temperature via the kinetic energy. In particular, the effect of background profile gradients on these measures is investigated. As a first step towards reducing the amplitude of the deviation δf, an adaptive Maxwellian f ₀ is implemented, whose time dependent temperature profiles are obtained by locally relaxing kinetic energy accumulating in δf into f ₀.