arXiv subjects

Stephan Brunner

Publications and source records attributed to Stephan Brunner.

32 records · Page 2Linked to original sources

arXiv2023

Verification of the Fourier-enhanced 3D finite element Poisson solver of the gyrokinetic full-f code PICLS

We introduce and derive the Fourier-enhanced 3D electrostatic field solver of the gyrokinetic full-f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily parallelizable and thus save run time. The presented solver is then verified using two different approaches of manufactured solutions. The test setup used for this effort is a pinch geometry with ITG-like electric potential, containing one non-periodic and two periodic directions, one of which will be discrete Fourier transformed. The results of these tests show that in all three dimensions the L2-error decreases with a constant rate close to the ideal prediction, depending on the degree of the chosen basis functions.

physics.plasm-ph↗

arXiv2022

Local gyrokinetic simulations of tokamaks with non-uniform magnetic shear

In this work, we modify the standard flux tube simulation domain to include arbitrary ion gyroradius-scale variation in the radial profile of the safety factor. To determine how to appropriately include such a modification, we add a strong ion gyroradius-scale source (inspired by electron cyclotron current drive) to the Fokker-Planck equation, then perform a multi-scale analysis that distinguishes the fast electrons driven by the source from the slow bulk thermal electrons. This allows us to systematically derive the needed changes to the gyrokinetic model. We find new terms that adjust the ion and electron parallel streaming to be along the modified field lines. These terms have been successfully implemented in a gyrokinetic code (while retaining the typical Fourier representation), which enables flux tube studies of non-monotonic safety factor profiles and the associated profile shearing. As an illustrative example, we investigate tokamaks with positive versus negative triangularity plasma shaping and find that the importance of profile shearing is not significantly affected by the change in shape.

physics.plasm-ph↗

arXiv2022

Gyrokinetic simulations of turbulence and zonal flows driven by steep profile gradients using a delta-f approach with an evolving background Maxwellian

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.

physics.plasm-ph↗

arXiv2021

A non-twisting flux tube for local gyrokinetic simulations

Local gyrokinetic simulations use a field-aligned domain that twists due to the magnetic shear of the background magnetic equilibrium. However, if the magnetic shear is strong and/or the domain is long, the twist can become so extreme that it fails to properly resolve the turbulence. In this work, we derive and implement the "non-twisting flux tube," a local simulation domain that remains rectangular at all parallel locations. Convergence and runtime tests indicate that it can calculate the heat flux more efficiently than the conventional flux tube. For one test case, it was 30 times less computationally expensive and we found no case for which it was more expensive. It is most advantageous when the magnetic shear is high and the domain includes at least two regions of turbulent drive (e.g. stellarator simulations, pedestal simulations, tokamak simulations with several poloidal turns). Additionally, it more accurately models the inboard midplane when the magnetic shear is large. Lastly, we show how the non-twisting flux tube can be generalized to allow further optimization and control of the simulation domain.

physics.plasm-ph↗

arXiv2021

Effect of collisions on non-adiabatic electron dynamics in ITG-driven microturbulence

Non-adiabatic electron response leads to significant changes in Ion Temperature Gradient (ITG) eigenmodes, leading in particular to fine-structures that are significantly extended along the magnetic field lines at corresponding Mode Rational Surfaces (MRSs). These eigenmodes can nonlinearly interact with themselves to drive zonal flows via the so-called self-interaction mechanism. In this paper, the effect of collisions on these processes are studied. In presence of non-adiabatic electrons, the linear growth rate of ITG eigenmodes decreases with increasing collisionality. Detailed velocity space analysis of the distribution function shows that this results from collisions leading to a more adiabatic-like response of electrons away from MRSs. In linear simulations, collisions are furthermore found to broaden the radial width of the fine-structures, which translates to narrower tails of the eigenmode in extended ballooning space. The characteristic parallel scale length associated to these tails is shown to scale with the mean free path of electrons. In nonlinear turbulence simulations accounting for physically relevant values of collisionality, the fine structures located at MRSs, together with the associated drive of zonal flows via self-interaction, are shown to persist and play a significant role.

physics.plasm-ph↗

arXiv2020

How eigenmode self-interaction affects zonal flows and convergence of tokamak core turbulence with toroidal system size

Self-interaction is the process by which a microturbulence eigenmode that is extended along the direction parallel to the magnetic field interacts with itself non-linearly. This effect is particularly significant in gyrokinetic simulations accounting for kinetic passing electron dynamics. Self-interaction is known to generate stationary $E\times B$ zonal flow shear layers at radial locations near low order mode rational surfaces [Weikl et. al., Phys. Plasmas 25, 072305 (2018)]. We find however that it also plays a significant role in generating fluctuating zonal flows, which is critical to regulating transport throughout the radial extent. Unlike the usual picture of zonal flow drive where microturbulence eigenmodes coherently amplify the flow, the self-interaction drive of zonal flows from these eigenmodes are uncorrelated with each other. It is shown that the associated shearing rate of the fluctuating zonal flows therefore reduces as more toroidal modes are resolved in the simulation. In flux-tube simulations accounting for the full toroidal domain, such an increase in the density of toroidal modes corresponds to an increase in the system size, leading to a finite system size effect that is distinct from the well-known profile shearing effect.

physics.plasm-ph↗

arXiv2020

Eliminating turbulent self-interaction through the parallel boundary condition in local gyrokinetic simulations

In this work, we highlight an issue that may reduce the accuracy of many local nonlinear gyrokinetic simulations - turbulent self-interaction through the parallel boundary condition. Given a sufficiently long parallel correlation length, individual turbulent eddies can span the full domain and "bite their own tails," thereby altering their statistical properties. Such self-interaction is only modeled accurately when the simulation domain corresponds to a full flux surface, otherwise it is artificially strong. For Cyclone Base Case parameters and typical domain sizes, we find that this mechanism modifies the heat flux by roughly 40% and it can be even more important. The effect is largest when using kinetic electrons, low magnetic shear, and strong turbulence drive (i.e. steep background gradients). It is found that parallel self-interaction can be eliminated by increasing the parallel length and/or the binormal width of the simulation domain until convergence is achieved.

physics.plasm-ph↗

arXiv2020

Gyrokinetic Simulations on Many- and Multi-core Architectures with the Global Electromagnetic Particle-In-Cell Code ORB5

Gyrokinetic codes in plasma physics need outstanding computational resources to solve increasingly complex problems, requiring the effective exploitation of cutting-edge HPC architectures. This paper focuses on the enabling of ORB5, a state-of-the-art, first-principles-based gyrokinetic code, on modern parallel hybrid multi-core, multi-GPU systems. ORB5 is a Lagrangian, Particle-In-Cell (PIC), finite element, global, electromagnetic code, originally implementing distributed parallelism through MPI-based on domain decomposition and domain cloning. In order to support multi/many cores devices, the code has been completely refactored. Data structures have been re-designed to ensure efficient memory access, enhancing data locality. Multi-threading has been introduced through OpenMP on the CPU and adopting OpenACC to support GPU acceleration. MPI can still be used in combination with the two approaches. The performance results obtained using the full production ORB5 code on the Summit system at ORNL, on Piz Daint at CSCS and on the Marconi system at CINECA are presented, showing the effectiveness and performance portability of the adopted solutions: the same source code version was used to produce all results on all architectures.

physics.comp-ph↗

arXiv2019

Collisional gyrokinetic full-f particle-in-cell simulations on open field lines with PICLS

Applying gyrokinetic simulations for theoretical turbulence and transport studies to the plasma edge and scrape-off layer (SOL) presents significant challenges. To in particular account for steep density and temperature gradients in the SOL, the "full-f" code PICLS was developed. PICLS is a gyrokinetic particle-in-cell (PIC) code and is based on an electrostatic model with a linearized field equation and uses kinetic electrons. In previously published results we were applying PICLS to the well-studied 1D parallel transport problem during an edge-localized mode (ELM) in the SOL without collisions. As an extension to this collision-less case and in preparation for 3D simulations, in this work a collisional model will be introduced. The implemented Lenard-Bernstein collision operator and its Langevin discretization will be shown. Conservation properties of the collision operator as well as a comparison of the collisional and non-collisional case will be discussed.

physics.plasm-ph↗

arXiv2019

The effect of background flow shear on gyrokinetic turbulence in the cold ion limit

The cold ion limit of the local gyrokinetic model is rigorously taken to produce a nonlinear system of fluid equations that includes background flow shear. No fluid closure is required. By considering a simple slab geometry with magnetic drifts, but no magnetic shear, these fluid equations reduce to the Charney-Hasegawa-Mima model in the presence of flow shear. Analytic solutions to this model are found to study the impact of ExB flow shear on the stability of a single Parallel Velocity Gradient (PVG) driven mode. Additionally, the model is used to investigate the effect of background ExB flow shear on the basic three-mode nonlinear coupling, which reveals differences between zonal and non-zonal modes. These analytic results agree with gyrokinetic simulations and can serve to benchmark the numerical implementation of flow shear and nonlinear coupling.

physics.plasm-ph↗

arXiv2019

First principles gyrokinetic analysis of electromagnetic plasma instabilities

A two-fold analysis of electromagnetic core tokamak instabilities in the framework of the gyrokinetic theory is presented. First principle theoretical foundations of the gyrokinetic theory are used to explain and justify the numerical results obtained with the global electromagnetic particle-in-cell code Orb5 whose model is derived from the Lagrangian formalism. The energy conservation law corresponding to the Orb5 model is derived from the Noether theorem and implemented in the code as a diagnostics for energy balance and conservation verification. An additional Noether theorem based diagnostics is implemented in order to analyse destabilising mechanisms for the electrostatic and the electromagnetic Ion Temperature Gradient (ITG) instabilities in the core region of the tokamak. The transition towards the Kinetic Ballooning Modes (KBM) at high electromagnetic $β$ is also investigated.

physics.plasm-ph↗

arXiv2018

Pullback scheme implementation in ORB5

The pullback scheme is implemented in the global gyrokinetic particle-in-cell code ORB5 [S. Jolliet et al, Comp. Phys. Comm., 177, 409 (2007)] to mitigate the cancellation problem in electromagnetic simulations. The equations and the discretisation used by the code are described. Numerical simulations of the Toroidal Alfven Eigenmodes are performed in linear and nonlinear regimes to verify the scheme. A considerable improvement in the code efficiency is observed. For the internal kink mode, it is shown that the pullback mitigation efficiently cures a numerical instability which would make the simulation more costly otherwise.

physics.plasm-ph↗

arXiv2012

Locality properties of the free energy fluxes in gyrokinetic turbulence

The nature of the nonlinear interactions in gyrokinetic (GK) turbulence, driven by an ion-temperature gradient instability, is investigated using numerical simulations of single ion species plasma in three-dimensional flux tube geometry. To account for the level of separation existing between scales involved in an energetic interaction, the degree of locality of the free energy scale flux is analyzed employing Kraichnan's infrared (IR) and ultraviolet locality functions. Due to the nontrivial dissipative nature of GK turbulence, an asymptotic level for the locality exponents, indicative of a universal dynamical regime for GK's, is not recovered and an accentuated non-local behavior of the IR interactions is found instead, in spite of the local energy cascade observed.

physics.plasm-ph↗

arXiv2004

Method for Computing Protein Binding Affinity

A Monte Carlo method is given to compute the binding affinity of a ligand to a protein. The method involves extending configuration space by a discrete variable indicating whether the ligand is bound to the protein and a special Monte Carlo move which allows transitions between the unbound and bound states. Provided that an accurate protein structure is given, that the protein-ligand binding site is known, and that an accurate chemical force field together with a continuum solvation model is used, this method provides a quantitative estimate of the free energy of binding.

cond-mat.stat-mech↗