ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry

This paper presents the current state of the global gyrokinetic code ORB5 as an update of the previous reference [Jolliet et al., Comp. Phys. Commun. 177 409 (2007)]. The ORB5 code solves the electromagnetic Vlasov-Maxwell system of equations using a PIC scheme and also includes collisions and strong flows. The code assumes multiple gyrokinetic ion species at all wavelengths for the polarization density and drift-kinetic electrons. Variants of the physical model can be selected for electrons such as assuming an adiabatic response or a ``hybrid'' model in which passing electrons are assumed adiabatic and trapped electrons are drift-kinetic. A Fourier filter as well as various control variates and noise reduction techniques enable simulations with good signal-to-noise ratios at a limited numerical cost. They are completed with different momentum and zonal flow-conserving heat sources allowing for temperature-gradient and flux-driven simulations. The code, which runs on both CPUs and GPUs, is well benchmarked against other similar codes and analytical predictions, and shows good scalability up to thousands of nodes

Global simulations of tokamak microturbulence: finite-β effects and collisions

In this paper, we present global nonlinear gyrokinetic simulations including finite beta effects and collisions in tokamak geometry. Global electromagnetic simulations using conventional delta-f particle in cell methods are very demanding, with respect to numerical resources, in order to correctly describe the evolution of the non-adiabatic part of the electron distribution function. This difficulty has been overcome using an appropriate adjustable control variate method in the conventional delta-f scheme. Linearized inter-species and like-species collision operators have also been introduced in the model. The inclusion of the collisional dynamics makes it possible to carry out simulations of microturbulence starting from a global neoclassical equilibrium and to study the effect of collisions on the transport induced by electrostatic microinstabilities

Mini-Workshop: Innovative Trends in the Numerical Analysis and Simulation of Kinetic Equations

In multiscale modeling hierarchy, kinetic theory plays a vital role in connecting microscopic Newtonian mechanics and macroscopic continuum mechanics. As computing power grows, numerical simulation of kinetic equations has become possible and undergone rapid development over the past decade. Yet the unique challenges arising in these equations, such as highdimensionality, multiple scales, random inputs, positivity, entropy dissipation, etc., call for new advances of numerical methods. This mini-workshop brought together both senior and junior researchers working on various fastpaced growing numerical aspects of kinetic equations. The topics include, but were not limited to, uncertainty quantification, structure-preserving methods, phase transitions, asymptotic-preserving schemes, and fast methods for kinetic equations

On the definition of a kinetic equilibrium in global gyrokinetic simulations

Nonlinear electrostatic global gyrokinetic simulations of collisionless ion temperature gradient (ITG) turbulence and ExB zonal flows in axisymmetric toroidal plasmas are examined for different choices of the initial distribution function. Using a local Maxwellian leads to the generation of axisymmetric ExB flows that can be so strong as to prevent ITG mode growth. A method using a canonical Maxwellian is shown to avoid this spurious generation of ExB flows. In addition, a revised delta f scheme is introduced and compared to the standard delta f method. (c) 2006 American Institute of Physics

Nonlinear gyrokinetic PIC simulations in stellarators with the code EUTERPE

In this work, the first nonlinear particle-in-cell simulations carried out in a stellarator with the global gyrokinetic code EUTERPE using realistic plasma parameters are reported. Several studies are conducted with the aim of enabling reliable nonlinear simulations in stellarators with this code. First, EUTERPE is benchmarked against ORB5 in both linear and nonlinear settings in a tokamak configuration. Next, the use of noise control and stabilization tools, a Krook-type collision operator, markers weight smoothing and heating sources is investigated. It is studied in detail how these tools influence the linear growth rate of instabilities in both tokamak and stellarator geometries and their influence on the linear zonal flow evolution in a stellarator. Then, it is studied how these tools allow improving the quality of the results in a set of nonlinear simulations of electrostatic turbulence in a stellarator configuration. Finally, these tools are applied to a W7-X magnetic configuration using experimental plasma parameters.Comment: 24 pages, 19 figure

A δf\delta f PIC method with auxiliary Forward-Backward Lagrangian reconstructions

In this note we describe a $\delta f$ particle method where the bulk density is periodically remapped on a coarse spline grid using a Forward-Backward Lagrangian (FBL) approach. We describe the method in the case of an electrostatic PIC scheme and validate its qualitative properties using a classical two-stream instability subject to a uniform oscillating drive

Ionisation effects for laser-plasma interactions by particle-in-cell code

The particle-in-cell code EPOCH was extended to include field and collisional ionisation for use in simulating initially neutral or partially-ionised targets in laser-plasma inter- actions. The means by which particles ionise in the the field of an intense laser was described and physical models were included to determine the instantaneous ionisa- tion rate at particles within the simulation domain for multiphoton, tunnelling, barrier- suppression and electron-impact ionisation. The algorithms used to implement these models were presented and demonstrated to produce the correct ionisation statistics. A scheme allowing for modelling small amounts of ionisation for an arbitrarily low number of superparticles was also presented for comparison and it was shown that for sufficient simulation time the two schemes converge. The three major mechanisms of ionisation in laser-plasma interactions were described as being ionisation-induced defocussing, fast shuttering and ionisation injection. Simulations for these three effects were presented and shown to be in good agreement with theory and experiment. For fast-shuttering, plasma mirrors were simulated using the pulse profile for the Astra Gemini laser at the Central Laser Facility. Rapid switch-on and the theoretical maximum for contrast ratio was observed. For ionisation injection, simulations for laser wakefield acceleration in a helium gas were performed and the accelerated electron population was shown to be greatly increased through use of a 1% nitrogen dopant consistent with the experimental results of McGuffey et al. A study of the laser filamentation instability due to SRS backscatter at the relativistically corrected quarter critical surface (RCQCS) was per- formed in collaboration with C.S. Brady and T.D. Arber at the University of Warwick [1]. It was found that for hydrogen and plastic the instability was unaffected by the in- clusion of ionisation. Further study with argon revealed a attening of the RCQCS and it was demonstrated that for a material with multiple ionisation levels ionising strongly near the self-focussed intensities at the RCQCS, rapid ionisation caused an inversion of the RCQCS that suppressed the filamentation instability