Session NO3: Simulation and Modeling

Simulation of plasma effects on rf power transport in vacuum waveguides

Researchers use rf power to heat tokamak plasmas and excite cavities for particle accelerators among other applications. Unwanted plasma can limit the power one can transmit from a source (such as a klystron) to the target (such as the tokamak plasma or the accelerating cavity). Researchers believe some possible sources for this plasma are ionization of residual gas or sputtering of material from the waveguide surface. We use computer simulation to model the effects of this plasma on the rf power transmission in a typical rf waveguide. In particular, we estimate using a coronal model the power radiated by ions in the plasma (these could be plasma ions or impurity ions). We calculate the ion density required to radiate all the incident rf power for various power levels up to 100 MW. We also use this density to estimate spot sizes on the waveguide surface, comparing these estimates with observations at the Stanford Linear Accelerator Center.   

Grid-Free Particle Method for Electrostatic Plasmas

A grid-free particle method for electrostatic plasmas is presented. The method is based on the Lagrangian formulation of the Vlasov-Poisson equations in terms of the flow map of the charge distribution. We employ several numerical techniques including: (1) regularizing the Coulomb singularity, (2) adaptive particle insertion, and (3) a treecode algorithm to accelerate the evaluation of the electric field. Simulations are presented for the instability of collisionless electron beams.   

Correlated Relativistic Current Sheet Systems

We study the non-linear evolution of interacting Relativistic Current Sheets (RCS) in 1D/2D/3D self-consistent kinetic plasma simulations within the framework of the Particle-In-Cell model. The intention is to extend the existing knowledge about individual RCS in pair plasma - where the physics is determined by the relativistic tearing and drift kink modes as competing RCS instabilities - towards a correlated RCS system. Such RCS systems are the key element of generic `striped wind' configurations proposed to model relativistic plasma flows like pulsar winds and gamma-ray bursts. Interactions are enforced in head-on collisions of systems consisting of up to ten individual and equi-distantly separated RCS. The global dynamics divides into a weakly and strongly correlated regime. In the weakly correlated case each RCS persists as an entity and non-thermal particle generation is attributed to a stochastic Fermi-type acceleration mechanism. In the complementary strongly correlated regime the RCS interpenetrate thouroughly and efficient magnetic field dissipation is observed within a 1D stratification. Localized regions persist where the electric supersedes the magnetic field, i.e. the transformation of particle orbits towards a de Hoffmann-Teller-frame is then inherently impossible.   

The Equilibrium Ensemble of Three-dimensional Hall Magnetohydrodynamics

The nonlinear dynamics of ideal and incompressible Hall Magnetohydrodynamics (HMHD) is investigated through classical Gibbs ensemble methods. The spectral structure of the HMHD is derived in a three dimensional periodic geometry and then compared with the MHD case. The purpose of the work is to provide a general picture of Hall MHD spectral transfers and cascades by the assumption that it follows equilibrium statistics. In the HMHD case the equilibrium ensemble is built on the conservation of three quadratic invariants, that is the total energy, the magnetic helicity, and the hybrid helicity. The latter replace the cross helicity in the one fluid case. In the HMHD equilibrium a tendency to have double cascade (inverse and direct) is observed, moreover the Alfven effect (dynamical alignment between velocity and magnetic field) is broken at ion skin depth scales. The ensemble predictions are compared to numerical simulations with a low order truncation Galerkin spectral code.   

Vlasov-Fokker-Planck Transport Simulations Of Magnetic Field Instabilities

Strong magnetic fields are well known to significantly affect the transport properties of plasmas. In addition to being externally applied, these can be self-generated spontaneously through non-linear processes. Magnetic field generating instabilities include thermomagnetic and pressure anisotropy (e.g. Weibel) effects. These are best described by the Vlasov-Fokker-Planck equation, in the presence of strong gradients where non-local effects are important, as is usually the case in laser-plasma interactions. We have further developed the 2-D Vlasov-Fokker-Planck code {\small IMPACT} to include terms in the cartesian tensor expansion of velocity space up to order 3. The previous code included only zero and first order terms, which are not sufficient to completely describe some of these magnetic instabilities. Analytic and numerical modeling of the semi-collisional regime of magnetic field generation is presented, which demonstrate spontaneous growth of magnetic fields and the effect of adding these higher order terms. We consider the ramifications of these for inertial fusion energy.   

Plasma microturbulence with dual drive

Turbulence driven by ITG modes and trapped electron modes (TEMs) is generally considered the key mechanism for anomalous transport in fusion devices on ion scales. But while there exist many theoretical studies of pure ITG turbulence, not much is presently known about the properties of pure TEM turbulence and about possible nonlinear interactions between ITG modes and TEMs. These important questions will be addressed here by means of nonlinear gyrokinetic simulations with the {\sc Gene} code. We find that temperature gradient driven TEM turbulence -- in contrast to ITG turbulence -- does not saturate via zonal flow generation. Instead, the transport dominating modes in the $k_y$ spectrum largely resemble the respective linear microinstabilities, and the action of the nonlinearity on long-wavelength TEMs is statistically equivalent to that of a diffusion operator. This is the basis for a rather simple transport model which is able to capture many features observed in the nonlinear simulations. In order to be able to examine the coexistence of TEM and ITG instabilities in certain regions of parameter space, {\sc Gene} has been extended by an eigenvalue solver which is capable of dealing with the very large matrices that occur in this context. Thus it becomes possible to detect and analyze also subdominant modes, and to relate their characteristics to those of the corresponding turbulent system. The nature of a dual turbulence drive and the consequences for transport modelling will be discussed.   

ETG Modeling of a TCV Multi-Phase H-Mode Shot

TCV is well suited for electron transport studies due to its well developed ECRH system. Ion heating is achieved by thermal equilibration at high density in combination with strong third harmonic X-mode (X3) ECRH heating. In TCV shot 29892, X3 heating was applied to an ohmic ELMy H-mode, either at full or modulated power. This shot covers four stationary H-mode phases, one ohmic followed by three ELMy or ELM-free X3 heated. The final two are akin to improved H-modes. Previous analysis with the GLF model implied the discharge to be ITG dominated, in accordance with a preliminary Weiland stability analysis. As the applied heating only affects the electrons it is important to analyze this discharge regarding ETG and/or TEM modes. The ETG turbulence calculated with the IFS-ETG model will be presented. This model has already successfully calculated electron transport in dominantly electron-heated NSTX and Tore Supra.   

Spatio-temporal correlations in edge tokamak plasma

Plasma fluctuations in the scrape-off layer (SOL) of tokamak TCV have been investigated by means of electrostatic probes, and compared directly with two-dimensional fluid interchange turbulence simulation ESEL. This model permits electron density, temperature and vorticity (potential) to evolve freely at the outside midplane region of a tokamak. The viscosity and parallel particle loss are based on the neoclassical Pfirsch-Schlutter diffusion and classical parallel transport, respectivelly. In this contribution we focus on comparing the time-scales, spatial scales of fast fluctuations of density and temperature, using the unique tunnel probe capable of fast (1 MHz) electron temperature measurement. Significant difference in statistical behaviour of both density and temperature fluctuations between the tokamak top and the low-field side location has been found experimentally on the small tokamak CASTOR, whilst still the statistical characteristics correspond well at the low-field side with the ESEL simulations. This further confirms dominance of the interchange turbulence at the low-field side, where the observed bursty events are generally attributed to the radial motion of blob-like structures through the SOL.   

Edge kinetic-MHD code coupling and monitoring with Kepler workflow

Simulations of edge pressure pedestal buildup and ELM crash in a typical DIII-D H-mode discharge are performed using Kepler, an open-source scientific workflow system that manages complex applications. A Kepler workflow conducts an edge plasma simulation that loosely couples the kinetic code XGC0 with an ideal MHD linear stability analysis code ELITE and a two-fluid MHD initial value code M3D. XGC0 simulation data are processed by the workflow into simple graphs that may be selectively displayed via the Dashboard, a monitoring tool that allows real-time data tracking within a standard Web browser. Kepler runs ELITE to assess plasma profiles from XGC0 for linear ELM instability. If unstable, Kepler launches M3D to simulate the nonlinear ELM crash. Periodic outputs of plasma fluid quantities are automatically imaged and may be displayed on the Dashboard. Finally, Kepler archives all simulation output, processed images, and provenance tracking data. Preparation, execution, and monitoring of this coupled-code simulation using the Kepler scientific workflow system are described.   

Noise control in global gyrokinetic particle simulations

The use of gyrokinetic PIC codes for long simulations is hindered by the accumulation of noise: we explore the use of a relaxation operator to prevent this noise accumulation. The simplest relaxation operator is the Krook operator, which acts somewhat like an artificial collisionality, and can effectively control noise; it also introduces an unphysical dissipation, which may damp persistent structures like zonal flows and significantly modify simulation results even when the relaxation time is very long. We describe a method for projecting out the effects of the Krook operator on the zonal flows, and use this in the ORB5 gyrokinetic code [1], thereby preventing the secular accumulation of noise without introducing a large inaccuracy in the model. The results of the simulations are consistent with previous studies. Numerical efficiency is greatly improved due to the smaller number of markers required per mode compared to long simulations without a relaxation operator. \newline [1] S. Jolliet {\it et al.}, to appear in Comput. Phys. Commun.   

Gyrokinetic simulations of electron density fluctuations and comparisons with measurement

Understanding transport is important for creating reliable predictions of plasma performance in fusion reactors. Plasma turbulence causes much of the transport seen in present experiments. Gyrokinetic codes can simulate turbulence and turbulent-driven transport. Further verifying and validating these simulations are needed. One class of tests is provided by electron density fluctuation $\tilde{n}_e$ measurements using techniques such as reflectometry and beam-emission-spectroscopy. The GYRO gyrokinetic code is being used to simulate turbulence and turbulent-driven energy, angular momentum, and species flows in experiments. GYRO can generate the time-evolving fluctuations of $\tilde{n}_e$ in three spatial dimensions. From this, profiles, along the diagnostic lines-of-sight, of the root-mean-square $\tilde{n}_e$, radial correlation lengths $\lambda_r$, and power spectra can be produced. This paper compares on GYRO simulations of reflectometry measurements in TFTR D and DT supershots and JET. Three kinetic species (2 ions and electrons) are assumed, about half the plasma radius is simulated. Realistic geometry and electron-ion collisions are included. Agreement to within about a factor of two is achieved.   

Gyrokinetic Simulation of Trapped Electron Mode Turbulence

Trapped electron mode (TEM) has long been considered as an important candidate to account for the anomalous transport in the core plasma. Global gyrokinetic particle simulation using the GTC code finds that the trapped electron mode (TEM) can be driven unstable by steep density gradient. Gyrokinetic particle simulation shows that in TEM turbulence trapped electrons can drive larger heat transport that ions. A second busty phenomenon is observed, which differs from its ITG counter part. It is also found that zonal flow plays an important role in regulating TEM turbulence with the current parameters, as it does for ITG turbulence.   

Instability modeling of homogenous and inhomogeneous plasmas using nonparametric distribution estimation and convex vector optimization algorithms

Due to departure from thermodynamic equilibrium, plasma instabilities are difficult to model. Velocity distributions in homogenous plasma and associated kinetic energies are modeled and simulated using nonparametric distribution estimation algorithms. The magnetic field and the spatial inhomogeneities for inhomogeneous plasmas are also modeled using vector optimization algorithms. Bounding probabilities and expected values provide excellent results for homogenous plasmas. Scalarization algorithms for Pareto optimization in inhomogenous plasmas are used. The problem eventually turns into a multicriterion vector optimization problem.