Collisional and Electromagnetic Physics in Gyrokinetic Models

Collisional and Electromagnetic Physics in Gyrokinetic Models
Author: Paul Crandall
Publisher:
Total Pages: 229
Release: 2019
Genre:
ISBN:

One of the most challenging problems facing plasma physicists today involves the modeling of plasma turbulence and transport in magnetic confinement experiments. The most successful model to this end so far is the reduced gyrokinetic model. Such a model cannot be solved analytically, but can be used to simulate the plasma behavior and transport with the help of present-day supercomputers. This has lead to the development of many different codes which simulate the plasma using the gyrokinetic model in various ways. These models have achieved a large amount of success in describing the core of the plasma for conventional tokamak devices. However, numerous difficulties have been encountered when applying these models to more extreme parameter regimes, such as the edge and scrape-off layer of the tokamak, and high plasma devices, such as spherical tokamaks. The development and application of the gyrokinetic model (specifically with the gyrokinetic code, GENE) to these more extreme parameter ranges shall be the focus of this thesis. One of the main accomplishments during this thesis project is the development of a more advanced collision operator suitable for studying the low temperature plasma edge. The previous collision operator implemented in the code was found to artificially create free energy at high collisionality, leading to numerical instabilities when one attempted to model the plasma edge. This made such an analysis infeasible. The newly implemented collision operator conserves particles, momentum, and energy to machine precision, and is guaranteed to dissipate free energy, even in a nonisothermal scenario. Additional finite Larmor radius correction terms have also been implemented in the local code, and the global code version of the collision operator has been adapted for use with an advanced block-structured grid scheme, allowing for more affordable collisional simulations. The GENE code, along with the newly implemented collision operator developed in this thesis, has been applied to study plasma turbulence and transport in the edge (tor = 0:9) of an L-mode magnetic confinement discharge of ASDEX Upgrade. It has been found that the primary microinstabilities at that radial position are electron drift waves destabilized by collisions and electromagnetic effects. At low toroidal mode numbers, ion temperature gradient driven modes and microtearing modes also seem to exist. In nonlinear simulations with the nominal experimental parameters, the simulated electron heat flux was four times higher than the experimental reconstruction, and the simulated ion heat flux was twice as high. However, both the ion and electron simulated heat flux could be brought into agreement with experimental values by lowering the input logarithmic electron temperature gradient by 40%. It was also found that the cross-phases between the electrostatic potential and the moments agreed well for the part of the binormal spectrum where the dominant transport occurred, and was fairly poor at larger scales where minimal transport occurred. Finally, a new scheme for evaluating the electromagnetic fields has been developed to address the instabilities occurring in nonlinear local and global gyrokinetic simulations at high plasma . This new scheme is based on evaluating the electromagnetic induction explicitly, and constructing the gyrokinetic equation based on the original distribution, rather than the modified distribution which implicitly takes into account the induction. This new scheme removes the artificial instability occurring in global simulations, enabling the study of high scenarios with GENE. The new electromagnetic scheme can also be generalized to a full-f implementation, however, it would require updating the field matrix every time-step to avoid the cancellation problem. The new scheme (including the parallel nonlinearity) does not remove the local instability, suggesting that that instability (caused by magnetic field perturbations shorting out zonal flows) is part of the physics of the local model.

A Parallel Spectral Method Approach to Model Plasma Instabilities

A Parallel Spectral Method Approach to Model Plasma Instabilities
Author: Kevin S. Scheiman
Publisher:
Total Pages: 82
Release: 2018
Genre: Computer science
ISBN:

The study of solar-terrestrial plasma is concerned with processes in magnetospheric, ionospheric, and cosmic-ray physics involving different particle species and even particles of different energy within a single species. Instabilities in space plasmas and the earth's atmosphere are driven by a multitude of free energy sources such as velocity shear, gravity, temperature anisotropy, electron, and, ion beams and currents. Microinstabilities such as Rayleigh-Taylor and Kelvin-Helmholtz instabilities are important for the understanding of plasma dynamics in presence of magnetic field and velocity shear.Modeling these turbulences is a computationally demanding processes; requiring large memory and suffer from excessively long runtimes. Previous works have successfully modeled the linear and nonlinear growth phases of Rayleigh-Taylor and Kelvin-Helmholtz type instabilities in ionospheric plasmas using finite difference methods. The approach here uses a two-fluid theoretical ion-electron model by solving two-fluid equations using iterative procedure keeping only second order terms. It includes the equation of motion for ions and electrons, the continuity equations for both species, and the assumption that the electric drift and gravitational drift are of the same order. The effort of this work is to focus on developing a new pseudo-spectral, highly-parallelizable numerical approach to achieve maximal computational speedup and efficiency. Domain decomposition along with Message Passing Interface (MPI) functionality was implemented for use of multiple processor distributed memory computing. The global perspective of using Fourier Transforms not only adds to the accuracy of the differentiation process but also limits memory calling when performing calculations. An original method for calculating the Laplacian for a periodic function was developed that obtained a maximum speedup of 2.98 when run on 16 processors, with a theoretical max of 3.63. Using this method as a backbone for parallelizing the RT-KH solution, the final program achieved a speedup of 1.70 when calculating only first order terms, and 1.43 when calculating up to second order.

Gyrokinetic Particle Simulation Model

Gyrokinetic Particle Simulation Model
Author:
Publisher:
Total Pages:
Release: 1986
Genre:
ISBN:

A new type of particle simulation model based on the gyrophase-averaged Vlasov and Poisson equations is presented. The reduced system, in which particle gyrations are removed from the equations of motion while the finite Larmor radius effects are still preserved, is most suitable for studying low frequency microinstabilities in magnetized plasmas. It is feasible to simulate an elongated system (L/sub parallel/” L/sub perpendicular/) with a three-dimensional grid using the present model without resorting to the usual mode expansion technique, since there is essentially no restriction on the size of .delta.x/sub parallel/ in a gyrokinetic plasma. The new approach also enables us to further separate the time and spatial scales of the simulation from those associated with global transport through the use of multiple spatial scale expansion. Thus, the model can be a very efficient tool for studying anomalous transport problems related to steady-state drift-wave turbulence in magnetic confinement devices. It can also be applied to other areas of plasma physics.

Kinetic Studies of Microinstabilities in Toroidal Plasmas

Kinetic Studies of Microinstabilities in Toroidal Plasmas
Author:
Publisher:
Total Pages: 8
Release: 1992
Genre:
ISBN:

A comprehensive program for the development and use of particle simulation techniques for solving the gyrokinetic Vlasov-Maxwell equations on massively parallel computers has been carried out at Princeton Plasma Physics Laboratory. This is a key element of our ongoing theoretical efforts to systematically investigate physics issues vital to understanding tokamak plasmas. In this paper, our focus is on spatial-gradient-driven microinstabilities. Their importance is supported by the recent progress in achieving a physics-based understanding of anomalous transport in toroidal systems which has been based on the proposition that these drift-type electrostatic modes dependent on ion temperature gradient (ITG) and trapped particle effects are dominant in the bulk (confinement'') region. Although their presence is consistent with a number of significant confinement trends, results from high temperature tokamaks such as TFTR have highlighted the need for better insight into the nonlinear properties of such instabilities in long-mean-free-path plasmas. In addressing this general issue, we report important new results including (i) the first fully toroidal 3D gyrokinetic simulation of ITG modes and (ii) realistic toroidal eigenmode calculations demonstrating the unique capability to deal with large scale kinetic behavior extending over many rational surfaces. The effects of ITG modes (iii) on the inward pinch of impurities in 3D slab geometry and (iv) on the existence of microtearing modes in 2D slab are also discussed. Finally, (v) sheared toroidal flow effects on trapped-particle modes are presented.