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Improvements In The Gyrokinetic Simulation Method
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Book Synopsis Improvements in the Gyrokinetic Simulation Method by :
Download or read book Improvements in the Gyrokinetic Simulation Method written by and published by . This book was released on 1991 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gyrokinetic particle-in-cell (PIC) simulations have been proven to be an important and useful tool for studying low frequency waves and instabilities below ion cyclotron frequency. The gyrokinetic formalism eliminates the cyclotron motion by analytically averaging the equation of motion in time, while keeping finite-Larmor radius effects, and therefore allows a time step of integration to be significantly longer than the cyclotron period. At the same time the thermal fluctuation level is reduced well below that of a conventional PIC simulation code. Recent simulations have been performed over a number of wave periods to study nonlinear evolution of drift waves and ion-temperature-gradient modes and the associated transport. With about a quarter million particles and a 64 x 128 x 32 grid in three dimensions, it takes about 100 hours on the Cray-2 single processor to follow the modes to a nonlinear quasi-steady state for relatively strong gradients and strong growth rates. Much more efficient simulations are needed in order to understand these low-frequency waves and the transport associated with them by the use of this tool, and to facilitate the simulation of more weakly unstable plasmas with parameters more relevant to experimental conditions. We have set a goal of achieving an efficiency gain of a factor of 100 on a present-day computer over what has been achieved on the Cray-2 for gyrokinetic simulations. To reach this goal we have begun a project with two components; one is the use of new PIC techniques such as subcycling, orbit-averaging, and semi-implicit algorithms, and the other is the use of massively parallel computers such as the BBN TC200 and the Thinking Machines CM-2. 6 refs.
Book Synopsis A Fully Nonlinear Characteristic Method for Gyrokinetic Simulation by : W. W. Lee
Download or read book A Fully Nonlinear Characteristic Method for Gyrokinetic Simulation written by W. W. Lee and published by . This book was released on 1992 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Fully Nonlinear Characteristic Method for Gyrokinetic Simulation by :
Download or read book A Fully Nonlinear Characteristic Method for Gyrokinetic Simulation written by and published by . This book was released on 1992 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new scheme which evolves the perturbed part of the distribution function along a set of characteristics that solves the fully nonlinear gyrokinetic equations. This nonlinear characteristic method for particle simulation is an extension of the partially linear weighting scheme, and may be considered an improvement of existing [delta] f methods. Some of the features of this new method are: the ability to keep all of the nonlinearities, particularly those associated with parallel acceleration; the loading of the physical equilibrium distribution function f{sub o} (e.g., a Maxwellian), with or without the multiple spatial scale approximation; the use of a single of trajectories for the particles; and also, the retention of the conservation properties of the original gyrokinetic system in the numerically converged limit. Therefore, one can take advantage of the low noise property of the weighting scheme together with the quiet start techniques to simulate weak instabilities, with a substantially reduced number of particles than required for a conventional simulation. The new method is used to study a one dimensional drift wave model which isolates the parallel velocity nonlinearity. A mode coupling calculation of the saturation mechanism is given, which is in good agreement with the simulation results and predicts a considerably lower saturation level then the estimate of Sagdeev and Galeev. Finally, we extend the nonlinear characteristic method to the electromagnetic gyrokinetic equations in general geometry.
Book Synopsis Advances in Quasilinear Gyrokinetic Modeling of Turbulent Transport by : Cole Darin Stephens
Download or read book Advances in Quasilinear Gyrokinetic Modeling of Turbulent Transport written by Cole Darin Stephens and published by . This book was released on 2021 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quest to harness fusion energy requires the successful modeling of plasma turbulence and transport in magnetic confinement devices. For such modeling, the requisite length and time scales span many orders of magnitude. Integrated modeling approaches are constructed to account for the wide range of physics involved in turbulent transport by coupling separate physical models together. The primary physical models used in this work are kinetic and designed to simulate microturbulence on the smallest scales associated with turbulent transport. However, high precision nonlinear kinetic simulations often cannot be easily coupled to integrated modeling suites due to the extreme computational costs that would be involved. Model reduction which drastically reduces the computational complexity of the problem is therefore necessary. One must of course ensure that the reduced model does not severely diminish the accuracy of the calculation; the model reduction itself must be founded on more exact computational approaches as well as fundamental theoretical principles. One of the most successful approaches in model reduction is quasilinear gyrokinetics. There are two fundamental assumptions for the quasilinear model examined in this work. First, the three adiabatic invariants (the magnetic moment, the longitudinal invariant, and the poloidal flux) must be appropriately conserved and their associated single charged particle motions (the gyromotion, the bounce-transit motion, and the toroidal drift motion) must be characterized accurately. Second, the quasilinear approximation must hold such that the coherent linear response is adequate enough to compute the quasilinear fluxes without full calculation of the nonlinear physics. The particular model used, QuaLiKiz, has been proven successful in reproducing local gyrokinetic fluxes in the tokamak core while remaining computationally tractable. There are three primary goals of this dissertation project. The first is to examine the fundamental physics underlying gyrokinetic and reduced model approaches at the single charged particle scale. To achieve this goal, we examine the assumption of magnetic moment invariance in a wide variety of electromagnetic fields. We successfully identify the dimensionless parameters that determine magnetic moment conservation in each scenario and then proceed to quantify the degree to which magnetic moment conservation is broken. In doing so, we confirm that the magnetic moment is sufficiently conserved for a wide range of regimes relevant to tokamak plasmas. In addition, we derive new analytic formulas for quantities associated with bounce-transit motion in circular tokamak fields. We compare these new, more exact calculations to approximations commonly used in reduced models (including QuaLiKiz) and determine the conditions such that the approximations break down. We then also confirm that the approximations are valid in the tokamak core for conventional, large aspect ratio devices. The second goal of this dissertation project is to rederive and compile the model equations for QuaLiKiz from first principles. Over the years of QuaLiKiz's development, there has never been a complete manuscript that sketches the derivation of QuaLiKiz from start to finish. The lack of such a document makes it difficult to extend the physics of QuaLiKiz to new parameter regimes of interest. Various possible extensions such as including electromagnetic effects or more realistic tokamak geometries require the adjustment of several different assumptions that would affect the derivation in key ways. As such, correct implementations of new physics would require an existing derivation as a reference point lest the implementation be handled in an incoherent fashion. In addition, a step-by-step outline of how each assumption of QuaLiKiz affects the derivation can be helpful in determining which assumptions can be relaxed for a more accurate model. The successful completion of this derivation, included in this dissertation, will be immensely useful for future QuaLiKiz improvement and validation. With the derivation in hand, we proceed to the third goal of this project: improving the collisional model of QuaLiKiz. Collisions play an essential role in characterizing the transport associated with trapped electron modes. It has become evident in recent studies that the collisional model in QuaLiKiz requires improvement; in integrated modeling, the imprecise treatment of collisional trapped electron modes leads to incorrect density profile predictions near the tokamak core for highly collisional regimes. We revisit the collision model implemented in QuaLiKiz and use the more exact gyrokinetic code GENE (Gyrokinetic Electromagnetic Numerical Experiment) to make improvements to QuaLiKiz's collision operator. We then use the new version of QuaLiKiz in integrated modeling to compare density profiles predicted by the old and new collision operators. We confirm that the new collision operator leads to density profiles that more accurately match the experimental profiles.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1995 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Gyrokinetic Theory with Applications in Magnetic Confinement Research in Plasma Physics by : W. M. Tang
Download or read book Introduction to Gyrokinetic Theory with Applications in Magnetic Confinement Research in Plasma Physics written by W. M. Tang and published by . This book was released on 2005 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Gyrokinetic Simulation of Ion Temperature Gradient Driven Turbulence in 3D Toroidal Geometry by :
Download or read book Gyrokinetic Simulation of Ion Temperature Gradient Driven Turbulence in 3D Toroidal Geometry written by and published by . This book was released on 1993 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from a fully nonlinear three dimensional toroidal electrostatic gyrokinetic simulation of the ion temperature gradient instability are presented. The model has fully gyro-averaged ion dynamics, including trapped particles, and adiabatic electrons. Simulations of large tokamak plasma volumes are made possible due to recent advances in ?f methods and massively parallel computing. Linearly, a coherent ballooning eigenmode is observed, where the mode is radially elongated. In the turbulent steady-state, the spectrum peaks around k? ?{sub s} ∼ 0.1 with the ballooning structure reduced, but still prevalent.
Book Synopsis Analysis and Gyrokinetic Simulation of MHD Alfvén Wave Interactions by : Kevin Derek Nielson
Download or read book Analysis and Gyrokinetic Simulation of MHD Alfvén Wave Interactions written by Kevin Derek Nielson and published by . This book was released on 2012 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfvén waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfvén waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfvén waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvénic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfvén waves by reproducing laboratory Alfvén dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfvén eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions ...
Book Synopsis Advances in the Simulation of Toroidal Gyro Landau Fluid Model Turbulence by :
Download or read book Advances in the Simulation of Toroidal Gyro Landau Fluid Model Turbulence written by and published by . This book was released on 1994 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The gyro-Landau fluid (GLF) model equations for toroidal geometry have been recently applied to the study ion temperature gradient (ITG) mode turbulence using the 3D nonlinear ballooning mode representation (BMR). The present paper extends this work by treating some unresolved issues conceming ITG turbulence with adiabatic electrons. Although eddies are highly elongated in the radial direction long time radial correlation lengths are short and comparable to poloidal lengths. Although transport at vanishing shear is not particularly large, transport at reverse global shear, is significantly less. Electrostatic transport at moderate shear is not much effected by inclusion of local shear and average favorable curvature. Transport is suppressed when critical E x B rotational shear is comparable to the maximum linear growth rate with only a weak dependence on magnetic shear. Self consistent turbulent transport of toroidal momentum can result in a transport bifurcation at suffciently large r/(Rq). However the main thrust of the new formulation in the paper deals with advances in the development of finite beta GLF models with trapped electron and BMR numerical methods for treating the fast parallel field motion of the untrapped electrons.
Book Synopsis Computational Many-Particle Physics by : Holger Fehske
Download or read book Computational Many-Particle Physics written by Holger Fehske and published by Springer Science & Business Media. This book was released on 2007-12-07 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: Looking for the real state of play in computational many-particle physics? Look no further. This book presents an overview of state-of-the-art numerical methods for studying interacting classical and quantum many-particle systems. A broad range of techniques and algorithms are covered, and emphasis is placed on their implementation on modern high-performance computers. This excellent book comes complete with online files and updates allowing readers to stay right up to date.
Book Synopsis New Methods in Gyrokinetic Particle in Cell Simulations by : Oleksiy Mishchenko
Download or read book New Methods in Gyrokinetic Particle in Cell Simulations written by Oleksiy Mishchenko and published by . This book was released on 2005 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Turbulent Transport in Magnetized Plasmas by : Wendell Horton
Download or read book Turbulent Transport in Magnetized Plasmas written by Wendell Horton and published by World Scientific. This book was released on 2012 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explains how magnetized plasmas self-organize in states of electromagnetic turbulence that transports particles and energy out of the core plasma faster than anticipated by the fusion scientists designing magnetic confinement systems in the 20th century. It describes theory, experiments and simulations in a unified and up-to-date presentation of the issues of achieving nuclear fusion power.
Book Synopsis Gyrokinetic Simulation of Pedestal Turbulence Using GENE by : Xing Liu (Ph. D. in physics)
Download or read book Gyrokinetic Simulation of Pedestal Turbulence Using GENE written by Xing Liu (Ph. D. in physics) and published by . This book was released on 2018 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present here a study based on gyrokinetic simulations (using GENE) to model turbulence in the pedestals on several well-diagnosed shots: two H-modes on DIII-D and one I-mode on Alcator C-Mod. We match frequencies, power balance, and other transport characteristics in multiple channels with the observations. The observed quasi-coherent fluctuations on the DIII-D shots are identified as Micro Tearing Modes (MTM). The MTMs match frequency and power balance (together with heat loss from Electron Temperature Gradient (ETG) driven turbulence), and cause low transport in the particle, ion heat and impurity particle transport channels – consistent with observed inter-ELM evolution of ion and electron temperature, electron and impurity density or transport analysis of those channels. We find the Weakly Coherent Mode on C-Mod I-mode to be an electrostatic Ion Temperature Gradient/Impurity density gradient (ITG/Impurity) driven mode. The ITG/Impurity mode match frequency and the impurity confinement time observed on the I-mode. Electron scale turbulence, ETG, provides energy transport to match power balance. A novel concept called the transport fingerprints is used throughout this work, which greatly assists in identifying the instabilities. This work shows that the concept should be very valuable in many future investigations of pedestal turbulence.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Gyrokinetic Approach in Particle Simulation by :
Download or read book Gyrokinetic Approach in Particle Simulation written by and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A new scheme for particle simulation based on the gyrophase-averaged Vlasov equation has been developed. It is suitable for studying low-frequency microinstabilities and the associated anomalous transport in magnetically confined plasmas. The scheme retains the gyroradius effects but not the gyromotion; it is, therefore, far more efficient and versatile than the conventional ones. Furthermore, the reduced Vlasov equation is also amenable to analytical studies.
Book Synopsis Gyrokinetic Simulation of Internal Kink Modes by :
Download or read book Gyrokinetic Simulation of Internal Kink Modes written by and published by . This book was released on 1995 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: Internal disruption in a tokamak has been simulated using a three-dimensional magneto-inductive gyrokinetic particle code. The code operates in both the standard gyrokinetic mode (total-f code) and the fully nonlinear characteristic mode ([delta]f code). The latter, a recent addition, is a quiet low noise algorithm. The computational model represents a straight tokamak with periodic boundary conditions in the toroidal direction. The plasma is initially uniformly distributed in a square cross section with perfectly conducting walls. The linear mode structure of an unstable m = 1 (poloidal) and n = 1 (toroidal) kinetic internal kink mode is clearly observed, especially in the [delta]f code. The width of the current layer around the x-point, where magnetic reconnection occurs, is found to be close to the collisionless electron skin depth. This is consistent with the theory in which electron inertia has a dominant role. The nonlinear behavior of the mode is found to be quite similar for both codes. Full reconnection in the Alfven time scale is observed along with the electrostatic potential structures created during the full reconnection phase. The E x B drift due to this electrostatic potential dominates the nonlinear phase of the development after the full reconnection.
Book Synopsis Annual Report 1989-90 by : New Brunswick. Department of Transportation
Download or read book Annual Report 1989-90 written by New Brunswick. Department of Transportation and published by . This book was released on 1991 with total page 1272 pages. Available in PDF, EPUB and Kindle. Book excerpt: General activity review of associated branches and agencies to the Department which includes corporate securities registrations, a list of tenders received, and general financial data. Branches and agencies reviewed are responsible for motor vehicle activity, highway construction, traffic engineering, telecommunications and public utilities.
