Download or read book Progress in Gyrokinetic Simulations of Toroidal ITG Turbulence written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The 3-D nonlinear toroidal gyrokinetic simulation code PG3EQ is used to study toroidal ion temperature gradient (ITG) driven turbulence--a key cause of the anomalous transport that limits tokamak plasma performance. Systematic studies of the dependence of ion thermal transport on various parameters and effects are presented, including dependence on {rvec E} x {rvec B} and toroidal velocity shear, sensitivity to the force balance in simulations with radial temperature gradient variation, and the dependences on magnetic shear and ion temperature gradient.

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 [delta]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[theta] [rho][sub s] [approximately] 0.1 with the ballooning structure reduced, but still prevalent.

Download or read book Gyrokinetic Simulation of Ion Temperature Gradient Driven Turbulence in 3D Toroidal Geometry written by W. W. Lee and published by . This book was released on 1993 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Gyrokinetic Simulations of ETG and ITG Turbulence written by D. Shumaker and published by . This book was released on 2006 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published gyrokinetic continuum-code simulations indicated levels of the electron thermal conductivity {chi}{sub e} due to electron-temperature-gradient (ETG) turbulence large enough to be significant in some tokamaks, while subsequent global particle-in-cell (PIC) simulations gave significantly lower values. We have carried out an investigation of this discrepancy. We have reproduced the key features of the aforementioned PIC simulations using the flux-tube gyrokinetic PIC code, PG3EQ, thereby eliminating global effects and as the cause of the discrepancy. We show that the late-time low-transport state in both of these sets of PIC simulations is a result of discrete particle noise, which is a numerical artifact. Thus, the low value of {chi}{sub e} along with conclusions about anomalous transport drawn from these particular PIC simulations are unjustified. In our attempts to benchmark PIC and continuum codes for ETG turbulence at the plasma parameters used above, both produce very large intermittent transport. We have therefore undertaken benchmarks at an alternate reference point, magnetic shear s=0.1 instead of s=0.796, and have found that PIC and continuum codes reproduce the same transport levels. Scans in the magnetic shear show an abrupt transition to a high-{chi}{sub e} state as the shear is increased above s=0.4. When nonadiabatic ions are used, this abrupt transition is absent, and {chi}{sub e} increases gradually reaching values consistent with transport analyses of DIII-D, JET, and JT60-U discharges. New results on the balances of zonal-flow driving and damping terms in late-time quasi-steady ITG turbulence and on real-geometry gyrokinetic simulations of shaped DIII-D discharges are also reported.

Download or read book Physics of Intrinsic Rotation in Flux Driven ITG Turbulence written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Global, heat flux-driven ITG gyrokinetic simulations which manifest the formation of macroscopic, mean toroidal flow profiles with peak thermal Mach number 0.05, are reported. Both a particle-in-cell (XGC1p) and a semi-Lagrangian (GYSELA) approach are utilized without a priori assumptions of scale-separation between turbulence and mean fields. Flux-driven ITG simulations with different edge flow boundary conditions show in both approaches the development of net unidirectional intrinsic rotation in the co-current direction. Intrinsic torque is shown to scale approximately linearly with the inverse scale length of the ion temperature gradient. External momentum input is shown to effectively cancel the intrinsic rotation profile, thus confirming the existence of a local residual stress and intrinsic torque. Fluctuation intensity, intrinsic torque and mean flow are demonstrated to develop inwards from the boundary. The measured correlations between residual stress and two fluctuation spectrum symmetry breakers, namely E x B shear and intensity gradient, are similar. Avalanches of (positive) heat flux, which propagate either outwards or inwards, are correlated with avalanches of (negative) parallel momentum flux, so that outward transport of heat and inward transport of parallel momentum are correlated and mediated by avalanches. The probability distribution functions of the outward heat flux and the inward momentum flux show strong structural similarity.

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.

Download or read book Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas written by and published by . This book was released on 2011 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-year project GPS-TTBP resulted in over 152 publications and 135 presentations. This summary focuses on the scientific progress made by the project team. A major focus of the project was on the physics intrinsic rotation in tokamaks. Progress included the first ever flux driven study of net intrinsic spin-up, mediated by boundary effects (in collaboration with CPES), detailed studies of the microphysics origins of the Rice scaling, comparative studies of symmetry breaking mechanisms, a pioneering study of intrinsic torque driven by trapped electron modes, and studies of intrinsic rotation generation as a thermodynamic engine. Validation studies were performed with C-Mod, DIII-D and CSDX. This work resulted in very successful completion of the FY2010 Theory Milestone Activity for OFES, and several prominent papers of the 2008 and 2010 IAEA Conferences. A second major focus was on the relation between zonal flow formation and transport non-locality. This culminated in the discovery of the ExB staircase - a conceptually new phenomenon. This also makes useful interdisciplinary contact with the physics of the PV staircase, well-known in oceans and atmospheres. A third topic where progress was made was in the simulation and theory of turbulence spreading. This work, now well cited, is important for understanding the dynamics of non-locality in turbulent transport. Progress was made in studies of conjectured non-diffusive transport in trapped electron turbulence. Pioneering studies of ITB formation, coupling to intrinsic rotation and hysteresis were completed. These results may be especially significant for future ITER operation. All told, the physics per dollar performance of this project was quite good. The intense focus was beneficial and SciDAC resources were essential to its success.

Download or read book ITG Turbulence Saturation and Near resonant Heat Flux Reduction in Gyrokinetic Dimits shift Analysis written by Ping-Yu Li and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Microturbulence is caused by gyroradius-scale instabilities such as the Ion-Temperature-Gradient-driven (ITG) instability, Trapped Electron Mode (TEM), Kinetic Ballooning Mode (KBM), etc. Understanding how these instabilities saturate and form turbulence is important for the ecient operation and optimization of magnetic connement fusion devices in the quest for sustained fusion energy. The objective of this thesis is to understand the important factors and mechanisms that saturate ITG turbulence and to utilize said understanding to build reduced models that capture key physical behavior , resolving which would otherwise require a complex full-physics approach. Zonal- ow-catalyzed interactions that involve large-scale stable, unstable modes and zonal ows are crucial for the saturation of curvature-driven ITG turbulence. A corresponding saturation theory is built based on a uid model and implemented and tested numerically. The crudest saturation theory drops the non-zonal interactions and also the nonlinear corrections to frequencies, while also truncating the wavenumber space to obtain scalings for the saturation level with a triplet correlation time based on linear frequencies and coupling coecients. It is then discovered that nonlinear interactions can cause nonnegligible modications on the mode oscillations for systems with higher turbulence level. Furthermore, the kx direction in wavenumber space needs to be resolved in order to break the symmetry between modes and build up the zonal ow, which is shown in both time-dependent and time-independent research. A two-predator-prey model based on the saturation theory, and with no free parameters, is also constructed. This will help build a predator-prey model from rst principles, which has the potential to further understanding of the limit-cycle oscillations observed in L-H transitions. The importance of large-scale stable modes and the triplet correlation time derived from saturation theory is tested in gyrokinetics. Numerical results show that the resonance between the stable and unstable modes through the coupling with zonal ows corresponds to long nonlinear interaction lifetimes, or large triplet correlation times, which increases nonlinear energy transfer and leads to strong turbulence suppression beyond any purely linear estimates. The triplet correlation time is further used to improve the standard quasilinear transport model for fast heat- ux prediction in gyrokinetics, which shows signicant improvement in cases that demonstrate heat- ux onset upshift from the linear critical gradient. The role of the coupling coecient in gyrokinetics is discussed and initial eorts to calculate the coupling coecient are described.

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.

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 Gyrokinetic Simulations in General Geometry and Applications to Collisional Damping of Zonal Flows written by Zhihong Lin and published by . This book was released on 2000 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Gyrokinetic Simulation of Microtearing Turbulence written by Hauke Doerk and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mode Analyses of Gyrokinetic Simulations of Plasma Microturbulence written by David R. Hatch and published by . This book was released on 2010 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Toroidal Gyrofluid Equations for Simulations of Tokamak Turbulence written by Michael Alan Beer and published by . This book was released on 1996 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Gyrokinetic Simulation of Current driven Instabilities written by Joseph Timothy McClenaghan and published by . This book was released on 2015 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The gyrokinetic toroidal code(GTC) capability has been extended for simulating current- driven instabilities in magnetized plasmas such as kink and resistive tearing modes with kinetic effects. This new gyrokinetic capability enables first-principles, integrated simulations of macroscopic magnetohydrodynamic(MHD) modes, which limit the performance of burning plasmas and threaten the integrity of fusion devices. The excitation and evolution of macroscopic MHD modes often depend on the kinetic effects at microscopic scales and the nonlinear coupling of multiple physical processes. GTC simulation in the fluid limit of the internal kink modes in cylindrical geometry has been verified by benchmarking with an MHD eigenvalue code. The global simulation domain covers the magnetic axis which is necessary for simulating the macroscopic MHD modes. Gyrokinetic simulations of the internal kink modes in the toroidal geometry find that ion kinetic effects significantly reduce the growth rate even when the banana orbit width is much smaller than the radial width of the perturbed current layer at the mode rational surface. This new GTC capability for current-driven instability has now been extended to simulate fishbone instabilities excited by energetic particles and resistive tearing modes. GTC has also been applied to study the internal kink modes in astrophysical jets that are formed around supermassive black holes. Linear simulations find that the internal kink modes in astrophysical jets are unstable with a broad eigenmode. Nonlinear saturation amplitude of these kink modes is observed to be small, suggesting that the jets can remain collimated even in the presence of the internal kink modes. Generation of a mean parallel electric field by the nonlinear dynamics of internal kink modes and the potential implication of this field on particle acceleration in jets has been examined.

Download or read book Comparisons of Gyrofluid and Gyrokinetic Simulations written by and published by . This book was released on 1994 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: The gyrokinetic and gyrofluid models show the most promise for large scale simulations of tokamak microturbulence. This paper discusses detailed comparisons of these two complementary approaches. Past comparisons with linear theory have been fairly good, therefore the emphasis here is on nonlinear comparisons. Simulations include simple two dimensional slab test cases, turbulent three dimensional slab cases, and toroidal cases, each modeling the nonlinear evolution of the ion temperature gradient instability. There is good agreement in both turbulent and coherent nonlinear slab comparisons in terms of the ion heat flux, both in magnitude and scaling with magnetic shear. However, the nonlinear saturation level for {vert_bar}[Phi]{vert_bar} in the slab comparisons show differences of approximately 40%. Preliminary toroidal comparisons show agreement within 50%, in terms of ion heat flux and saturation level.

Download or read book Analysis and Gyrokinetic Simulation of MHD Alfv n 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 ...