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Gyrokinetics Simulation Of Energetic Particle Turbulence And Transport
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Book Synopsis Gyrokinetics Simulation of Energetic Particle Turbulence and Transport by :
Download or read book Gyrokinetics Simulation of Energetic Particle Turbulence and Transport written by and published by . This book was released on 2011 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Progress in research during this year elucidated the physics of precession resonance and its interaction with radial scattering to form phase space density granulations. Momentum theorems for drift wave-zonal flow systems involving precession resonance were derived. These are directly generalizable to energetic particle modes. A novel nonlinear, subcritical growth mechanism was identified, which has now been verified by simulation. These results strengthen the foundation of our understanding of transport in burning plasmas.
Book Synopsis Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas (GPS - TTBP) Final Report by :
Download or read book Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas (GPS - TTBP) Final Report written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this project is the development of the Gyrokinetic Toroidal Code (GTC) Framework and its applications to problems related to the physics of turbulence and turbulent transport in tokamaks, . The project involves physics studies, code development, noise effect mitigation, supporting computer science efforts, diagnostics and advanced visualizations, verification and validation. Its main scientific themes are mesoscale dynamics and non-locality effects on transport, the physics of secondary structures such as zonal flows, and strongly coherent wave-particle interaction phenomena at magnetic precession resonances. Special emphasis is placed on the implications of these themes for rho-star and current scalings and for the turbulent transport of momentum. GTC-TTBP also explores applications to electron thermal transport, particle transport; ITB formation and cross-cuts such as edge-core coupling, interaction of energetic particles with turbulence and neoclassical tearing mode trigger dynamics. Code development focuses on major initiatives in the development of full-f formulations and the capacity to simulate flux-driven transport. In addition to the full-f -formulation, the project includes the development of numerical collision models and methods for coarse graining in phase space. Verification is pursued by linear stability study comparisons with the FULL and HD7 codes and by benchmarking with the GKV, GYSELA and other gyrokinetic simulation codes. Validation of gyrokinetic models of ion and electron thermal transport is pursed by systematic stressing comparisons with fluctuation and transport data from the DIII-D and NSTX tokamaks. The physics and code development research programs are supported by complementary efforts in computer sciences, high performance computing, and data management.
Book Synopsis Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasma by :
Download or read book Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasma written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The UCLA work on this grant was to design and help implement an object-oriented version of the GTC code, which is written in Fortran90. The GTC code is the main global gyrokinetic code used in this project, and over the years multiple, incompatible versions have evolved. The reason for this effort is to allow multiple authors to work together on GTC and to simplify future enhancements to GTC. The effort was designed to proceed incrementally. Initially, an upper layer of classes (derived types and methods) was implemented which called the original GTC code 'under the hood.' The derived types pointed to data in the original GTC code, and the methods called the original GTC subroutines. The original GTC code was modified only very slightly. This allowed one to define (and refine) a set of classes which described the important features of the GTC code in a new, more abstract way, with a minimum of implementation. Furthermore, classes could be added one at a time, and at the end of the each day, the code continued to work correctly. This work was done in close collaboration with Y. Nishimura from UC Irvine and Stefan Ethier from PPPL. Ten classes were ultimately defined and implemented: gyrokinetic and drift kinetic particles, scalar and vector fields, a mesh, jacobian, FLR, equilibrium, interpolation, and particles species descriptors. In the second state of this development, some of the scaffolding was removed. The constructors in the class objects now allocated the data and the array data in the original GTC code was removed. This isolated the components and now allowed multiple instantiations of the objects to be created, in particular, multiple ion species. Again, the work was done incrementally, one class at a time, so that the code was always working properly. This work was done in close collaboration with Y. Nishimura and W. Zhang from UC Irvine and Stefan Ethier from PPPL. The third stage of this work was to integrate the capabilities of the various versions of the GTC code into one flexible and extensible version. To do this, we developed a methodology to implement Design Patterns in Fortran90. Design Patterns are abstract solutions to generic programming problems, which allow one to handle increased complexity. This work was done in collaboration with Henry Gardner, a computer scientist (and former plasma physicist) from the Australian National University. As an example, the Strategy Pattern is being used in GTC to support multiple solvers. This new code is currently being used in the study of energetic particles. A document describing the evolution of the GTC code to this new object-oriented version is available to users of GTC.
Book Synopsis Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas by :
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.
Book Synopsis Center for Gyrokinetic Particle Simulations of Turbulent Transport in Burning Plasmas by :
Download or read book Center for Gyrokinetic Particle Simulations of Turbulent Transport in Burning Plasmas written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the Final Technical Report for University of Colorado's portion of the SciDAC project 'Center for Gyrokinetic Particle Simulation of Turbulent Transport.' This is funded as a multi-institutional SciDAC Center and W.W. Lee at the Princeton Plasma Physics Laboratory is the lead Principal Investigator. Scott Parker is the local Principal Investigator for University of Colorado and Yang Chen is a Co-Principal Investigator. This is Cooperative Agreement DE-FC02-05ER54816. Research personnel include Yang Chen (Senior Research Associate), Jianying Lang (Graduate Research Associate, Ph. D. Physics Student) and Scott Parker (Associate Professor). Research includes core microturbulence studies of NSTX, simulation of trapped electron modes, development of efficient particle-continuum hybrid methods and particle convergence studies of electron temperature gradient driven turbulence simulations. Recently, the particle-continuum method has been extended to five-dimensions in GEM. We find that actually a simple method works quite well for the Cyclone base case with either fully kinetic or adiabatic electrons. Particles are deposited on a 5D phase-space grid using nearest-grid-point interpolation. Then, the value of delta-f is reset, but not the particle's trajectory. This has the effect of occasionally averaging delta-f of nearby (in the phase space) particles. We are currently trying to estimate the dissipation (or effective collision operator). We have been using GEM to study turbulence and transport in NSTX with realistic equilibrium density and temperature profiles, including impurities, magnetic geometry and ExB shear flow. Greg Rewoldt, PPPL, has developed a TRANSP interface for GEM that specifies the equilibrium profiles and parameters needed to run realistic NSTX cases. Results were reported at the American Physical Society - Division of Plasma Physics, and we are currently running convergence studies to ensure physical results. We are also studying the effect of parallel shear flows, which can be quite strong in NSTX. Recent long-time simulations of electron temperature gradient driven turbulence, show that zonal flows slowly grow algebraically via the Rosenbluth-Hinton random walk mechanism. Eventually, the zonal flow gets to a level where it shear suppresses the turbulence. We have demonstrated this behavior with Cyclone base-case parameters, except with a 30% lower temperature gradient. We can demonstrate the same phenomena at higher gradients, but so far, have been unable to get a converged result at the higher temperature gradient. We find that electron ion collisions cause the zonal flows to grow at a slower rate and results in a higher heat flux. So, far all ETG simulations that come to a quasi-steady state show continued build up of zonal flow, see it appears to be a universal phenomena (for ETG). Linear and nonlinear simulations of Collisional and Collisionless trapped electron modes are underway. We find that zonal flow is typically important. We can, however, reproduce the Tannert and Jenko result (that zonal flow is unimportant) using their parameters with the electron temperature three times the ion temperature. For a typical weak gradient core value of density gradient and no temperature gradient, the CTEM is dominant. However, for a steeper density gradient (and still no temperature gradient), representative of the edge, higher k drift-waves are dominant. For the weaker density gradient core case, nonlinear simulations using GEM are routine. For the steeper gradient edge case, the nonlinear fluctuations are very high and a stationary state has not been obtained. This provides motivation for the particle-continuum algorithm. We also note that more physics, e.g. profile variation and equilibrium ExB shear flow should be significantly stabilizing, making such simulations feasible using standard delta-f techniques. This research is ongoing.
Book Synopsis SciDAC Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas by :
Download or read book SciDAC Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: During the first year of the SciDAC gyrokinetic particle simulation (GPS) project, the GPS team (Zhihong Lin, Liu Chen, Yasutaro Nishimura, and Igor Holod) at the University of California, Irvine (UCI) studied the tokamak electron transport driven by electron temperature gradient (ETG) turbulence, and by trapped electron mode (TEM) turbulence and ion temperature gradient (ITG) turbulence with kinetic electron effects, extended our studies of ITG turbulence spreading to core-edge coupling. We have developed and optimized an elliptic solver using finite element method (FEM), which enables the implementation of advanced kinetic electron models (split-weight scheme and hybrid model) in the SciDAC GPS production code GTC. The GTC code has been ported and optimized on both scalar and vector parallel computer architectures, and is being transformed into objected-oriented style to facilitate collaborative code development. During this period, the UCI team members presented 11 invited talks at major national and international conferences, published 22 papers in peer-reviewed journals and 10 papers in conference proceedings. The UCI hosted the annual SciDAC Workshop on Plasma Turbulence sponsored by the GPS Center, 2005-2007. The workshop was attended by about fifties US and foreign researchers and financially sponsored several gradual students from MIT, Princeton University, Germany, Switzerland, and Finland. A new SciDAC postdoc, Igor Holod, has arrived at UCI to initiate global particle simulation of magnetohydrodynamics turbulence driven by energetic particle modes. The PI, Z. Lin, has been promoted to the Associate Professor with tenure at UCI.
Book Synopsis Final Report on Work for Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas -- Tools for Improved Data Logistics by :
Download or read book Final Report on Work for Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas -- Tools for Improved Data Logistics written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This project focused on the use of Logistical Networking technology to address the challenges involved in rapid sharing of data from the the Center's gyrokinetic particle simulations, which can be on the order of terabytes per time step, among researchers at a number of geographically distributed locations. There is a great need to manage data on this scale in a flexible manner, with simulation code, file system, database and visualization functions requiring access. The project used distributed data management infrastructure based on Logistical Networking technology to address these issues in a way that maximized interoperability and achieved the levels of performance the required by the Center's application community. The work focused on the development and deployment of software tools and infrastructure for the storage and distribution of terascale datasets generated by simulations running at the National Center for Computational Science at Oak Ridge National Laboratory.
Book Synopsis Gyrokinetic Particle Simulation of Compressible Electromagnetic Turbulence in High-? Plasmas by :
Download or read book Gyrokinetic Particle Simulation of Compressible Electromagnetic Turbulence in High-? Plasmas written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Supported by this award, the PI and his research group at the University of California, Irvine (UCI) have carried out computational and theoretical studies of instability, turbulence, and transport in laboratory and space plasmas. Several massively parallel, gyrokinetic particle simulation codes have been developed to study electromagnetic turbulence in space and laboratory plasmas. In space plasma projects, the simulation codes have been successfully applied to study the spectral cascade and plasma heating in kinetic Alfven wave turbulence, the linear and nonlinear properties of compressible modes including mirror instability and drift compressional mode, and the stability of the current sheet instabilities with finite guide field in the context of collisionless magnetic reconnection. The research results have been published in 25 journal papers and presented at many national and international conferences. Reprints of publications, source codes, and other research-related information are also available to general public on the PI's webpage (http://phoenix.ps.uci.edu/zlin/). Two PhD theses in space plasma physics are highlighted in this report.
Book Synopsis Gyrokinetic Simulations of Turbulent Transport in Fusion Plasmas by :
Download or read book Gyrokinetic Simulations of Turbulent Transport in Fusion Plasmas written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the final report for a DOE award that was targeted at understanding and simulating turbulence and transport in plasma fusion devices such as tokamaks.
Book Synopsis Center for Gyrokinetic/MHD Hybrid Simulation of Energetic Particle Physics in Toroidal Plasmas (CSEPP). Final Report by :
Download or read book Center for Gyrokinetic/MHD Hybrid Simulation of Energetic Particle Physics in Toroidal Plasmas (CSEPP). Final Report written by and published by . This book was released on 2012 with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt: At Colorado University-Boulder the primary task is to extend our gyrokinetic Particle-in-Cell simulation of tokamak micro-turbulence and transport to the area of energetic particle physics. We have implemented a gyrokinetic ion/massless fluid electron hybrid model in the global [delta] f-PIC code GEM, and benchmarked the code with analytic results on the thermal ion radiative damping rate of Toroidal Alfven Eigenmodes (TAE) and with mode frequency and spatial structure from eigenmode analysis. We also performed nonlinear simulations of both a single-n mode (n is the toroidal mode number) and multiple-n modes, and in the case of single-n, benchmarked the code on the saturation amplitude vs. particle collision rate with analytical theory. Most simulations use the f method for both ions species, but we have explored the full-f method for energetic particles in cases where the burst amplitude of the excited instabilities is large as to cause significant re-distribution or loss of the energetic particles. We used the hybrid model to study the stability of high-n TAEs in ITER. Our simulations show that the most unstable modes in ITER lie in the rage of 10
Book Synopsis Gyrokinetic Simulation of Global Turbulent Transport Properties in Tokamak Experiments by :
Download or read book Gyrokinetic Simulation of Global Turbulent Transport Properties in Tokamak Experiments written by and published by . This book was released on 2006 with total page 92505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.
Book Synopsis Turbulent Transport In Magnetized Plasmas by : C Wendell Horton, Jr
Download or read book Turbulent Transport In Magnetized Plasmas written by C Wendell Horton, Jr and published by World Scientific. This book was released on 2012-08-22 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 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.
Book Synopsis Turbulence and Transport in Enhanced Confinement Regimes of Tokamaks by :
Download or read book Turbulence and Transport in Enhanced Confinement Regimes of Tokamaks written by and published by . This book was released on 1996 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Gyrokinetic Studies of Particle Transport in Tokamaks by : Carlos Andres Estrada-Mila
Download or read book Gyrokinetic Studies of Particle Transport in Tokamaks written by Carlos Andres Estrada-Mila and published by . This book was released on 2006 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation a systematic study of particle transport in tokamaks, using gyrokinetic simulations and theory, is presented. This work can be divided into three major parts. The first part studies particle transport in pure plasmas and investigates the origin and nature of flows against density gradients, also known as particle pinches. It is found that these pinches, which are primarily driven by temperature gradients, can also be responsible for the density peaking observed in experiments such as ASDEX-U, DIII-D or JET. The second part of this work studies plasmas with multiple ion species. First, we study helium ash transport and its effects in the core of a reactor plasma, finding that a helium pinch driven by finite toroidicity can be created in some cases. Second, we study deuterium and tritium plasmas from the point of view of isotope flow separation, finding that in a 50-50 deuterium-tritium plasma, a small fuel separation may occur. Finally, the last part studies the behavior of energetic species in reactor plasmas. It is found that alpha particles interact strongly with the background turbulence. Perhaps the most surprising finding is that the fluxes per particle of alphas can be stronger than the fluxes per particle of deuterium (i.e. main ion), as opposed to ``conventional wisdom'' which assumes that species with large gyroradii do not significantly interact with the turbulence.
Book Synopsis Gyrokinetic Particle Simulation of Neoclassical Transport by : W. W. Lee
Download or read book Gyrokinetic Particle Simulation of Neoclassical Transport written by W. W. Lee and published by . This book was released on 1995 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
