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Author: Publisher: ISBN: Category : Languages : en Pages : 325
Book Description
In simulations of turbulent plasma transport due to long wavelength, (k(up tack)pi (less-than or equal to) 1), electrostatic drift-type instabilities we find that a nonlinear upshift of the effective threshold persists. This 'Dimits shift' represents the difference between the linear threshold, at the onset of instability, and the nonlinear threshold, where transport increases suddenly as the driving temperature gradient is increased. As the drive increases, the magnitudes of turbulent eddies and zonal ows grow until the zonal flows become nonlinearly unstable to 'tertiary' modes and their sheared ows no longer grow fast enough to strongly limit eddy size. The tertiary mode threshold sets the effective nonlinear threshold for the heat transport, and the Dimits shift arises when this occurs at a zonal flow magnitude greater than that needed to limit transport near the linear threshold. Nextgeneration tokamaks will likely benefit from the higher effective threshold for turbulent transport, and transport models should incorporate suitable corrections to linear thresholds. These gyrokinetic simulations are more realistic than previous reports of a Dimits shift because they include nonadiabatic electron dynamics, strong collisional damping of zonal flows, and finite electron and ion collisionality together with realistic shaped magnetic geometry. Reversing previously reported results based on idealized adiabatic electrons, we find that increasing collisionality reduces the heat flux because collisionality reduces the nonadiabatic electron drive.
Author: Publisher: ISBN: Category : Languages : en Pages : 325
Book Description
In simulations of turbulent plasma transport due to long wavelength, (k(up tack)pi (less-than or equal to) 1), electrostatic drift-type instabilities we find that a nonlinear upshift of the effective threshold persists. This 'Dimits shift' represents the difference between the linear threshold, at the onset of instability, and the nonlinear threshold, where transport increases suddenly as the driving temperature gradient is increased. As the drive increases, the magnitudes of turbulent eddies and zonal ows grow until the zonal flows become nonlinearly unstable to 'tertiary' modes and their sheared ows no longer grow fast enough to strongly limit eddy size. The tertiary mode threshold sets the effective nonlinear threshold for the heat transport, and the Dimits shift arises when this occurs at a zonal flow magnitude greater than that needed to limit transport near the linear threshold. Nextgeneration tokamaks will likely benefit from the higher effective threshold for turbulent transport, and transport models should incorporate suitable corrections to linear thresholds. These gyrokinetic simulations are more realistic than previous reports of a Dimits shift because they include nonadiabatic electron dynamics, strong collisional damping of zonal flows, and finite electron and ion collisionality together with realistic shaped magnetic geometry. Reversing previously reported results based on idealized adiabatic electrons, we find that increasing collisionality reduces the heat flux because collisionality reduces the nonadiabatic electron drive.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
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.
Author: Cole Darin Stephens Publisher: ISBN: Category : Languages : en Pages : 312
Book Description
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.
Author: A. Yoshizawa Publisher: CRC Press ISBN: 1420033697 Category : Science Languages : en Pages : 459
Book Description
Theory and modelling with direct numerical simulation and experimental observations are indispensable in the understanding of the evolution of nature, in this case the theory and modelling of plasma and fluid turbulence. Plasma and Fluid Turbulence: Theory and Modelling explains modelling methodologies in depth with regard to turbulence phenomena a
Author: Yan Yang Publisher: Springer ISBN: 9811381496 Category : Science Languages : en Pages : 144
Book Description
This book revisits the long-standing puzzle of cross-scale energy transfer and dissipation in plasma turbulence and introduces new perspectives based on both magnetohydrodynamic (MHD) and Vlasov models. The classical energy cascade scenario is key in explaining the heating of corona and solar wind. By employing a high-resolution hybrid (compact finite difference & WENO) scheme, the book studies the features of compressible MHD cascade in detail, for example, in order to approximate a real plasma cascade as “Kolmogorov-like” and to understand features that go beyond the usual simplified theories based on incompressible models. When approaching kinetic scales where plasma effects must be considered, it uses an elementary analysis of the Vlasov–Maxwell equations to help identify the channels through which energy transfer must be dissipated. In addition, it shows that the pressure–strain interaction is of great significance in producing internal energy. This analysis, in contrast to many other recent studies, does not make assumptions about wave-modes, instability or other specific mechanisms responsible for the dynamics – the results are direct consequences of the Vlasov–Maxwell system of equations. This is an important step toward understanding dissipation in turbulent collisionless plasma in space and astrophysics.
Author: Tom Neiser Publisher: ISBN: Category : Languages : en Pages : 163
Book Description
The main purpose of this thesis is the validation of the gyrokinetic method in the near-edge region of L-mode plasmas. Our primary finding is that gyrokinetic simulations are able to match the heat-flux in the near-edge region of an L-mode plasma at = 0.80 and = 0.90 within the combined statistical and systematic uncertainty of the experiment at the 1.6 and 1.3 levels, respectively. At = 0.95, gyrokinetic simulations are able to match the total experimental heat flux with nominal experimental parameters. In the big picture, this successful validation exercise helps push the gyrokinetic validation frontier closer to the L-mode edge region. In the course of this validation study, we make three secondary findings that may be helpful to the fusion community. First, the current heuristic rules for the relevance of multi-scale effects appear to be on the cautious side. Multi-scale simulations at = 0.80 suggest that single-scale simulations can be sufficient in a scenario when multi-scale effects are expected. This is helpful, because it could increase the realm of applicability of single-scale simulations, which are computationally more affordable than multi-scale simulations. Second, the effect of edge E B shear is found to become important already in the near-edge (at = 0.90) rather than at larger radial positions. This was unexpected and is relevant for future simulations in the near-edge. Third, nonlinear simulations at = 0.90 find a hybrid ion temperature gradient (ITG)/ trapped electron mode (TEM) scenario, which was not obvious from linear simulations due to the stability of ITG modes. This could also be an important result for spherical tokamaks, where ITG modes are more often linearly stable than in conventional tokamaks.
Author: Paul Crandall Publisher: ISBN: Category : Languages : en Pages : 229
Book Description
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.
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Author: Florian Merz
Author: Cole Darin Stephens
Author: Moritz Johannes Püschel
Author: A. Yoshizawa
Author: Yan Yang
Author: Tom Neiser
Author: Paul Crandall