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Author : Oliver Zacharias
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (935 download)
Download or read book Gyrokinetic Simulations of Tearing Modes written by Oliver Zacharias and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joseph Timothy McClenaghan
Publisher :
ISBN 13 : 9781321672169
Total Pages : 123 pages
Book Rating : 4.6/5 (721 download)
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.
Author : Taweesak Jitsuk
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (144 download)
Download or read book Multi-scale Interactions of Tearing Modes with Microturbulence and Itg Saturation-channel Selection written by Taweesak Jitsuk and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global tearing modes (TMs) can interact among themselves or with small-scale instabilities, exerting profound influence on fusion plasma performance. Experiments in reversed-field pinches (RFPs) demonstrate that TMs couple, cascade, and cause robust transport, while partial suppression of their activity can result in enhanced confinement. The presence of unstable drift waves during the TM cascade in the RFP allows interactions with microinstabilities. Local gyrokinetic simulations with externally imposed magnetic perturbations modeling TMs have demonstrated that the magnetic perturbations erode zonal flows that are nonlinearly generated by the microinstabilities, resulting in higher turbulence levels. Similarly, when resonant magnetic perturbations (RMPs) are applied to mitigate edge-localized modes in tokamaks, the RMPs suppress the zonal flows, which in turn can increase the heat flux. These phenomena highlight the importance of multi-scale interactions between large-scale magnetic fluctuations and zonal-flow-regulated microturbulence, an incompletely understood topic. For a comprehensive understanding of these interactions, self-consistent computations simultaneously evolving TMs and small-scale fluctuations are needed. Here, calculations are performed with the global gyrokinetic code GENE, which was modified to include a background current density. This provides the TM drive, and it is verified that the modified GENE code properly models global TMs. Working towards multi-scale simulations, a non-reversed RFP discharge is studied; linear simulations show that the non-reversed equilibrium is unstable to large-scale TMs, which dominate in the core region, while small-scale density-gradient-driven TEMs dominate near the plasma edge. Nonlinear simulations with only TMs show that large-scale TMs in the core are coupled and excite smaller-scale stable TMs. The latter resonates at rational surfaces closer to the edge, where TEMs are active, indicating that multi-scale interactions are possible. In nonlinear global TEM simulations, zonal flows dominate the saturated state, leading to negligible transport in the absence of TMs, consistent with local simulations. When TMs and TEMs are simultaneously included in nonlinear simulations, TMs partially erode zonal flows. This erosion of zonal flows disrupts energy mediation by zonal flows, leading to a significant increase in heat flux. However, the zonal flows remain a dominant characteristic of fluctuations, causing the transport fluxes to remain much smaller than in experiments. To quantitatively reproduce experiments in future work, higher density gradients are required to weaken the zonal flows, or a stronger TM drive is needed to intensify the magnetic perturbations. These multi-scale simulations offer valuable insights for understanding RFP experiments and studying potential interactions of MHD phenomena and microturbulence in tokamaks. In contrast to TEM behavior, static magnetic perturbations do not strongly affect the ITG-driven turbulence of RFPs. This is because the ITG in RFPs is characterized by a slab limit and does not rely as strongly on zonal flows for saturation; instead, it depends on marginal modes. Zonal flows, on the other hand, play a crucial role in toroidal-ITG saturation. This prompts the exploration of saturation-channel selection rules that capture the preference of the toroidal limit for zonal flows and of the slab limit for marginal modes. Nonlinear coupling quantities are determined, and the triplet correlation time and mode overlap results are presented. Combining these metrics allows for predicting the dominant saturation channel for a given physical-parameter scenario, providing a powerful new tool that will aid a deeper understanding of nonlinear interactions and may also be used to enhance reduced models of anomalous transport.
Author :
Publisher :
ISBN 13 :
Total Pages : 47 pages
Book Rating : 4.:/5 (871 download)
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.
Author :
Publisher :
ISBN 13 :
Total Pages : 47 pages
Book Rating : 4.:/5 (871 download)
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.
Author : Xing Liu (Ph. D. in physics)
Publisher :
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.:/5 (15 download)
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.
Author : Laszlo Bardoczi
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.:/5 (17 download)
Download or read book Multi-Field/-Scale Interaction of Neoclassical Tearing Modes with Turbulence and Impact on Plasma Confinement written by Laszlo Bardoczi and published by . This book was released on 2017 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neoclassical Tearing Modes (NTMs) are a major impediment in the development of operational scenarios of present toroidal fusion devices. The multi-scale and non-linear interaction of NTMs with turbulence has been an active field of theoretical plasma research in the past decade for its role in plasma confinement. However, little to no experimental effort has been devoted to explore this interaction. As part of this thesis, dedicated experiments were conducted utilizing the full complement of the DIII-D turbulence diagnostics to study the effect of NTM on turbulence as well as the effect of turbulence on NTM growth. The first localized measurements of long and intermediate wavelength turbulent density fluctuations and long wavelength turbulent electron temperature fluctuations modified by magnetic islands are presented. These long and intermediate wavelengths correspond to the expected Ion Temperature Gradient (ITG) and Trapped Electron Mode (TEM) scales, respectively.\newpage Two regimes were observed when tracking density fluctuations during NTM evolution: (1) small islands are characterized by steep electron temperature radial profile and turbulence levels comparable to that of the background; (2) large islands have a flat electron temperature profile and reduced turbulence level at the O-point. Radially outside of the large island, the electron temperature profile is steeper and the turbulence level increased compared to the no or small island case. It was also found that turbulence is reduced in the O-point region compared to the X-point region. This helical structure of turbulence modification leads to a 15\% modulation of the density fluctuation power as the island rotates in the lab frame and this modulation is nearly in phase with the electron temperature modulation. These measurements were also used to determine the turbulence penetration length scale at the island separatrix and was found that the turbulence penetration length scale is on the order of the threshold island width for temperature flattening and turbulence reduction to occur at the O-point. This suggests that the physics of island transition could be related to turbulence penetration into the island. In addition, a novel, anisotropic, non-linear heat transport model of magnetic islands with spatially non-uniform cross-field thermal diffusivity was developed. This model was utilized to derive the diffusivity at the O-point from measured electron temperature data and it was found that the diffusivity at the O-point is 1 to 2 orders of magnitude smaller than the background plasma transport. As the anomalously large values of the diffusivity are often attributed to turbulence driven transport, the reduction of the diffusivity is consistent with the found turbulence reduction at the O-point. Complementing the experimental results of turbulence-NTM interaction described in this thesis, qualitative comparisons were carried out for the first time to GENE non-linear gyrokinetic turbulence simulations employing static magnetic islands. These simulations qualitatively replicate the measured 2D response of turbulence as well as the observed scaling with island size. The consequences of the observed NTM-turbulence interaction on the global plasma confinement were studied via analyses of simultaneous changes in NTM amplitude, plasma profiles, turbulence, fluxes and confinement. It was found that the global confinement degradation is intimately linked to the turbulence enhancement outside of the island region (induced by the island). Experimentally observed local turbulence and transport reduction at the O-point, as well as the effect of global confinement decrease was incorporated in the dynamical equation of NTMs, which shows that the NTM growth rate increases when turbulence and gradients are reduced inside the island (right after the transition from small to large island regime). Additionally, the shrinking of NTM islands due to strong temperature perturbations associated with Edge Localized Modes was observed. Simultaneous increase in turbulence level at the O-point was also observed and the data suggests that this temporal increase of turbulence level at the O-point accelerates NTM recovery after the ELM-crash. This is facilitated via the fast turbulent cross-field transport that leads to a rapid restoration of the flat profile (and bootstrap current perturbation) at the O-point. Finally, a series of low torque H-mode experiments were carried out to measure the perturbed ion temperature and toroidal flow profiles via CER across slowly rotating islands. Comparison of the observed flow perturbation to the gyrokinetic simulations suggests that large islands develop a vortex like plasma flow circulating around the O-point.
Author : David R. Hatch
Publisher :
ISBN 13 :
Total Pages : 171 pages
Book Rating : 4.:/5 (747 download)
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:
Author :
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (727 download)
Download or read book Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows written by and published by . This book was released on 2008 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n> 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q95 in the absence of obvious evidence that there is a strong q dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.
Author : James P. Martin Collar
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (12 download)
Download or read book Global Gyrokinetic Simulations of Kinetic Ballooning Modes written by James P. Martin Collar and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : C Wendell Horton, Jr
Publisher : #N/A
ISBN 13 : 9813225904
Total Pages : 522 pages
Book Rating : 4.8/5 (132 download)
Download or read book Turbulent Transport In Magnetized Plasmas (Second Edition) written by C Wendell Horton, Jr and published by #N/A. This book was released on 2017-07-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a few seconds with large machines, scientists and engineers have now created the fusion power of the stars in the laboratory and at the same time find the rich range of complex turbulent electromagnetic waves that transport the plasma confinement systems. The turbulent transport mechanisms created in the laboratory are explained in detail in the second edition of 'Turbulent Transport in Magnetized Plasmas' by Professor Horton.The principles and properties of the major plasma confinement machines are explored with basic physics to the extent currently understood. For the observational laws that are not understood — the empirical confinement laws — offering challenges to the next generation of plasma students and researchers — are explained in detail. An example, is the confinement regime — called the 'I-mode' — currently a hot topic — is explored.Numerous important problems and puzzles for the next generation of plasma scientists are explained. There is growing demand for new simulation codes utilizing the massively parallel computers with MPI and GPU methods. When the 20 billion dollar ITER machine is tested in the 2020ies, new theories and faster/smarter computer simulations running in near real-time control systems will be used to control the burning hydrogen plasmas.
Download or read book Gyrokinetic Electron and Fully Kinetic Ion Particle Simulation of Collisionless Plasma Dynamics written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully kinetic-particle simulations and hybrid simulations have been utilized for decades to investigate various fundamental plasma processes, such as magnetic reconnection, fast compressional waves, and wave-particle interaction. Nevertheless, due to disparate temporal and spatial scales between electrons and ions, existing fully kinetic-particle codes have to employ either unrealistically high electron-to-ion mass ratio, me/mi, or simulation domain limited to a few or a few ten's of the ion Larmor radii, or/and time much less than the global Alfven time scale in order to accommodate available computing resources. On the other hand, in the hybrid simulation, the ions are treated as fully kinetic particles but the electrons are treated as a massless fluid. The electron kinetic effects, e.g., wave-particle resonances and finite electron Larmor radius effects, are completely missing. Important physics, such as the electron transit time damping of fast compressional waves or the triggering mechanism of magnetic reconnection in collisionless plasmas is absent in the hybrid codes. Motivated by these considerations and noting that dynamics of interest to us has frequencies lower than the electron gyrofrequency, we planned to develop an innovative particle simulation model, gyrokinetic (GK) electrons and fully kinetic (FK) ions. In the GK-electron and FK-ion (GKe/FKi) particle simulation model, the rapid electron cyclotron motion is removed, while keeping finite electron Larmor radii, realistic me/mi ratio, wave-particle interactions, and off-diagonal components of electron pressure tensor. The computation power can thus be significantly improved over that of the full-particle codes. As planned in the project DE-FG02-05ER54826, we have finished the development of the new GK-electron and FK-ion scheme, finished its benchmark for a uniform plasma in 1-D, 2-D, and 3-D systems against linear waves obtained from analytical theories, and carried out a further convergence test and benchmark for a 2-D Harris current sheet against tearing mode and other instabilities in linear theories/models. More importantly, we have, for the first time, carried out simulation of linear instabilities in a 2-D Harris current sheet with a broad range of guide field BG and the realistic mi/me, and obtained important new results of current sheet instabilities in the presence of a finite BG. Indeed the code has accurately reproduced waves of interest here, such as kinetic Alfven waves, compressional Alfven/whistler wave, and lower-hybrid/modified two-stream waves. Moreover, this simulation scheme is capable of investigating collisionless kinetic physics relevant to magnetic reconnection in the fusion plasmas, in a global scale system for a long-time evolution and, thereby, produce significant new physics compared with both full-particle and hybrid codes. The results, with mi/me=1836 and moderate to large BG as in the real laboratory devices, have not been obtained in previous theory and simulations. The new simulation model will contribute significantly not only to the understanding of fundamental fusion (and space) plasma physics but also to DOE's SciDAC initiative by further pushing the frontiers of simulating realistic fusion plasmas.
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.
Author : Michael Alan Beer
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (713 download)
Download or read book Comparisons of Gyrofluid and Gyrokinetic Simulations written by Michael Alan Beer and published by . This book was released on 1994 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tjerk P. Straatsma
Publisher : CRC Press
ISBN 13 : 1351999249
Total Pages : 607 pages
Book Rating : 4.3/5 (519 download)
Download or read book Exascale Scientific Applications written by Tjerk P. Straatsma and published by CRC Press. This book was released on 2017-11-13 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes practical programming approaches for scientific applications on exascale computer systems Presents strategies to make applications performance portable Provides specific solutions employed in current application porting and development Illustrates domain science software development strategies based on projected trends in supercomputing technology and architectures Includes contributions from leading experts involved in the development and porting of scientific codes for current and future high performance computing resources
Author : Jerome L. V. Lewandowski
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (713 download)
Download or read book Optimized Loading for Particle-in-cell Gyrokinetic Simulations written by Jerome L. V. Lewandowski and published by . This book was released on 2004 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Zhixuan Wang
Publisher :
ISBN 13 : 9781321024265
Total Pages : 126 pages
Book Rating : 4.0/5 (242 download)
Download or read book Gyrokinetic Simulation of TAE in Fusion Plasmas written by Zhixuan Wang and published by . This book was released on 2014 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear gyrokinetic simulation of fusion plasmas finds a radial localization of the toroidal Alfvén eigenmodes (TAE) due to the non-perturbative energetic particles (EP) contribution. The EP-driven TAE has a radial mode width much smaller than that predicted by the magnetohydrodynamic (MHD) theory. The TAE radial position stays around the strongest EP pressure gradients when the EP profile evolves. The non-perturbative EP contribution is also the main cause for the breaking of the radial symmetry of the ballooning mode structure and for the dependence of the TAE frequency on the toroidal mode number. These phenomena are beyond the picture of the conventional MHD theory. Linear gyrokinetic simulation of the electron cyclotron heating (ECH) experiments on DIII-D successfully recover the TAE and RSAE. The EP profile, rather than the electron temperature, is found to be the key factor determining whether TAE or RSAE is the dominant mode in the system in our simulation. Investigation on the nonlinear gyrokinetic simulation model reveals a missing nonlinear term which has important contributions to the zonal magnetic fields. A new fluid-electron hybrid model is proposed to keep this nonlinear term in the lowest order fluid part. Nonlinear simulation of TAE using DIII-D parameters confirms the importance of this new term for the zonal magnetic fields. It is also found that zonal structures dominated by zonal electric fields are forced driven at about twice the linear growth rate of TAE in the linear phase. The zonal flows then limit the nonlinear saturation level by tearing the eigenmode structures apart. In the nonlinear phase of the simulation, the major frequency in the system chirps down by about 30% and stays there.
