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The quasilinear mixing-length approach to efficient prediction of transport in fusion devices is improved to account for the ‘Dimits’ upshift between linear and nonlinear critical pressure gradients in zonal-flow-saturated turbulence regimes. This modification uses the frequency mismatch between modes interacting turbulently to track changes in saturation efficiency. Near criticality, energy is transferred exclusively to stable eigenmodes, rapidly increasing the efficacy of the nonlinearity. The modified quasilinear model is able to predict below-threshold turbulent ion-temperature-gradient-driven transport accurately and also yields significantly improved predictions for trapped-electron-mode transport.

We report on a detailed study of magnetic fluctuations in the JET pedestal, employing basic theoretical considerations, gyrokinetic simulations, and experimental fluctuation data to establish the physical basis for their origin, role, and distinctive characteristics. We demonstrate quantitative agreement between gyrokinetic simulations of microtearing modes (MTMs) and two magnetic frequency bands with corresponding toroidal mode numbers n = 4 and 8. Such disparate fluctuation scales, with substantial gaps between toroidal mode numbers, are commonly observed in pedestal fluctuations. Here we provide a clear explanation, namely the alignment of the relevant rational surfaces (and not others) with the peak in the ω * profile, which is localized in the steep gradient region of the pedestal. We demonstrate that a global treatment is required to capture this effect. Nonlinear simulations suggest that the MTM fluctuations produce experimentally-relevant transport levels and saturate by relaxing the background electron temperature gradient, slightly downshifting the fluctuation frequencies from the linear predictions. Scans in collisionality are compared with a simple MTM dispersion relation. At the experimental points considered, MTM growth rates can either increase or decrease with collision frequency depending on the parameters thus defying any simple characterization of collisionality dependence.

Microtearing turbulence in an idealized pedestal scenario is found to saturate via zonal fields, while also exciting strong zonal flows; a concurrent upshift of the non-linear critical gradient is observed. The zonal flows cause electron-temperature-gradient-driven turbulence to be ameliorated. When applying resonant magnetic perturbations, the prompt charge loss off the flux surface erodes the zonal flow, leading to higher electron-scale fluxes, while leaving microtearing saturation physics unaffected.

We theoretically assess two mechanisms thought to be responsible for the enhanced performance observed in plasma discharges of the Wendelstein 7-X stellarator experiment fueled by pellet injection. The effects of the ambipolar radial electric field and the electron density peaking on the turbulent ion heat transport are separately evaluated using large-scale gyrokinetic simulations. The essential role of the stellarator magnetic geometry is demonstrated, by comparison with a tokamak.

Microtearing (MT) turbulence affects plasma confinement and profile evolution in many different magnetic-confinement scenarios, ranging from tokamak core plasmas to the H-mode pedestal and from spherical tokamaks to reversed-field pinches. Thus, an urgent need exists to design and test reduced models of MT turbulence and transport. Here, a heuristic quasilinear model is composed and verified by comparing its predictions against nonlinear MT simulations. It is found to yield good predictions of magnetic flutter transport as key parameters are varied: the collision frequency, the electron temperature gradient, and the normalized plasma pressure.

Ion-temperature-gradient-driven (ITG) turbulence is compared for two quasi-symmetric (QS) stellarator configurations to determine the relationship between linear growth rates and nonlinear heat fluxes. We focus on the quasi-helically symmetric (QHS) stellarator HSX and the quasi-axisymmetric (QAS) stellarator NCSX. In normalized units, HSX exhibits higher growth rates than NCSX, while heat fluxes in gyro-Bohm units are lower in HSX. These results hold for simulations made with both adiabatic and kinetic electrons. The results show that HSX has a larger number of subdominant modes than NCSX and that eigenmodes are more spatially extended in HSX. We conclude that the consideration of nonlinear physics is necessary to accurately assess the heat flux due to ITG turbulence when comparing QS stellarator equilibria.

Energy transfer in ion-temperature-gradient-driven (ITG) turbulence and its role in modeling transport are examined for finite normalized plasma pressure β for a number of test cases and experimental discharges. The analysis shows that like the zero-β case, finite-β ITG turbulence saturates by nonlinear energy transfer to stable modes mediated by a zonal flow. Electromagnetic effects reliably increase stable mode amplitudes but affect heat fluxes only at the ≈5% level. The most important change with increased β is an increase in the correlation time of the triplet interaction of the unstable mode, stable mode, and zonal flow, thus providing a heightened nonlinear energy transfer efficiency, which allows the instability to saturate at lower amplitude. The heat flux is examined in connection with nonlinear electromagnetic stabilization, the phenomenon where the flux falloff with β is more pronounced than the falloff predicted by quasilinear transport models. The inclusion of the triplet correlation time in the quasilinear model captures most of the nonlinearly enhanced stabilization for the configurations studied here.Energy transfer in ion-temperature-gradient-driven (ITG) turbulence and its role in modeling transport are examined for finite normalized plasma pressure β for a number of test cases and experimental discharges. The analysis shows that like the zero-β case, finite-β ITG turbulence saturates by nonlinear energy transfer to stable modes mediated by a zonal flow. Electromagnetic effects reliably increase stable mode amplitudes but affect heat fluxes only at the ≈5% level. The most important change with increased β is an increase in the correlation time of the triplet interaction of the unstable mode, stable mode, and zonal flow, thus providing a heightened nonlinear energy transfer efficiency, which allows the instability to saturate at lower amplitude. The heat flux is examined in connection with nonlinear electromagnetic stabilization, the phenomenon where the flux falloff with β is more pronounced than the falloff predicted by quasilinear transport models. The inclusion of the triplet correlation time in ...

The physical causes for the strong stabilizing effect of finite plasma β on ion-temperature-gradient-driven turbulence, which far exceeds quasilinear estimates, are identified from nonlinear gyrokinetic simulations. The primary contribution stems from a resonance of frequencies in the dominant nonlinear interaction between the unstable mode, the stable mode, and zonal flows, which maximizes the triplet correlation time and therefore the energy transfer efficiency. A modification to mixing-length transport estimates is constructed, which reproduces nonlinear heat fluxes throughout the examined β range.

Non-physical effects of discretization schemes on simulations of plasma microturbulence are investigated, and different types of hyperdiffusion terms in the gyrokinetic Vlasov equation are employed to cancel or mitigate these effects. Widely applicable rules on how to operate parallel spatial and velocity space diffusion – to avoid numerically excited high- k ∥ modes and recurrence phenomena, respectively – are presented. The impact of diffusion terms on and the applicability of these findings to results obtained in the context of a benchmark scenario are demonstrated.

The emerging understanding of instability-driven plasma-turbulence saturation in terms of energy transfer to stable modes in the same scale range as the instability is employed to derive a saturation theory for the toroidal branch of ion temperature gradient turbulence that provides the scaling of turbulence and zonal flow levels for all physical parameters. The theory is based on the eigenmode decomposition of a nonlinear fluid model, which is subjected to a statistical closure and simplified via an ordering expansion consistent with zonal-flow catalyzed energy transfer from the unstable mode to the stable mode at large scale. Solution of the closed energy balance equations yields a turbulence level that is proportional to the ratio of the zonal flow damping rate and the inverse of the triplet correlation time of the zonal-flow catalyzed wavenumber triplet interaction. The zonal flow energy is proportional to the ratio of the growth rate and the inverse triplet correlation time. The saturation scalings a...

The robustness and the effect of zonal flows in trapped electron mode (TEM) turbulence and Ion Temperature Gradient (ITG) turbulence in the reversed-field pinch (RFP) are investigated from numerical solutions of the gyrokinetic equations with and without magnetic external perturbations introduced to model tearing modes. For simulations without external magnetic field perturbations, zonal flows produce a much larger reduction of transport for the density-gradient-driven TEM turbulence than they do for the ITG turbulence. Zonal flows are studied in detail to understand the nature of their strong excitation in the RFP and to gain insight into the key differences between the TEM- and ITG-driven regimes. The zonal flow residuals are significantly larger in the RFP than in tokamak geometry due to the low safety factor. Collisionality is seen to play a significant role in the TEM zonal flow regulation through the different responses of the linear growth rate and the size of the Dimits shift to collisionality, wh...

The core micro-instability characteristics of hybrid and baseline plasmas in a selected set of JET plasmas with carbon wall are investigated through local linear and non-linear and global linear gyro-kinetic simulations with the GYRO code [J. Candy and E. Belli, General Atomics Report GA-A26818 (2011)]. In particular, we study the role of plasma pressure on the micro-instabilities, and scan the parameter space for the important plasma parameters responsible for the onset and stabilization of the modes under experimental conditions. We find that a good core confinement due to strong stabilization of the micro-turbulence driven transport can be expected in the hybrid plasmas due to the stabilizing effect of the fast ion pressure that is more effective at the low magnetic shear of the hybrid discharges. While parallel velocity gradient destabilization is important for the inner core, at outer radii the hybrid plasmas may benefit from a strong quench of the turbulence transport by $\mathbf{E}\times\mathbf{B}$ rotation shear., accepted for publication in Nuclear Fusion

A current sheet susceptible to the tearing instability is used to drive reconnection turbulence in the presence of a strong guide field. Through nonlinear gyrokinetic simulations, the dependencies of central quantities such as the heating rate on parameters like collisionality or plasma β are studied, revealing that linear physics tends to predict only some aspects of the quasi-saturated state, with the nonlinear cascade responsible for additional features. For the solar corona, it is demonstrated that the kinetic heating associated with this type of turbulence agrees quantitatively with observational volumetric heating rates. In the context of short particle acceleration events, the self-consistent emergence of plasmoids or flux ropes in the turbulent bath is found to be important: ubiquitously occurring merger events of these objects cause strong bursts in the heating rate, the timescale of which is consistent with nanoflare observations. Furthermore, anisotropy of the temperature fluctuations is seen to emerge, hinting at a new means of generating coronal ion temperature anisotropy in the absence of cyclotron resonances.

This overview of results from the MST reversed field pinch program summarizes physics im- portant for the advancement of the RFP as well as for improved understanding of toroidal magnetic confinement in general. Topics include energetic particle effects, 3D helical equilibria, and density limit studies, microturbulence, ion heating, and magnetic self-organization physics. With neutral beam injection, several bursty energetic particle (EP) modes are observed. The profiles of the magnetic and density fluctuations associated with these EP-modes are measured using an FIR interferometer- polarimeter. Equilibrium reconstructions of the quasi-single-helicity 3D helical state are provided by the V3FIT code that now incorporates several of MST's advanced diagnostics. A predator-prey theoretical model based on sheared flow and/or magnetic field has been developed that captures key QSH dynamics. Upgraded pellet injection permits study of density and limits over MST's full range of operation, and an MST-record line-average density of 0 : 9 10 20 { m 3 ( n { n G 1 : 4 ) has been obtained. Plasma exhibits saturation at tot § 20% for a wide range of density, 0 : 2 + n { n G + 1 : 6 . Gyrokinetic simulations (GENE) based on experimental toroidal equilibrium reconstructions predict unstable trapped electron modes. Nonlinear simulations show that the "Dimits shift" is large and persists at finite . Experimentally, small-scale density fluctuations are detected in improved confine- ment plasmas. Impurity ion temperature measurements reveal a charge-to-mass-ratio dependence in the rapid heating that occurs during a sawtooth crash. Also, a toroidal asymmetry in the ion temper- ature is measured, correlated with 3D magnetic structure associated with tearing modes. Magnetic self-organization studies include measurements and modeling of the dynamo emf in standard RFP operation as well as with an applied ac inductive electric field to investigate the dynamics of oscillating field current drive (OFCD). Extended MHD computation for standard RFP conditions using NIMROD predicts dynamical coupling of current and plasma flow relaxation. The dynamo emf has also been measured when OFCD is applied, strengthening the understanding of and possibility for steady-state current sustainment using inductive current drive.

Extensive linear and non-linear gyrokinetic simulations, including kinetic electrons, collisions, flow shear, realistic geometry, electromagnetic effects, impurities, as well as perpendicular and parallel magnetic fluctuations, and linear MHD analyses performed respectively with the GENE and MISHKA codes, have shown for the first time that the large population of fast ions found in the plasma core under particular heating conditions has a strong impact on core microturbulence and edge MHD. In particular, nonlinear electromagnetic stabilization of Ion Temperature Gradient (ITG) turbulence can be very much enhanced by fast ion pressure gradients. These results can explain the improved ion energy confinement regime observed in L-mode ion heat transport studies at the JET tokamak which manifests itself as a reduction of the ion temperature stiffness and which, until now had not been reproduced by nonlinear gyrokinetic simulations. The same effect has been shown to be important in high- hybrid scenarios from JET and JT-60U with a large population of fast ions. Up to 4 times of lower ion heat flux for the same R/LTi is obtained in these plasmas when the fast ions contribution is taken into account. This can explain the higher core ion temperature gradients obtained in these regimes as the flow shear is found to play a much weaker role. In addition to the core transport stabilization, the fast ions have been seen to favorably impact edge transport. The high core total pressure achieved due to fast ions modifies the Shafranov-shift leading to a pedestal pressure which can increase by 10% when the extra core pressure is taken into account. Therefore, a virtuous circle starts in these plasmas when the fast ions increase the total core pressure without increasing the turbulence drive, even reducing the ITG microturbulence. This leads to an improved edge pedestal pressure by means of the increased Shafranov-shift in a manner unachievable by simple thermal pressure, which is strongly limited by microturbulence. This work was supported by EURATOM and carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

Recent experimental observations at JET show evidence of reduced ion temperature profile stiffness, hypothesised to be due to concomitant low magnetic shear (s) and significant toroidal rotational flow shear. Non-linear gyrokinetic simulations are performed, aiming to investigate the physical mechanism behind the observations. A comprehensive set of simulations are carried out, comparing the impact on the ion heat flux of various parameters that differ within the data-set. These parameters include q, s, rotation, effect of rotation on the magnetohydrodynamic (MHD) equilibrium, R/L_n, beta_e, Z_eff, and the fast particle content. The effect of toroidal flow shear itself is not predicted by the simulations to lead to a significant reduction in ion heat flux, due both to an insufficient magnitude of flow shear and significant parallel velocity gradient destabilisation. It is however found that non-linear electromagnetic effects due to both thermal and fast-particle pressure gradients, even at low beta_e, can significantly reduce the profile stiffness. A total of five discharges are examined, at both inner and outer radii. For all cases studied, the simulated and experimental ion heat flux values agree within reasonable variations of input parameters around the experimental uncertainties., Comment: 33 pages, 25 figures, 4 tables. To be submitted to Nucl. Fusion

From numerical solutions of a gyrokinetic model for ion temperature gradient turbulence it is shown that nonlinear coupling is dominated by three-wave interactions that include spectral components of the zonal flow and damped subdominant modes. Zonal flows dissipate very little energy injected by the instability, but facilitate its transfer from the unstable mode to dissipative subdominant modes, in part due to the small frequency sum of such triplets. Although energy is transferred to higher wave numbers, consistent with shearing, a large fraction is transferred to damped subdominant modes within the instability range. This is a new aspect of regulation of turbulence by zonal flows.

Nonlinear electromagnetic stabilization by suprathermal pressure gradients found in specific regimes is shown to be a key factor in reducing tokamak microturbulence, augmenting significantly the thermal pressure electromagnetic stabilization. Based on nonlinear gyrokinetic simulations investigating a set of ion heat transport experiments on the JET tokamak, described by Mantica et al. [Phys. Rev. Lett. 107 135004 (2011)], this result explains the experimentally observed ion heat flux and stiffness reduction. These findings are expected to improve the extrapolation of advanced tokamak scenarios to reactor relevant regimes., 5 pages, 5 figures

Providing an important step towards validating gyrokinetics under comparatively little-explored conditions, simulations of pressure-gradient-driven plasma turbulence in the Large Plasma Device (LAPD) are compared with experimental observations. The corresponding signatures confirm the existence of a novel regime of turbulence, based on the recently-discovered gradient-driven drift coupling (GDC) instability, which is thus confirmed as a candidate mechanism for turbulence in basic, space and astrophysical plasmas. Despite the limitations of flux-tube gyrokinetics for this scenario, when accounting for box size scaling by applying a scalar factor , agreement between simulations and experiment improves to within a factor of two for key observables: compressional magnetic, density, and temperature fluctuations, both in amplitude and structure. Thus, a first, strong indication is presented that the GDC instability seen in gyrokinetics appears to operate in the experiment and that the essential instability physics is present in the numerical model. Overall, the gyrokinetic framework and its numerical implementation in the Gene code therefore perform well for LAPD plasmas very different from their brethren in fusion experiments.

In light of planned ITER operation, it is important to improve understanding of fast particle behavior. This work focuses on the influence of both electrostatic and electromagnetic background microturbulent fields by studying passive fast ions in gyrokinetic turbulence simulations. Since magnetic fluctuations are the primary source of fast particle diffusion at high energies, the threshold values are investigated where this regime starts to dominate over the effects of electrostatic turbulence. Comparisons with analytical theory are presented.

Nonlinear excitation of linearly stable microtearing modes--with zonal modes acting as a catalyst--is shown to be responsible for the near-ubiquitous magnetic stochasticity and associated electromagnetic electron heat transport in electromagnetic gyrokinetic simulations of plasma microturbulence.

The nonlinear dynamics of microtearing modes in standard tokamak plasmas are investigated by means of ab initio gyrokinetic simulations. The saturation levels of the magnetic field fluctuations can be understood in the framework of a balance between (small poloidal wave number) linear drive and small-scale dissipation. The resulting heat transport is dominated by the electron magnetic component, and the transport levels are found to be experimentally relevant. Microtearing modes thus constitute another candidate for explaining turbulent transport in such toroidal systems.

Via nonlinear gyrokinetic simulations, microturbulent transport is investigated for electromagnetic trapped electron mode (TEM) and ion temperature gradient (ITG) tokamak core turbulence with β up to and beyond the kinetic ballooning mode threshold. Deviations from linear expectations are explained by zonal flow activity in the TEM case. For the ITG scenario, β-induced changes are observed in the nonlinear critical gradient upshift—from a certain β, a strong increase is observed in the Dimits shift. Additionally, a Rechester–Rosenbluth-type model for magnetic transport is applied, and the amplitudes of magnetic field fluctuations are quantified for different types of turbulence.

Plasma microinstabilities are one of the key physics problems on the way to efficient power plants based on nuclear fusion. They cause anomalous heat and particle transport which significantly degrades the plasma confinement quality, thus preventing self-sustaining plasma burning in present-day experiments. Hence, extensive experimental studies are dedicated to understanding and predicting turbulence features. They are accompanied by numerical simulations which are typically based on the gyrokinetic theory. While experimental diagnostics are about to address the role of fine-scale turbulence within a bath of large-scale turbulence, nonlinear gyrokinetic codes are already able to investigate turbulent transport at a wide range of wave numbers simultaneously. However, such simulations covering several space and time scales self-consistently are computationally extremely demanding and thus need to be massively parallelized.

Recent results on electromagnetic turbulence from gyrokinetic studies in different magnetic configurations are overviewed, detailing the physics of electromagnetic turbulence and transport, and the effect of equilibrium magnetic field scale lengths. Ion temperature gradient (ITG) turbulence is shown to produce magnetic stochasticity through nonlinear excitation of linearly stable tearing-parity modes. The excitation, which is catalyzed by the zonal flow, produces an electron heat flux proportional to beta(2) that deviates markedly from quasilinear theory. Above a critical beta known as the non-zonal transition (NZT), the magnetic fluctuations disable zonal flows by allowing electron streaming that shorts zonal potential between flux surfaces. This leads to a regime of very high transport levels. Kinetic ballooning mode (KBM) saturation is described. For tokamaks saturation involves twisted structures arising from magnetic shear; for helical plasmas oppositely inclined convection cells interact by mutual shearing. Microtearing modes are unstable in the magnetic geometry of tokamaks and the reversed field pinch (RFP). In NSTX instability requires finite collisionality, large beta, and is favored by increasing magnetic shear and decreasing safety factor. In the RFP, a new branch of microtearing with finite growth rate at vanishing collisionality is shown from analytic theory to require the electron grad-B/curvature drift resonance. However, gyrokinetic modeling of experimental MST RFP discharges at finite beta reveals turbulence that is electrostatic, has large zonal flows, and a large Dimits shift. Analysis shows that the shorter equilibrium magnetic field scale lengths increase the critical gradients associated with the instability of trapped electron modes, ITG and microtearing, while increasing beta thresholds for KBM instability and the NZT.

The gyrokinetic GENE code is used to study the inter-ELM H-mode pedestal profile evolution for an ASDEX Upgrade discharge. Density gradient driven trapped electron modes are the dominant pedestal instability during the early density-buildup phase. Nonlinear simulations produce particle transport levels consistent with experimental expectations. Later inter-ELM phases appear to be simultaneously constrained by electron temperature gradient (ETG) and kinetic ballooning mode (KBM) turbulence. The electron temperature gradient achieves a critical value early in the ELM cycle, concurrent with the appearance of both microtearing modes and ETG modes. Nonlinear ETG simulations demonstrate that the profiles lie at a nonlinear critical gradient. The nominal profiles are stable to KBM, but moderate increases in β are sufficient to surpass the KBM threshold. Certain aspects of the dynamics support the premise of KBM-constrained pedestal evolution; the density and temperature profiles separately undergo large changes, but in a manner that keeps the pressure profile constant and near the KBM limit.

Experimental discharges with pulsed poloidal current drive (PPCD) in the Madison Symmetric Torus reversed field pinch are investigated using a semi-analytic equilibrium model in the gyrokinetic turbulence code Gene. PPCD cases, with plasma currents of 500 kA and 200 kA, exhibit a density-gradient-driven trapped electron mode (TEM) and an ion temperature gradient mode, respectively. Relative to expectations of tokamak core plasmas, the critical gradients for the onset of these instabilities are found to be greater by roughly a factor of the aspect ratio. A significant upshift in the nonlinear TEM transport threshold, previously found for tokamaks, is confirmed in nonlinear reversed field pinch simulations and is roughly three times the threshold for linear instability. The simulated heat fluxes can be brought in agreement with measured diffusivities by introducing a small, resonant magnetic perturbation, thus modeling the residual fluctuations from tearing modes. These fluctuations significantly enhance tr...

Zonal flows, widely accepted to be the secondary instability process leading to the nonlinear saturation of ion temperature gradient modes, are shown to grow at higher rates relative to the linear mode amplitude as the plasma pressure β is increased—thus, confirming that zonal flows become increasingly important in the turbulent dynamics at higher β. At the next level of nonlinear excitation, radial corrugations of the distribution function (zonal flow, zonal density, and zonal temperature) are demonstrated to modify linear growth rates moderately through perturbed-field, self-consistent gradients: on smaller scales, growth rates are reduced below the linear rate. In particular, excitation of kinetic ballooning modes well below their usual threshold is not to be expected under normal conditions. These findings strengthen the theory of the non-zonal transition [M. J. Pueschel et al., Phys. Rev. Lett. 110, 155005 (2013)].

Fast magnetic reconnection, believed to be a mechanism for rearranging the magnetic topology and creating energetic particles in many astrophysical and laboratory plasmas, is investigated with the nonlinear gyrokinetic code Gene. After some code-code benchmarking, extensive linear studies are presented, covering all relevant parameter dependencies of two-dimensional slab reconnection. The results are used to ascertain the validity of a fluid model and understand for which parameters it fails to describe the physics correctly. The nonlinear phase is studied for two scenarios: decaying and driven turbulence. In the former case, the initially injected energy is cascading towards the largest scales of the system, whereas a fully turbulent, quasi-stationary state develops if the system is driven through a Krook-type term in the gyrokinetic Vlasov equation.

A cross-comparison and verification of state-of-the-art European codes describing gradient-driven plasma turbulence in the core and edge regions of tokamaks, carried out within the EFDA Task Force on Integrated Tokamak Modelling, is presented. In the case of core ion temperature gradient (ITG) driven turbulence with adiabatic electrons (neglecting trapped particles), good/reasonable agreement is found between various gyrokinetic/gyrofluid codes. The main physical reasons for some deviations observed in nonlocal simulations are discussed. The edge simulations agree very well on collisionality scaling and acceptably well on beta scaling (below the MHD boundary) for cold-ion cases, also in terms of the non-linear mode structure.

Numerical simulations of electron temperature gradient (ETG) turbulence are presented that characterize the ETG fluctuation spectrum, establish limits to the validity of the adiabatic ion model often employed in studying ETG turbulence, and support the tentative conclusion that plasma-operating regimes exist in which ETG turbulence produces sufficient electron heat transport to be experimentally relevant. We resolve prior controversies regarding simulation techniques and convergence by benchmarking simulations of ETG turbulence from four microturbulence codes, demonstrating agreement on the electron heat flux, correlation functions, fluctuation intensity, and rms flow shear at fixed simulation cross section and resolution in the plane perpendicular to the magnetic field. Excellent convergence of both continuum and particle-in-cell codes with time step and velocity-space resolution is demonstrated, while numerical issues relating to perpendicular (to the magnetic field) simulation dimensions and resolution are discussed. A parameter scan in the magnetic shear, s, demonstrates that the adiabatic ion model is valid at small values of s (s < 0.4 for the parameters used in this scan) but breaks down at higher magnetic shear. A proper treatment employing gyrokinetic ions reveals a steady increase in the electron heat transport with increasing magnetic shear, reaching electron heat transport rates consistent with analyses of experimental tokamak discharges. (c) 2006 American Institute of Physics.

Analytical and numerical work is used in tandem to address the problem of turbulent transport of energetic ions in magnetized plasmas. It is shown that orbit averaging is not valid under rather generic conditions, and that perpendicular decorrelation effects lead to a slow 1/E decay of the electrostatic particle diffusivity of beam ions, while the respective magnetic quantity is even independent of the particle energy E.

The observation of distinct peaks in tokamak core reflectometry measurements—named quasi-coherent-modes (QCMs)—are identified as a signature of trapped-electron-mode (TEM) turbulence (Arnichand et al 2016 Plasma Phys. Control. Fusion 58 014037). This phenomenon is investigated with detailed linear and nonlinear gyrokinetic simulations using the Gene code. A Tore-Supra density scan is studied, which traverses through a linear (LOC) to saturated (SOC) ohmic confinement transition. The LOC and SOC phases are both simulated separately. In the LOC phase, where QCMs are observed, TEMs are robustly predicted unstable in linear studies. In the later SOC phase, where QCMs are no longer observed, ion-temperature-gradient (ITG) modes are identified. In nonlinear simulations, in the ITG (SOC) phase, a broadband spectrum is seen. In the TEM (LOC) phase, a clear emergence of a peak at the TEM frequencies is seen. This is due to reduced nonlinear frequency broadening of the underlying linear modes in the TEM regime compared with the ITG regime. A synthetic diagnostic of the nonlinearly simulated frequency spectra reproduces the features observed in the reflectometry measurements. These results support the identification of core QCMs as an experimental marker for TEM turbulence.