Gyrofluid Model Research Articles

Gyro-fluid and two-fluid theory and simulations of edge-localized-modes

This paper reports on the theoretical and simulation results of a gyro-Landau-fluid extension of the BOUT++ code, which contributes to increasing the physics understanding of edge-localized-modes (ELMs). Large ELMs with low-to-intermediate-n peeling-ballooning (P-B) modes are significantly suppressed due to finite Larmor radius (FLR) effects when the ion temperature increases. For type-I ELMs, it is found from linear simulations that retaining complete first order FLR corrections as resulting from the incomplete “gyroviscous cancellation” in Braginskii's two-fluid model is necessary to obtain good agreement with gyro-fluid results for high ion temperature cases (Ti≽3 keV) when the ion density has a strong radial variation, which goes beyond the simple local model of ion diamagnetic stabilization of ideal ballooning modes. The maximum growth rate is inversely proportional to Ti because the FLR effect is proportional to Ti. The FLR effect is also proportional to toroidal mode number n, so for high n cases, the P-B mode is stabilized by FLR effects. Nonlinear gyro-fluid simulations show results that are similar to those from the two-fluid model, namely that the P-B modes trigger magnetic reconnection, which drives the collapse of the pedestal pressure. Due to the additional FLR-corrected nonlinear E × B convection of the ion gyro-center density, for a ballooning-dominated equilibrium the gyro-fluid model further limits the radial spreading of ELMs. In six-field two fluid simulations, the parallel thermal diffusivity is found to prevent the ELM encroachment further into core plasmas and therefore leads to steady state L-mode profiles. The simulation results show that most energy is lost via ion channel during an ELM event, followed by particle loss and electron energy loss. Because edge plasmas have significant spatial inhomogeneities and complicated boundary conditions, we have developed a fast non-Fourier method for the computation of Landau-fluid closure terms based on an accurate and tunable approximation. The accuracy and the fast computational scaling of the method have been demonstrated.

Fast gyrofluid reconnection in high temperature plasmas

The nonlinear evolution of collisionless magnetic reconnection in the presence of a strong guide field is analyzed on the basis of a gyrofluid model for compressible plasmas. It is found that, in a certain regime of plasma parameters, ion gyration contributes to generate two distinctive nonlinear acceleration phases of the growth rate. Furthermore, in the advanced nonlinear phase, finite values of the ion Larmor radius are identified to be responsible for a splitting of the narrow layer structures of ion guiding-center parallel velocity and density perturbations around the magnetic equilibrium null line.

Ion diamagnetic effects in gyrofluid collisionless magnetic reconnection

Ion diamagnetic effects on collisionless magnetic reconnection are investigated by means of numerical simulations of a Hamiltonian gyrofluid model. The work is focused in particular on the effects of inhomogeneous density equilibria in the large Δ' regime. The linear growth rates predicted by asymptotic theory are recovered. Nonlinearly the island shape is strongly modified and the flow changes its typical four-cell structure into a simpler two cell one. Contrary to the resistive reconnection process, we find that in Hamiltonian (i.e. collisionless) reconnection the width of the final saturated island is independent from the diamagnetic effects and the magnetic island grows up to the equilibrium scale length.

Progress in GYRO validation studies of DIII-D H-mode plasmas

The need for a validated predictive capability of turbulent transport in ITER is now widely recognized. However, to date most validation studies of nonlinear codes such as GYRO (Candy and Waltz 2003 J. Comput. Phys. 186 545) have focused upon low power L-mode discharges, which have significant differences in key dimensionless parameters such as ρ* = ρs/a from more ITER-relevant H-mode discharges. In order to begin addressing this gap, comparisons of the turbulent transport and fluctuations predicted by nonlinear GYRO simulations for a number of DIII-D (Luxon 2002 Nucl. Fusion 42 614) H-mode discharges to power balance analyses and experimental measurements are presented. The results of two H-mode studies are presented in this paper, this first of which investigates the importance of nonlocality at typical DIII-D H-mode ρ* values. Electrostatic global GYRO simulations of H-mode discharges at low and high rotation are shown to predict turbulence and transport levels lower than corresponding local simulations, and which are consistent with or slightly above experimental measurements and power balance analyses, even at ‘near-edge’ radii where gyrofluid and gyrokinetic models systematically underpredict turbulence and transport levels. The second study addresses the stabilizing effect of a significant density of energetic particles on turbulent transport. The results of local GYRO simulations of low-density QH-mode plasmas are presented, which model the fast beam ion population as a separate, dynamic ion species. The simulations show a significant reduction of transport with this fast ion treatment, which helps to understand previously reported results (Holland et al 2011 Phys. Plasmas 18 056113) in which GYRO simulations without this treatment significantly overpredicted (by a factor of 10 or more) power balance calculations. These results are contrasted with simulations of a high-density, low fast ion fraction QH-mode discharge, which predict transport levels consistent with power balance, regardless of the fast ion treatment.

Numerical investigation of a compressible gyrofluid model for collisionless magnetic reconnection

Ion Larmor radius effects on collisionless magnetic reconnection in the presence of a guide field are investigated by means of numerical simulations based on a gyrofluid model for compressible plasmas. Compressibility along the magnetic field is seen to favour the distribution of ion guiding center density along the neutral line, rather than along the separatrices, unlike the electron density. On the other hand, increasing ion temperature reduces the intensity of localized ion guiding center flows that develop in the direction parallel to the guide field. Numerical simulations suggest that the width of these bar-shaped velocity layers scale linearly with the ion Larmor radius. The increase of ion temperature radius causes also a reduction of the electron parallel velocity. As a consequence, it is found that the cusp-like current profiles distinctive of non-dissipative reconnection are strongly attenuated. The field structures are interpreted in terms of the behavior of the four topological invariants of the system. Two of these are seen to behave similarly to invariants of simpler models that do not account for parallel ion flow. The other two exhibit different structures, partly as a consequence of the small electron/ion mass ratio. The origin of these invariants at the gyrokinetic level is also discussed. The investigation of the field structures is complemented by an analysis of the energetics of the system.

The influence of finite Larmor radius effects on the radial interchange motions of plasma filaments

The influence of finite Larmor radius (FLR) effects on the perpendicular convection of isolated particle density filaments driven by interchange motions in magnetized plasmas is investigated using a two-moment gyrofluid model. By means of numerical simulations on a two-dimensional, bi-periodic domain perpendicular to the magnetic field, it is demonstrated that the radial velocities of the blob-like filaments are roughly described by the inertial scaling, which prescribes a velocity proportional to the square root of the summed electron and ion pressures times the square root of the blob width. Due to FLR effects, the poloidal up-down symmetry in the particle density field observed in the zero Larmor radius limit is broken. The symmetry breaking implies a poloidal motion of the blobs in the B×∇B direction. At later times, the direction of the poloidal motion is reversed when the blob is decelerated. It is shown that the spatial structure of the blobs depends on the ratio of the ion gyroradius to the initial filament size ρi/σ. Blobs with ρi/σ≳0.2 remain coherent as they move through the scrape-off layer, whereas blobs with ρi/σ≲0.1 form plume-like structures that loose their coherence and eventually become fragmented. After having traveled approximately five times their initial widths, coherent blobs carry ∼2–3 times the particle density of fragmented blobs. It is shown that FLR effects reduce mixing, stretching, and generation of small spatial scales in the particle density field by setting up a sheared flow surrounding the blob.

A Key to Improved Ion Core Confinement in the JET Tokamak: Ion Stiffness Mitigation due to Combined Plasma Rotation and Low Magnetic Shear

New transport experiments on JET indicate that ion stiffness mitigation in the core of a rotating plasma, as described by Mantica et al. [Phys. Rev. Lett. 102, 175002 (2009)] results from the combined effect of high rotational shear and low magnetic shear. The observations have important implications for the understanding of improved ion core confinement in advanced tokamak scenarios. Simulations using quasilinear fluid and gyrofluid models show features of stiffness mitigation, while nonlinear gyrokinetic simulations do not. The JET experiments indicate that advanced tokamak scenarios in future devices will require sufficient rotational shear and the capability of q profile manipulation.

A compressible Hamiltonian electromagnetic gyrofluid model

A Lie–Poisson bracket is presented for a four-field gyrofluid model with magnetic field curvature and compressible ions, thereby showing the model to be Hamiltonian. The corresponding Casimir invariants are presented, and shown to be associated to four Lagrangian invariants advected by distinct velocity fields. This differs from a cold ion limit, in which the Lie–Poisson bracket transforms into the sum of direct and semidirect products, leading to only three Lagrangian invariants.

Models for Sub-Alfvénic Magnetodynamics of Fusion Plasmas

The models describing macroscopic magnetic perturbations that evolve slowly compared to the Alfvén velocity are reviewed. The perturbations of interest include tearing modes, resistive interchange and ballooning modes, internal kink modes, resistive wall modes, and resonant magnetic perturbations. Two important features that distinguish the various models are their descriptions of parallel dynamics and of ion gyration. The evolution of macroscopic modes is generally characterized by resonances that result in the development of small scales. For processes involving magnetic reconnection, for example, all scales from the ion down to the electron Larmor radius are generated nonlinearly. The magnetohydrodynamic model assumes that the gradient lengths are always greater than the ion Larmor radius and thus is unable to properly describe the resonances. The drift models rely on a much more detailed description of the motion that enables them to capture many of the features of the short-scale phenomena, but they remain limited by their local description of the effects of gyration, and by their inability to describe the effects of wave-particle interactions in the parallel dynamics. These limitations are remedied by the gyrokinetic model, which provides a consistent, first-principles description of all the dynamics below the ion cyclotron frequency, but this model is computationally costly and its range of practical applicability remains to be established. Lastly, the gyrofluid models constitute a family of closures based on the moments of the gyrokinetic equations. These models offer an attractive compromise between fidelity and computational cost but have only recently begun to be applied to macroscopic evolution.

Stabilization of ion temperature gradient driven instability by a vortex flow

Stabilization of ion temperature gradient (ITG) driven mode by a large-scale vortex flow is investigated using a gyrofluid model in slab geometry. Extending a recent work [Z. X. Wang et al., Phys. Rev. Lett. 103, 015004 (2009)], the focus in this work is put on the effect of magnetic shear. It is shown that the vortex flow can effectively stabilize the ITG mode by inducing both radial and poloidal mode couplings. Furthermore, decreasing magnetic shear is identified to weaken the stabilizing role of the vortex flow. The effects of the magnetic shear on the ITG mode structure and on the growth rate in the presence of various shear flows are obtained and the relevant mechanisms are discussed in detail.

Noether derivation of exact conservation laws for dissipationless reduced-fluid models

The energy-momentum conservation laws for general reduced-fluid (e.g., gyrofluid) models are derived by Noether method from a general reduced variational principle. The reduced canonical energy-momentum tensor (which is explicitly asymmetric and has the Minkowski form) exhibits polarization and magnetization effects associated with dynamical reduction. In particular, the asymmetry in the reduced canonical momentum-stress tensor produces a nonvanishing reduced intrinsic torque that can drive spontaneous toroidal rotation in axisymmetric tokamak plasmas.

Gyrofluid simulations of collisionless reconnection in the presence of diamagnetic effects

The effects of the ion Larmor radius on magnetic reconnection are investigated by means of numerical simulations, with a Hamiltonian gyrofluid model. In the linear regime, it is found that ion diamagnetic effects decrease the growth rate of the dominant mode. Increasing ion temperature tends to make the magnetic islands propagate in the ion diamagnetic drift direction. In the nonlinear regime, diamagnetic effects reduce the final width of the island. Unlike the electron density, the guiding center density does not tend to distribute along separatrices and at high ion temperature, the electrostatic potential exhibits the superposition of a small scale structure, related to the electron density, and a large scale structure, related to the ion guiding-center density.

Electron response in gyrofluid simulations of magnetic reconnection

We investigate the behaviour of an electron population during the evolution of a spontaneous collisionless magnetic reconnection event, reproduced by a two-dimensional version of a Hamiltonian gyrofluid model. This model can be applied in electromagnetic problems where nonlinear effects are important, such as the sawtooth crash in the core of fusion devices. The electron dynamics in the presence of the reconnection fields is reconstructed by means of a test particle code, based on a relativistic Hamiltonian guiding centre formulation of the electron motion. The moments of the electron distribution function and the effects determined by the peculiar structure of the parallel electric field on the electron temperature in the reconnection region are reconstructed and compared with the corresponding quantities evolved by the fluid reconnection model.

GGEM: A Gyrofluid Model to be Used on Distributed Platforms

The study of core turbulence represents a key line of research in fusion plasmas. By adding collisions and electromagnetic induction to the parallel dynamics of the standard six-moment toroidal model, it is possible to study the gyrofluid electromagnetic phenomena in the context of edge turbulence with the GEM code. Currently, the code describes the fluctuation free-energy conservation in a gyrofluid model by means of the polarization equation which relates the ExB flow and eddy energy to the combinations of the potential, the density, and the perpendicular temperature. To do so, supercomputers have been used only to date. In this paper, we demonstrate its feasibility as a cluster application on a production environment based on any kind of distributed memory, enhancing in this way its scope. The scalability (which grows linearly with a correlation factor of 0.99978) and the correctness of our solution with respect to the previous GEM version have been evaluated in a local cluster of 88 nodes. The fault tolerance and the Grid suitability have been demonstrated by executing our application in the EUrope Fusion for ITER Applications infrastructure by adapting the code to this paradigm and by improving its parallel Grid performance. It can be employed on its own or belonging to workflows in order to perform a wider more complex analysis of fusion reactors.

Nonlinear gyrofluid simulations of collisionless reconnection

The Hamiltonian gyrofluid model recently derived by Waelbroeck et al. [Phys. Plasmas 16, 032109 (2009)] is used to investigate nonlinear collisionless reconnection with a strong guide field by means of numerical simulations. Finite ion Larmor radius gives rise to a cascade of the electrostatic potential to scales below both the ion gyroradius and the electron skin depth. This cascade is similar to that observed previously for the density and current in models with cold ions. In addition to density cavities, the cascades create electron beams at scales below the ion gyroradius. The presence of finite ion temperature is seen to modify, inside the magnetic island, the distribution of the velocity fields that advect two Lagrangian invariants of the system. As a consequence, the fine structure in the electron density is confined to a layer surrounding the separatrix. Finite ion Larmor radius effects produce also a different partition between the electron thermal, potential, and kinetic energy, with respect to the cold-ion case. Other aspects of the dynamics such as the reconnection rate and the stability against Kelvin-Helmholtz modes are similar to simulations with finite electron compressibility but cold ions.

Magnetic-island-induced ion temperature gradient mode

Characteristics of ion temperature gradient (ITG) instability in the presence of a magnetic island are investigated numerically using a gyrofluid model. It is shown that when the magnetic island is wide enough to produce a broad distribution of rational surfaces near the O-point region, the ITG perturbations at these rational surfaces form a radially global-type eigenmode with a fast growth rate, which is referred to as the magnetic-island-induced ITG mode. Moreover, the magnetic island also causes both radial and poloidal mode couplings, which play a stabilizing role.

Influence of the centrifugal force and parallel dynamics on the toroidal momentum transport due to small scale turbulence in a tokamak

The paper derives the gyro-kinetic equation in the comoving frame of a toroidally rotating plasma, including both the Coriolis drift effect [A. G. Peeters et al., Phys. Rev. Lett. 98, 265003 (2007)] as well as the centrifugal force. The relation with the laboratory frame is discussed. A low field side gyro-fluid model is derived from the gyro-kinetic equation and applied to the description of parallel momentum transport. The model includes the effects of the Coriolis and centrifugal force as well as the parallel dynamics. The latter physics effect allows for a consistent description of both the Coriolis drift effect as well as the ExB shear effect [R. R. Dominguez and G. M. Staebler, Phys. Fluids B 5, 3876 (1993)] on the momentum transport. Strong plasma rotation as well as parallel dynamics reduce the Coriolis (inward) pinch of momentum and can lead to a sign reversal generating an outward pinch velocity. Also, the ExB shear effect is, in a similar manner, reduced by the parallel dynamics and stronger rotation.

A Hamiltonian electromagnetic gyrofluid model

An isothermal truncation of the electromagnetic gyrofluid model of Snyder and Hammett [Phys. Plasmas 8, 3199 (2001)] is shown to be Hamiltonian. The corresponding noncanonical Lie–Poisson bracket and its Casimir invariants are presented. The invariants are used to obtain a set of coupled Grad–Shafranov equations describing equilibria and propagating coherent structures.

Role of secondary long wavelength structures in the saturation of electron temperature gradient driven turbulence

The dynamics of secondary long wavelength structures (LWSs) in electron temperature gradient (ETG) driven turbulence are investigated by performing gyrofluid simulations and modeling analyses in a slab geometry with an emphasis of the underlying nonlinear interaction processes. It is shown that the back-reaction of the secondary LWS on the ambient fluctuations essentially contributes to saturating ETG instability and limiting the electron transport. The LWS is nonlinearly generated mainly through the beating of the most unstable ETG modes, even a weak modulation instability. The back-reaction is identified as the enhanced stabilization of the ETG modes due to the streamer-type feature of the LWS, which dominantly produces a local poloidal mode coupling among unstable and highly damped spectral components to form a global mode, besides the suppression effect of the LWS due to the radial shearing decorrelation and/or the radial mode coupling. Finally, the correspondence between the LWS in the slab model and the quasimode observed in toroidal ETG simulation [Z. Lin et al., Phys. Plasmas 12, 056125 (2005)] and the importance of the nonlinear mode coupling in the multiscale turbulence interaction are discussed.

Gyrofluid simulation on the nonlinear excitation and radial structure of geodesic acoustic modes in ITG turbulence

The nonlinear excitation and saturation mechanism of geodesic acoustic mode (GAM), as well as its radial structure, in tokamak plasmas are investigated by applying a newly well-benchmarked gyrofluid model. At first, an empirical closure relation for the conventional three-field gyrofluid modeling is presented for ion temperature gradient (ITG) fluctuations and the GAMs. The zonal flow damping is precisely examined by comparing with theoretical predictions and other kinetic calculations. Then, a local code and the global version are advanced to simulate the nonlinear excitation of the GAMs by ITG fluctuations through the Reynolds stress. It is found that the GAM instability can be nonlinearly excited under the competition between the nonlinear driving and the collisionless damping. The pump amplitude threshold of the GAM instability is higher than that of the zonal flow instability. Meanwhile, the unstable GAMs are mainly saturated by the intrinsic Landau damping, which is different from the stationary zonal flow counterpart. It is testified that the sound waves are damped fluctuations in ITG turbulence. Furthermore, the radial structure of the GAMs is shown as krρi ≤ 1.0, which is shorter than that of the pure zonal flows.