Tokamak Plasma Turbulence Research Articles

Gyrokinetic flux-driven simulations in mixed TEM/ITG regime using a delta-f PIC scheme with evolving background

In the context of global gyrokinetic simulations of turbulence using a particle-in-cell framework, verifying the delta-f assumption with a fixed background distribution becomes challenging when determining quasi-steady state profiles corresponding to given sources over long time scales, where plasma profiles can evolve significantly. The advantage of low relative sampling noise afforded by the delta-f scheme is shown to be retained by considering the background as a time-evolving Maxwellian with time-dependent density and temperature profiles. Implementation of this adaptive scheme to simulate electrostatic collisionless flux-driven turbulence in tokamak plasmas show small and nonincreasing sampling noise levels, which would otherwise increase indefinitely with a stationary background scheme. The adaptive scheme furthermore allows one to reach numerically converged results of quasi-steady state with much lower marker numbers.

Lagrangian Chaotic Mixing in a Nonlinear Model of Resistive Drift-wave Turbulence in Tokamak Plasmas

In fusion plasma, numerical simulations are commonly employed to investigate the confinement properties of plasma in the bulk region of tokamaks. The modified Hasegawa-Wakatani (MHW) equations are used to model the behavior of the plasma, which enables us to understand the radial transport in two-dimensional numerical simulations of electrostatic resistive drift-wave turbulence. By utilizing the MHW equations, we have gained insights into the low-to-high confinement (L-H) transitions that occur spontaneously in the plasma when it moves from a low confinement stage, characterized by turbulent flow, to a turbulence-suppressed regime known as zonal flow. To investigate these transitions, we vary the value of a control parameter \(\alpha\), which is related to adiabaticity, in numerical simulations, and observe the transition between the two regimes. This simplified model of L-H transitions can provide valuable information for tokamaks. To identify the Lagrangian coherent structures (LCS) and to better characterize the chaotic mixing during the L-H transition, we computed the finite-time Lyapunov exponent (FTLE) of the calculated velocity field derived from the electrostatic potential. We further compared the statistics of the chaotic mixing of the two regimes. The results of our study offer insights into the turbulent transport processes in magnetic confinement fusion plasmas.

Global gyrofluid simulations of turbulence in tokamak plasmas

We develop a tokamak plasma turbulence simulation code based on a fluid model using the BOUT++ framework. The model corresponds to a global extension of the local gyrofluid model (Beer and Hammett, 1996 [11]), where external sources and neoclassical equilibrium flows are included but some higher-order kinetic effect terms are ignored for the global nonlinear simulation. Hyper-viscous damping terms are introduced to compensate for the stabilizing effect of the missing kinetic terms. With an appropriate hyper-viscosity, we obtain reasonable linear and nonlinear results on ion temperature gradient modes compared to global gyrokinetic simulations. We perform global flux-driven simulations with self-consistently evolving profiles with external heat sources/sinks. A spectral analysis of heat flux in flux-driven turbulence exhibits a broad 1/f (f is the frequency) spectrum observed in gyrokinetic simulations, indicating the prevalence of self-organized criticality-like heat avalanches. We also investigate the effect of an externally imposed vorticity source on turbulence suppression and transport barrier formation. It is shown that internal transport barrier can form even for a monotonic safety factor profile when a sufficiently strong vorticity source is applied.

Experimental Evidence of Intrinsic Current Generation by Turbulence in Stationary Tokamak Plasmas.

High-β_{θe} (a ratio of the electron thermal pressure to the poloidal magnetic pressure) steady-state long-pulse plasmas with steep central electron temperature gradient are achieved in the Experimental Advanced Superconducting Tokamak. An intrinsic current is observed to be modulated by turbulence driven by the electron temperature gradient. This turbulent current is generated in the countercurrent direction and can reach a maximum ratio of 25% of the bootstrap current.Gyrokinetic simulations and experimental observations indicate that the turbulence is the electron temperature gradient mode (ETG). The dominant mechanism for the turbulent current generation is due to the divergence of ETG-driven residual flux of current. Good agreement has been found between experiments and theory for the critical value of the electron temperature gradient triggering ETG and for the level of the turbulent current. The maximum values of turbulent current and electron temperature gradient lead to the destabilization of an m/n=1/1 kink mode, which by counteraction reduces the turbulence level (m and n are the poloidal and toroidal mode number, respectively). These observations suggest that the self-regulation system including turbulence, turbulent current, and kink mode is a contributing mechanism for sustaining the steady-state long-pulse high-β_{θe} regime.

Excitation of zonal flow by intermediate-scale toroidal electron temperature gradient turbulence

On the basis of gyrokinetic theory, we derive nonlinear equations for the zonal flow (ZF) generation in intermediate-scale electron temperature gradient (ETG) turbulence (with wavelength much shorter than the ion Larmor radius but much longer than the electron Larmor radius) in nonuniform tokamak plasmas. Both the spontaneous and forced generation of ZFs are kept on the same footing. The resultant Schrödinger equation for the ETG amplitude is characterized by a Navier–Stokes type nonlinearity, which is typically stronger than the Hasegawa–Mima type nonlinearity resulting from the fluid approximation. The physics underlying the three stages of ZF generation process is clarified, and the role of parallel mode structure decoupling is discussed. It is found that ZFs can be more easily excited in the intermediate-scale ETG turbulence than in the short wavelength regime.

Internal measurement of magnetic turbulence in ELMy H-mode tokamak plasmas

Magnetic turbulence is directly observed internally in the pedestal of ELMy H-mode tokamak plasmas using a newly developed Faraday-effect polarimetry measurement. Fluctuation amplitude is δbr≥15 G (150–500 kHz), with a ratio of magnetic to density fluctuation |δbr/B|/|δn/n|≥0.15. Magnetic turbulence is identified as resulting from micro-tearing-instability and mode growth accompanied by degraded plasma confinement is observed.

The role of collisionless trapped electron mode turbulence on removal of helium ash and transport of deuterium-tritium ions

Removal of helium ash and the anomalous transport of deuterium (D) and tritium (T) ions driven by collisionless trapped electron mode (CTEM) turbulence in tokamak plasmas with weak magnetic shear are studied. We derive the eigenvalue of CTEM with helium ash, and calculate the quasi-linear turbulent fluxes of helium ash, D and T ions simultaneously. Based on the analytical results, the parametric dependence of CTEM instability as well as the anomalous transport of helium ash and D-T ions is investigated, in order to explore the parameter region that is favorable for expelling more helium ash than D and T ions. It is found that helium ash with higher temperature and steeper density profile plays a role of destabilizing CTEM instability, and has higher transport level than that of T ions. We also find that increasing electron temperature and flattening electron density profile are favorable for exhausting helium ash. Isotopic effects (i.e. increasing the fraction of T ions) enhance the transport of both helium ash and D-T ions. Moreover, the trend of stronger transport level of helium ash than that of D-T ions is enhanced by raising electron temperature and flattening electron density profile as well as isotopic effects. Besides, the diffusivity is much larger than the convection. This indicates that the CTEM turbulence driven helium ash transport is favorable for removing helium ash under the parameter region used in the present paper. The possible relevance of our theoretical results to experimental observations is also discussed.

Recent progress on turbulence and multi-scale interactions in tokamak plasmas

Studies on nonlinear interactions and multi-scale physics are crucial in the physical understanding of the turbulence and transport in the complex nonlinear system of fusion plasmas. This paper reviews recent studies on the turbulence and the related transport. The prominent results are mainly from tokamaks, such as HL-2A, Tore Supra and J-TEXT. First, turbulence behaviors and its role in transport will be introduced. Critical gradients in heat and particle transports have been observed and reproduced by simulations. Turbulence modes and its role in the transport are identified using advanced diagnostics. The measured turbulence transition is consistent with the observation of particle convection reversal and the simulation prediction. In addition, the excitation of an electromagnetic turbulence by either edge self-accumulated or externally seeded impurities has been observed. The impurity-driven turbulence plays an essential role in regulating the impurity transport. Then, the effect of plasma flows on turbulence and multi-scale interactions (micro-turbulence, meso-scale fluctuations, and large scale MHD activities) will be presented. Moreover, a new meso-scale electrostatic fluctuation has been observed. The results indicate that geodesic acoustic modes and magnetic fluctuations can transfer energy through nonlinear synchronization. At last, the enhancement of nonlinear interactions by external actuators will be reported. Theoretical studies in comparisons with experimental findings will be discussed.

A new hybrid simulation model for tokamak plasma turbulence

A novel kinetic-fluid hybrid model is developed for electromagnetic plasma turbulence in tokamak geometry. In this model, by combining kinetic and fluid approaches, ions are treated with the conventional gyrokinetic particle-in-cell method, while the bounce averaged drift-kinetic method is used for trapped electrons, and passing electrons are modeled as a massless fluid to avoid numerical instabilities due to fast parallel motions of electrons. The new model is implemented in a global gyrokinetic code gKPSP (Kwon et al., 2012). In benchmark tests for linear electromagnetic instabilities, this model shows good agreement with the global gyrokinetic codes GENE and GTC. By combining kinetic and fluid approaches, it is demonstrated that electromagnetic simulations can be reliably performed with only a modest increase of numerical costs. The new model is employed to study the effects of plasma elongation on kinetic ballooning mode (KBM). It is found that the elongation has a stabilizing effect on KBM, which is consistent with the broadened parallel wave number spectrum of KBM instabilities.

A conservative gyrofluid model: Effect of closure on energetics

We develop a conservative gyrofluid model that is suitable for global flux-driven simulations of electrostatic tokamak plasma turbulence. On the basis of the general gyrofluid moment equations, we derive energy equations which enable us to manipulate the impact of a gyrofluid closure on energetics. We demonstrate that an artificial manipulation of high order moment contributions to gyrofluid moment equations via a closure model can lead to the violation of the energy conservation. A fluid closure is also found to restrict the maximum attainable order of finite Larmor radius terms, implying the loss of dynamical information by the closure.

Multi-scale multi-mode nonlinear interaction in tokamak plasma turbulence with moderate small-scale shear flow

Effects of moderate small-scale shear flow, e.g., which may be created by the trapped electron mode, on electromagnetic (EM) ion-scale turbulence in tokamak plasmas are numerically investigated via a self-consistent Landau-fluid model. A modeling analysis is carried out in slab geometry to reveal the underlying mechanism of the multi-scale multi-mode nonlinear interaction. Results show that while a Kelvin–Helmholtz (KH) instability with long wavelengths may be excited by the shear flows to dominate the multi-scale EM fluctuation, shorter wavelength ion temperature gradient (ITG) modes experience multiple quasi-steady (QS) stages with enhanced fluctuation level through different driving and saturation mechanisms. One mechanism is the secondary ITG instability due to the decrease in flow stabilization modified by the zonal flow. Meanwhile, the other one is the modulational interaction between the EM ITG and KH modes through the nonlinear mode coupling. Moreover, the synergism of these two mechanisms may sustain the final QS state near the marginal KH instability threshold. Complex linear and nonlinear interactions among multiple modes and external flow, as well as self-generated zonal flow, result in a weak dependence of the final saturation level of the dominant EM ITG mode on the small-scale flow amplitude. The turbulent heat transport is visibly suppressed by weaker shear flow, but is almost not affected by stronger shear flows. The underlying mechanism is elaborated.

Diffusive impurity transport driven by trapped particle turbulence in tokamak plasmas

The diffusive impurity transport as a function of charge and mass numbers is investigated in ion driven or electron driven turbulence, in the limit of zero impurity temperature gradient. It is found that the impurity transport decreases slightly with increasing mass number and depends much more strongly on the charge number. Moreover, this transport depends on the nature of the instability that drives turbulence. The impurity flux due to Trapped Electron Mode (TEM) turbulence increases with the charge number Z. In contrast, it is found to decrease with Z when the Trapped Ion Mode (TIM) dominated. In order to explain these observations, the quasilinear flux is derived and is compared with the results obtained from the nonlinear simulations. Quasilinear theory qualitatively reproduces the gyrokinetic numerical observations.

Neoclassical and turbulent E × B flows in flux-driven gyrokinetic simulations of Ohmic tokamak plasmas

The interplay of flows and turbulence in Ohmic FT-2 tokamak plasmas is analysed via gyrokinetic simulations with the flux-driven ELMFIRE code. The simulation predictions agree qualitatively with analytical estimates for the scaling of the neoclassical radial electric field as a function of collisionality for ad hoc parameters. For the experimental parameters, the global full-f modeling agrees well with the analytical estimates in a neoclassical setting, while including kinetic electrons and impurities has a small impact. Allowing turbulence to develop modifies the flow profile through relaxation of profiles caused by turbulent transport, non-adiabatic response of passing electrons around rational surfaces, and turbulent flow drive. Geodesic acoustic mode (GAM) is the main zonal flow component in the simulations, and its frequency and amplitude agree with theoretical predictions and experimental measurements. In the simulations, the non-linear energy transfer from the turbulence to the flows through the Reynolds force is balanced by the collisional flow dissipation. Temporal relationship between the oscillating flow, Reynolds force, and turbulent particle flux is consistent with the fundamental physics picture of GAM modulating turbulent transport on the time scale of the mode. Experimental evidence also suggests anti-correlation of GAM amplitude and turbulent fluctuations.

The parallel boundary condition for turbulence simulations in low magnetic shear devices

Flux tube simulations of plasma turbulence in stellarators and tokamaks typically employ coordinates which are aligned with the magnetic field lines. Anisotropic turbulent fluctuations can be represented in such field-aligned coordinates very efficiently, but the resulting non-trivial boundary conditions involve all three spatial directions, and must be handled with care. The standard ‘twist-and-shift’ formulation of the boundary conditions (Beer et al 1995 Phys. Plasmas 2 2687) was derived assuming axisymmetry and is widely used because it is efficient, as long as the global magnetic shear is not too small. A generalization of this formulation is presented, appropriate for studies of non-axisymmetric, stellarator symmetric configurations, as well as for axisymmetric configurations with small global shear. The key idea is to replace the ‘twist’ of the standard approach (which accounts only for global shear) with the integrated local shear. This generalization allows one significantly more freedom when choosing the extent of the simulation domain in each direction, without losing the natural efficiency of field line-following coordinates. It also corrects some errors associated with naive application of axisymmetric boundary conditions to non-axisymmetric configurations. Simulations of stellarator turbulence that employ the generalized boundary conditions generally require much less resolution than simulations that use the conventional, axisymmetric boundary conditions. We also demonstrate the surprising result that (at least in some cases) an easily implemented but manifestly incorrect formulation of the boundary conditions does not change important predicted quantities, such as the turbulent heat flux.

Intrinsic current driven by electromagnetic electron temperature gradient turbulence in tokamak plasmas

The mean parallel current density evolution equation is presented using the electromagnetic (EM) gyrokinetic equation. There are two types of intrinsic current driving mechanisms resulting from EM electron temperature gradient (ETG) turbulence. The first type is the divergence of residual turbulent flux including a residual stress-like term and a kinetic stress-like term. The second type is a residual turbulent source, which is driven by the correlation between density and parallel electric field fluctuations. The intrinsic current density driven by the residual turbulent source is negligible as compared to that driven by the residual turbulent flux. The ratio of intrinsic current density driven by EM ETG turbulence to the background bootstrap (BS) current density is estimated. The local intrinsic current density driven by the residual turbulent flux for mesoscale variation of turbulent flux can reach about 80% of the BS current density in the core region of an ITER standard scenario, but there is no net intrinsic current on a global scale. Based on this, the local intrinsic current driven by EM micro-turbulence and its effects on local modification of the profile of the safety factor may need to be carefully taken into account in future devices with high , which is the ratio between electron pressure to magnetic pressure.

Fast-ion stabilization of tokamak plasma turbulence

A significant reduction of the turbulence-induced anomalous heat transport has been observed in recent studies of magnetically confined plasmas in the presence of a significant fast-ion fractions. Therefore, the control of fast-ion populations with external heating might open the way to more optimistic scenarios for future fusion devices. However, little is known about the parameter range of relevance of these fast-ion effects which are often only highlighted in correlation with substantial electromagnetic fluctuations. Here, a significant fast ion induced stabilization is also found in both linear and nonlinear electrostatic gyrokinetic simulations which cannot be explained with the conventional assumptions based on pressure profile and dilution effects. Strong wave-fast particle resonant interactions are observed for realistic parameters where the fast particle trace approximation clearly failed and explained with the help of a reduced Vlasov model. In contrast to previous interpretations, fast particles can actively modify the Poisson field equation—even at low fast particle densities where dilution tends to be negligible and at relatively high temperatures, i.e. T < 30Te. Further key parameters controlling the role of the fast ions are identified in the following and various ways of further optimizing their beneficial impact are explored. Finally, possible extensions into the electromagnetic regime are briefly discussed and the relevance of these findings for ITER standard scenarios is highlighted.

Influence of hot and cold neutrals on scrape-off layer tokamak plasma turbulence

The modification of interchange plasma turbulence in the scrape-off layer (SOL) region by the presence of hot and cold neutral gas molecules has been studied. The nonlinear equations have been solved numerically using two different simulations (“uniform-Te” and “varying-Te”), and the results obtained from both of the models have been compared. The hot neutrals, responsible for the increase in the electron density in the SOL, also account for more ionization of the cold molecules. The effect of hot and cold neutrals on the interchange turbulence is almost similar in the “uniform-Te” model, but in the “varying-Te” model, the influence of the hot neutrals is very small, specifically in the far SOL region. The neutral gas in the “varying Te” model decreases the heat load on the material walls by about 7%. A reduction in the radial velocity by about 25% and effective diffusion coefficient of the plasma particles has been found by the influence of the neutral gas.

Benchmarking of flux-driven full-F gyrokinetic simulations

Two full-F global gyrokinetic codes are benchmarked to compute flux-driven ion temperature gradient (ITG) turbulence in tokamak plasmas. For this purpose, the Semi-Lagrangian code GYrokinetic SEmi-LAgrangian and the Eulerian code GT5D are employed, which solve the full-F gyrokinetic equation with a realistic fixed flux condition. The equilibrium poloidal flow profile formation processes are benchmarked and compared against the local neoclassical theory. The simulations above are carried out without turbulence, which agree well with each other and with the theoretical estimates. Here, a lot of attention has been paid to the boundary conditions, which have huge impacts on the global shape of radial electric field. The behaviors of micro-instabilities are benchmarked for linear and nonlinear cases without a heat source, where we found good agreements in the linear growth rates and nonlinear critical gradient level. In the nonlinear case, initial conditions are chosen to be identical since they dominate the transient turbulence behavior. Using the appropriate settings for the boundary and initial conditions obtained in the benchmarks above, a flux-driven ITG turbulence simulation is carried out. The avalanche-like transport is assessed with a focus on spatio-temporal properties. A statistical analysis is performed to discuss this self-organized criticality (SOC) like behaviors, where we found a 1/f spectra and a transition to 1/f3 spectra at high-frequency side in both codes. Based on these benchmarks, it is verified that the SOC-like behavior is robust and not dependent on numerics.

Global 3D two-fluid simulations of the tokamak edge region: Turbulence, transport, profile evolution, and spontaneous E × B rotation

We present global two-fluid simulations of L-mode edge tokamak plasma turbulence and profile evolution including both closed field lines and the scrape-off-layer. We consider a shifted-circle magnetic configuration with realistic Alcator C-Mod inner wall limited discharge parameters. The dominant driver of turbulence in the simulations is the resistive ballooning mode. We observe spontaneous E × B rotation in the electron diamagnetic drift direction in the closed flux region in all cases. We explain this based on the steady state ion continuity relation ∇·nv→i≈0. We find that the E × B rotation in the closed flux region mostly cancels the ion diamagnetic drift as H-mode-like regimes are approached and exceeds it by a factor of 2 or more at lower temperatures due to parallel ion flows.

Transition to subcritical turbulence in a tokamak plasma

Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A parameter scan in the local values of the ion-temperature gradient and flow shear is performed. It is demonstrated that the experimentally observed state is near the stability threshold and that this stability threshold is nonlinear: sheared turbulence is subcritical, i.e. the system is formally stable to small perturbations, but, given a large enough initial perturbation, it transitions to a turbulent state. A scenario for such a transition is proposed and supported by numerical results: close to threshold, the nonlinear saturated state and the associated anomalous heat transport are dominated by long-lived coherent structures, which drift across the domain, have finite amplitudes, but are not volume filling; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they overlap and a more conventional chaotic state emerges. Whereas this appears to represent a new scenario for transition to turbulence in tokamak plasmas, it is reminiscent of the behaviour of other subcritically turbulent systems, e.g. pipe flows and Keplerian magnetorotational accretion flows.