Stability Of Drift Waves Research Articles

Wave-kinetic approach to zonal-flow dynamics: Recent advances

The basic physics of drift-wave turbulence and zonal flows has long been studied within the framework of the wave-kinetic theory. Recently, this framework has been reexamined from first principles, which has led to more accurate yet still tractable “improved” wave-kinetic equations. In particular, these equations reveal an important effect of the zonal-flow “curvature” (the second radial derivative of the flow velocity) on the dynamics and stability of drift waves and zonal flows. We overview these recent findings and present a consolidated high-level picture of (mostly quasilinear) zonal-flow physics within reduced models of drift-wave turbulence.

Drift wave in strong collisional dusty magnetoplasma

The study about the wave mechanism of magnetized dusty plasmas has important value to related experiment, industrial processing and exploring celestial space. The linear and nonlinear fluctuation characteristics of the nonuniform magnetized dust plasma system are researched in this paper. For the homogeneous external magnetic field and the nonuniform environment with density and temperature gradients, a two-dimensional nonlinear dynamic magnetoplasma equation is derived considering the strong impact between dust and neutral particles. The linear dispersion relation is obtained by the linearized method. There are both the damping wave causing by strong collision and the harmonic wave by particle drift. Employing the typical numerical parameters for analysis, the results display that the quantum parameter modifies the system lengths; the real wave frequency is proportion to the drift frequency; the imaginary wave frequency has complex relationship with the collision frequency between dust and neutrals, and the collision of particles causes the dissipation effects to the system. Besides, the analytical solutions of drift shock wave and explosive wave are solved by function change method. The variation about the electrostatic potential with the main physical parameters is discussed in detail. It is shown that the strength of the electrostatic shock wave and the width of the explosive wave increase with increasing the dust density and magnetic field intensity, decrease with increasing the collision frequency, change with the drift velocity. When the space-time phase is small, the electrostatic potential changes quickly; once big enough, the potential tends to be stable value and reaches stable state eventually. Finally, the stability of the system is discussed. It is found that the dusty charge, quantum parameter, drift velocity all appear in the disturbed solution. All these results in the paper show that the strong collision effect, quantum effect, particle drift and magnetic field all play important role to the generation, evolution and stability of drift waves.

Cross-separatrix simulations of turbulent transport in the field-reversed configuration

Recent local simulations of the field-reversed configuration (FRC) have reported drift-wave stability in the core and instability in the scrape-off layer (SOL). However, experimental measurements indicate the existence of fluctuations in both FRC core and SOL, with much lower amplitude fluctuations measured in the core. With the updated cross-separatrix capabilities of the simulation code used in this paper, nonlinear turbulence simulations find that linear instabilities grow in the SOL, generating fluctuations which spread from SOL to core. After saturation of the linear instabilities, a balance of the inward spread and local damping in the core is achieved. The steady state toroidal wavenumber spectrum shows lower amplitude core fluctuations and larger SOL fluctuations with amplitude decreasing towards shorter wavelengths, which are consistent with experimental measurements.

Investigation of drift-wave instability in the presence of zonal flows using spatial averaging

The interaction of micro-scale turbulence with zonal flows is one of the key topics in magnetically confined plasma research. We study the stability of drift waves in the presence of large scale flows in the Hasegawa-Wakatani system using spatial averaging. The dispersion relation obtained by this treatment is independent of the radial coordinate and includes resonant terms, which become dominant when the phase speed of the drift wave is comparable to the local advection speed of zonal flow. This dispersion relation is then solved numerically to yield linear growth rates for a small drift wave perturbation against a zonal flow background. The growth rates are similar to those found without zonal flows, when far from the resonant conditions. Close to resonance, both the real frequency and the growth rates differ significantly from the usual case. The stability of zonal flows is also examined.

Drift-wave stability in the field-reversed configuration

Gyrokinetic simulations of C-2-like field-reversed configuration (FRC) find that electrostatic drift-waves are locally stable in the core. The stabilization mechanisms include finite Larmor radius effects, magnetic well (negative grad-B), and fast electron short circuit effects. In the scrape-off layer (SOL), collisionless electrostatic drift-waves in the ion-to-electron-scale are destabilized by electron temperature gradients due to the resonance with locally barely trapped electrons. Collisions can suppress this instability, but a collisional drift-wave instability still exists at realistic pressure gradients. Simulation results are in qualitative agreement with C-2 FRC experiments. In particular, the lack of ion-scale instability in the core is not inconsistent with experimental measurements of a fluctuation spectrum showing a depression at ion-scales. The pressure gradient thresholds for the SOL instability from simulations are also consistent with the critical gradient behavior observed in experiments.

Global theory to understand toroidal drift waves in steep gradient

Toroidal drift waves with unconventional mode structures and non-ground eigenstates, which differ from a typical ballooning structure mode, are found to be important recently by large scale global gyrokinetic simulations and especially become dominant at strong gradient edge plasmas [cf. H. S. Xie and Y. Xiao, Phys. Plasmas 22, 090703 (2015)]. The global stability and mode structures of drift wave in this steep edge density and temperature gradients are examined by both direct numerical solutions of a model two-dimensional eigen equation and analytical theory employing WKB-ballooning approach. Theory agrees with numerical solutions quite well. Our results indicate that (i) non-ground eigenstates and unconventional mode structures generally exist and can be roughly described by two parameters “quantum number” l and ballooning angle ϑk, (ii) local model can overestimate the growth rate largely, say, >50%, and (iii) the narrow steep equilibrium profile leads to twisting (triangle-like) radial mode structures. With velocity space integral, semi-local theory predicts that the critical jump gradient of the most unstable ion temperature gradient mode from ground state l = 0 to non-ground state l = 1 is LT−1R∼50. These features can have important consequences to turbulent transport.

Finite system size effects on drift wave stability

Unstable electrostatic resistive modes, driven by density gradients, are identified in a bounded sheared slab. The boundary conditions play a crucial role and are shown to change the nature of the problem, which is related to so called “universal” mode. The dispersion relation and the structure of the eigenmodes of the instability are derived and are shown to depend on a limited set of dimensionless parameters. The occurrence and possible impact of these modes on numerical simulations and actual plasmas are discussed.

Finite-β simulation of microinstabilities

A new split-weight perturbative particle simulation scheme for finite-β plasmas in the presence of background inhomogeneities is presented. The scheme is an improvement over the original split-weight scheme, which splits the perturbed particle response into adiabatic and non-adiabatic parts to improve numerical properties. In the new scheme, by further separating out the adiabatic response of the particles associated with the quasi-static bending of the magnetic field lines in the presence of background inhomogeneities of the plasma, we are able to demonstrate the finite-β stabilization of drift waves and ion temperature gradient modes using a simple gyrokinetic particle code based on realistic fusion plasma parameters. However, for βmi/me ≫ 1, it becomes necessary to use the electron skin-depth as the grid size of the simulation to achieve accuracy in solving the resulting equations, unless special numerical arrangement is made for the cancelling of the two large terms on the either side of the governing...

Gyrokinetic studies of the effect of β on drift-wave stability in the National Compact Stellarator Experiment

The gyrokinetic turbulence code GS2 was used to investigate the effects of plasma β on linear, collisionless ion temperature gradient (ITG) modes and trapped electron modes (TEM) in National Compact Stellarator Experiment (NCSX) geometry. Plasma β affects stability in two ways: through the equilibrium and through magnetic fluctuations. The first was studied here by comparing ITG and TEM stability in two NCSX equilibria of differing β values, revealing that the high β equilibrium was marginally more stable than the low β equilibrium in the adiabatic-electron ITG mode case. However, the high β case had a lower kinetic-electron ITG mode critical gradient. Electrostatic and electromagnetic ITG and TEM mode growth rate dependencies on temperature gradient and density gradient were qualitatively similar. The second β effect is demonstrated via electromagnetic ITG growth rates' dependency on GS2's β input parameter. A linear benchmark with gyrokinetic codes GENE and GKV-X is also presented.

Sensitivity of transport and stability to the current profile in steady-state scenario plasmas in DIII-D

Recent experiments on DIII-D have provided the first systematic data on the impact of the current profile on the transport and stability properties of high-performance, steady-state scenario plasmas. In a future tokamak, to achieve 100% noninductive conditions and produce net power, the current profile J must be sustained by a large fraction of bootstrap current JBS, which is nonlinearly coupled with the kinetic profiles. Systematic scans of qmin and q95 were performed to determine empirically the best alignment of the noninductive currents with J and the variation of the transport properties with q. Transport analysis indicates that χe and χi are sensitive to the details of J in a way that makes the pressure profile peaking and JBS scale nonlinearly with both q and β in the experiment. Drift wave stability analysis yields linear growth rates that do not reproduce experimental trends in χ with qmin and q95. At high beta, necessary to maximize fBS, the plasma duration is often limited by n=1 tearing modes, whose stability also depends on the J profile. Broadly deposited electron cyclotron (EC) current at mid-radius was found to supply part of the required noninductive current and to positively affect the tearing stability. The modes appear when JEC is turned off for stable cases and always appear when the EC deposition is shifted outwards. The variation in the EC scan results is consistent with PEST3 calculations, showing that the tearing stability becomes extremely sensitive to small perturbations of the equilibrium in wall-stabilized plasmas run close to the ideal MHD limit. These modeling results are being used to design new experiments with higher ideal and tearing limits. A new capability for off-axis neutral beam injection system will be used to explore higher qmin scenarios and different current alignments.

Rotation shear and drift wave stability

The stability of short wavelength (high n, where n is the toroidal mode number) drift eigenmodes in toroidally confined plasma is conventionally analysed using the ballooning transformation. In lowest order in 1/n there is a local eigenvalue, λ(x, k), where k is a parameter representing the radial wave-number. Usually profile variation defines a radial position where the growth rate is a maximum. In next order one finds that this position determines the mode's radial location and that the parameter k is such as to maximise the growth rate. However, if the effects of sheared plasma rotation, dΩ/dq, dominate other profile variation, the growth rate is smaller and, instead, involves an average over a period of k. In this paper we consider a generic drift wave model that generates a local eigenvalue having quadratic radial variations of frequency, ω(x), and growth rate, γ(x), and a periodic variation with k. We derive an analytic dispersion relation for the global eigenvalue, ω. Although requiring numerical solution, this shows that there is a continuous evolution between these two limits as dΩ/dq increases, the transition being quite sharp for high n. The transition can be associated with a critical rotation shear, dΩcrit/dq ∼ O(1/n). The detailed character of the results depends on which of the radial variations, ω(x) or γ(x), dominates.

Electron drift waves in an advanced tokamak plasma

The influence of details of an international thermonuclear experimental reactor (ITER)-like geometry on drift wave stability is studied. The eigenvalue problem for electrostatic electron drift waves is solved numerically by following the ballooning mode formalism and using a standard shooting technique. The real frequencies and growth rates of the most unstable modes and their eigenfunctions are calculated for two specific magnetic flux surfaces. For the equilibrium under investigation, the modes are found to be unstable for peak density profiles and their stability is found to be strongly affected by the local magnetic shear (LMS). The presence of positive LMS is found to be destabilizing on the magnetic surface where global magnetic shear is reverse. The stability behaviour is however different for a positive magnetic shear surface where the effect of large positive LMS is found to be stabilizing. The eigenfunctions are more localized in the regions where normal curvature is bad and magnetic field is weak.

Drift wavs in helically symmetric stellarators

The local linear stability of electron drift waves and ion temperature gradient modes (ITG) is investigated in a quasihelically symmetric (QHS) stellarator and a conventional asymmetric (Mirror) stellarator. The geometric details of the different equilibria are emphasized. Eigenvalue equations for the models are derived using the ballooning mode formalism and solved numerically using a standard shooting technique in a fully three-dimensional stellarator configuration. While the eigenfunctions have a similar shape in both magnetic geometries, they are slightly more localized along the field line in the QHS case. The most unstable electron drift modes are strongly localized at the symmetry points (where stellarator symmetry is present) and in the regions where normal curvature is unfavorable and magnitude of the local magnetic shear and magnetic field is minimum. The presence of a large positive local magnetic shear in the bad curvature region is found to be destabilizing. Electron drift modes are found to be more affected by the normal curvature than by the geodesic curvature. The threshold of stability of the ITG modes in terms of ηi is found to be 2∕3 in this fluid model consistent with the smallest threshold for toroidal geometry with adiabatic electrons. Optimization to favorable drift wave stability has small field line curvature, short connection lengths, the proper combination of geodesic curvature and local magnetic shear, large values of local magnetic shear, and the compression of flux surfaces in the unfavorable curvature region.

Microstability in tokamaks with low magnetic shear

The stability of drift waves in configurations with low magnetic shear, s, including the case with a minimum in the safety factor, qmin, which is a situation relevant to the formation of internal transport barriers, is analysed. First the small s limit of the ballooning representation is shown to, indeed, coincide with the result of a shear free calculation. Then, the limitations associated with using the ballooning transformation at low shear are discussed. Radially extended ballooning modes can be considered to result from the toroidal coupling of ‘modelets’ (each of which can contain a number of poloidal harmonics) centred on adjacent resonant surfaces. In a region of low magnetic shear, a modelet situated on a particular resonant surface does not extend to the adjacent surface and therefore the coupling of these is weak and the ballooning theory fails. An alternative approach based on a recurrence relation between modelets is used to analyse these situations with small s. This is then applied to electron drift waves and ion temperature gradient modes as examples. These studies show that for sufficiently long wavelengths, radially extended ballooning modes cannot exist close to a point of zero magnetic shear; however, independent modelets can still exist at resonant surfaces near qmin. The criteria on the wavelength for this situation to prevail are presented. The example of electron drift waves centred on qmin is analysed and it is found that, even for this ‘slab-like’ electron drift wave, damping from an outgoing wave can be entirely suppressed.Corrections were made to this article on 6 August 2004. The corrected electronic version is identical to the print version.

Resistive Drift Waves in a Bumpy Torus

A computational study of resistive drift waves in the edge plasma of a bumpy torus is presented. The magnetohydrodynamic equilibrium is obtained from a three-dimensional local equilibrium model. The use of a local magnetohydrodynamic equilibrium model allows for a computationally-efficient systematic study of the impact of the magnetic field structure on drift wave stability.

Poloidal momentum transport due to drift-waves in toroidal geometry

The aim of this paper is to provide the theoretical framework for a quasi-linear drift-wave model of poloidal and toroidal momentum transport in magnetically confined plasmas in toroidal geometry. Axisymmetry is not required. The new feature is the inclusion of poloidal flow in the coupled equations for linear drift-wave stability and quasilinear mean field transport. It is shown how both toroidal and poloidal rotations can be included in a distribution function which is an equilibrium of the Vlasov equation in a rotating reference frame. The equations for the fluctuation driven toroidal and poloidal viscous stresses are determined and the toroidal form of the E×B and parallel velocity shear terms are found. In order to be able to follow the electric field evolution during a transport bifurcation, the neoclassical constraint on the poloidal rotation is not imposed. Instead, the common poloidal flow is evolved as part of the system of transport equations.

Stability of drift waves in the presence of dust

In the presence of dust particles in the plasma, it is shown that the well-known stability of the drift wave in a sheared slab geometry does not hold. Due to the presence of dust particles in tokamaks, the magnetic shear damping is reduced drastically. As a result, both the collisionless and collisional (dissipative) drift modes become unstable under the typical parameter regimes of a tokamak. Consequently, drift waves must still be considered as an underlying dynamic of anomalous transport in tokamak edges, where dust particles are found to be abundant.

Collisional drift waves in stellarator plasmas

A computational study of resistive drift waves in the edge plasma of a stellarator with an helical magnetic axis is presented. Three coupled field equations, describing the collisional drift-wave dynamics in the linear approximation, are solved as an initial-value problem along the magnetic field line. The magnetohydrodynamic equilibrium is obtained from a three-dimensional local equilibrium model. The use of a local magnetohydrodynamic equilibrium model allows for a computationally efficient systematic study of the impact of the magnetic field structure on drift-wave stability. PACS Nos.: 52.35.Kt, 52.30.Jb, 52.35.Ra

Geometrical effects on drift wave stability in low shear stellarator plasmas

Modern stellarators are designed with neoclassical transport in mind, potentially leading to anomalous transport originating from drift wave turbulence as the primary cause of energy and particle losses. It is therefore of interest to consider the influence of details of geometry on drift wave stability. In this paper the eigenvalue drift wave equation is therefore solved numerically in fully three-dimensional stellarator geometries using the ballooning mode formalism. The correlation between the details of the configurations such as local magnetic shear (LMS), normal curvature, geodesic curvature and magnetic field strength and the drift wave spectrum is discussed for two different stellarator configurations. A detailed discussion of the localization of the most unstable modes is presented and analysed. It is found that the most unstable modes are localized where the stabilizing effect of integrated LMS is minimum or where the coupling between the integrated LMS and geodesic curvature is strong. Since the more the modes are localized the stronger they will be influenced by the local geometrical effects, the most unstable modes are also highly localized.

Comparison of electron drift waves in numerical and analytical tokamak equilibria

In this paper, we demonstrate the importance of the details of the equilibria on the stability of electron drift waves. A comparison of electrostatic electron drift waves in numerical and analytical tokamak equilibria is presented in fully three-dimensional circular and non-circular tokamaks. The numerical equilibria are obtained using the variational moments equilibrium code and the analytical equilibria used is the generalized model. An eigenvalue equation for the model is derived using the ballooning mode formalism and solved numerically using a standard shooting technique. The stability and the localization of the electron drift wave is found to be strongly dependent on the local shear of the magnetic field. Large values of the local shear are found to be stabilizing. A disagreement in the results is found between analytical and numerical equilibria at aspect ratios of typical tokamaks, suggesting that the latter approach should be used in the transport calculations. The effects of the local shaping of the magnetic surfaces are complicated and can be both stabilizing and destabilizing, depending on the details of the equilibria.