Collisionless Drift Waves Research Articles

Role of phase space structures in collisionless drift wave turbulence and impact on transport modeling

In fusion plasmas, several mechanisms such as heating, wave-particle interaction etc can drive deviations of distribution function from Maxwelian to form phase space structures. This article discusses the impact of phase space structures in drift wave turbulence on dynamics and transport modeling. The two cases of (i) coherent holes and (ii) incoherent granulations (clusters of correlated resonant particles with finite life time) are treated. Their dynamical impact on driving subcritical instability is analyzed by explicitly calculating the nonlinear growth rate. The role of zonal flows is also addressed. It is explained how phase space structures can be related to transient events and non-diffusive transport, issues in current confinement research.

Second order kinetic theory of parallel momentum transport in collisionless drift wave turbulence

A second order kinetic model for turbulent ion parallel momentum transport is presented. A new nonresonant second order parallel momentum flux term is calculated. The resonant component of the ion parallel electrostatic force is the momentum source, while the nonresonant component of the ion parallel electrostatic force compensates for that of the nonresonant second order parallel momentum flux. The resonant component of the kinetic momentum flux can be divided into three parts, including the pinch term, the diffusive term, and the residual stress. By reassembling the pinch term and the residual stress, the residual stress can be considered as a pinch term of parallel wave-particle resonant velocity, and, therefore, may be called as “resonant velocity pinch” term. Considering the resonant component of the ion parallel electrostatic force is the transfer rate between resonant ions and waves (or, equivalently, nonresonant ions), a conservation equation of the parallel momentum of resonant ions and waves is obtained.

Electromagnetic drift waves dispersion for arbitrarily collisional plasmas

The impacts of the electromagnetic effects on resistive and collisionless drift waves are studied. A local linear analysis on an electromagnetic drift-kinetic equation with Bhatnagar-Gross-Krook-like collision operator demonstrates that the model is valid for describing linear growth rates of drift wave instabilities in a wide range of plasma parameters showing convergence to reference models for limiting cases. The wave-particle interactions drive collisionless drift-Alfvén wave instability in low collisionality and high beta plasma regime. The Landau resonance effects not only excite collisionless drift wave modes but also suppress high frequency electron inertia modes observed from an electromagnetic fluid model in collisionless and low beta regime. Considering ion temperature effects, it is found that the impact of finite Larmor radius effects significantly reduces the growth rate of the drift-Alfvén wave instability with synergistic effects of high beta stabilization and Landau resonance.

Lattice Boltzmann model for collisionless electrostatic drift wave turbulence obeying Charney–Hasegawa–Mima dynamics

A lattice Boltzmann method (LBM) approach to the Charney–Hasegawa–Mima (CHM) model for adiabatic drift wave turbulence in magnetised plasmas is implemented. The CHM-LBM model contains a barotropic equation of state for the potential, a force term including a cross-product analogous to the Coriolis force in quasigeostrophic models, and a density gradient source term. Expansion of the resulting lattice Boltzmann model equations leads to cold-ion fluid continuity and momentum equations, which resemble CHM dynamics under drift ordering. The resulting numerical solutions of standard test cases (monopole propagation, stable drift modes and decaying turbulence) are compared to results obtained by a conventional finite difference scheme that directly discretizes the CHM equation. The LB scheme resembles characteristic CHM dynamics apart from an additional shear in the density gradient direction. The occurring shear reduces with the drift ratio and is ascribed to the compressible limit of the underlying LBM.

Collisionless Drift Waves Ranging from Current‐Driven, Shear‐Modified, and Electron‐Temperature‐Gradient Modes

AbstractThe specific history of collisionless drift waves is marked by focusing upon current‐driven, shear‐modified, and electron‐temperature‐gradient modes. Studies of current‐driven collisionless drift waves started in 1977 using the Innsbruck Q machine and was continued over 30 years until 2009 with topics such as plasma heating by drift waves in fusion‐oriented confinement and space/astrophysical plasmas. Superposition of perpendicular flow velocity shear on parallel shear intensively modifies the drift wave characteristics through the variation of its azimuthal structure, where the parallel‐shear driven instability is suppressed for strong perpendicular shears, while hybrid‐ion velocity shear cause unexpected stabilization of the parallel‐shear‐modified drift wave. An electron temperature gradient can be formed easily by control of thermionic electron superimposed on ECR plasma, and is found to excite low‐frequency fluctuation in the range of drift waves (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Parallel-velocity-shear-modified drift wave in negative ion plasmas

A systematic investigation of the effects of a parallel velocity shear and negative ions on the collisionless drift wave instability has for the first time been realized by simultaneously using a segmented tungsten hot plate of a Q-machine and sulfur hexafluoride (SF6) gas in a magnetized potassium plasma. The parallel velocity shear of the positive ion flow tends to decrease the fluctuation level of the drift wave. The introduction of negative ions first increases the fluctuation level and then starts to decrease it at the negative ion exchange fraction of around 10%, while keeping the above-mentioned shear effect qualitatively. In addition, a simple dispersion relation based on the local model has been calculated to show that it can predict wave characteristics similar to the experimental results. Our findings provide a potential for gaining a more profound insight into the physics of space/circumterrestrial plasmas.

Transport of parallel momentum by collisionless drift wave turbulence

This paper presents a novel, unified approach to the theory of turbulent transport of parallel momentum by collisionless drift waves. The physics of resonant and nonresonant off-diagonal contributions to the momentum flux is emphasized, and collisionless momentum exchange between waves and particles is accounted for. Two related momentum conservation theorems are derived. These relate the resonant particle momentum flux, the wave momentum flux, and the refractive force. A perturbative calculation, in the spirit of Chapman–Enskog theory, is used to obtain the wave momentum flux, which contributes significantly to the residual stress. A general equation for mean k∥ (⟨k∥⟩) is derived and used to develop a generalized theory of symmetry breaking. The resonant particle momentum flux is calculated, and pinch and residual stress effects are identified. The implications of the theory for intrinsic rotation and momentum transport bifurcations are discussed.

Magnetic electron drift waves in electron magnetohydrodynamic plasmas

The dynamics of nonuniform, magnetized, cold electron plasma in a stationary charge neutral ion background is considered. In the high frequency limit, electromagnetic modification of electron plasma oscillation is obtained in homogeneous plasma, whereas in inhomogeneous plasma in the low frequency regime a driftlike mode is found. Nonlinear evolution of this mode is derived to describe the two-dimensional (2D) dynamics. The equation has a close resemblance to 2D electrostatic collisionless drift wave equation thereby called as “magnetic electron drift” wave. In addition to the usual small amplitude dispersive modes the stationary state nonlinear vortexlike solutions are also discussed. The magnetic electron drift wave in the electron magnetohydrodynamic regime can find applications in laboratory as well as in space plasmas.

Response to “Comment on ‘Dynamics of zonal flow saturation in strong collisionless drift wave turbulence’ ” [Phys. Plasmas 11, 1744 (2004)

The Comment of Krommes is addressed. It is shown that all of the substantive claims therein are incorrect.

Dynamics of zonal flow saturation in strong collisionless drift wave turbulence

Generalized Kelvin–Helmholtz (GKH) instability is examined as a mechanism for the saturation of zonal flows in the collisionless regime. By focusing on strong turbulence regimes, GKH instability is analyzed in the presence of a background of finite-amplitude drift waves. A detailed study of a simple model with cold ions shows that nonlinear excitation of GKH modes via modulational instability can be comparable to their linear generation. Furthermore, it is demonstrated that zonal flows are likely to grow faster than GKH mode near marginality, with insignificant turbulent viscous damping by linear GKH. The effect of finite ion temperature fluctuations is incorporated in a simple toroidal ion temperature gradient model, within which both zonal flow and temperature are generated by modulational instability. The phase between the two is calculated self-consistently and shown to be positive. Furthermore, the correction to nonlinear generation of GKH modes appears to be small, being of order O(ρi2k2). Thus, the role of linear GKH instability in the saturation of collisionless zonal flows, in general, seems dubious.

Particle pinch in collisionless drift-wave turbulence

Nonlinear numerical simulations show that the particle flux from collisionless drift-wave turbulence is directed up-gradient for sufficiently high values of ηe=Ln/LTe. This “particle pinch” results from the completely different perpendicular dynamics of slow (resonant) and fast (nonresonant) electrons, making it a genuinely kinetic effect which cannot easily be described by fluid models. Moreover, the linearly stable system self-sustains its turbulent state through a finite-amplitude (nonlinear) instability. Therefore, quasilinear estimates of turbulent transport caused by collisionless drift waves are practically useless and have to be replaced by nonlinear kinetic simulations like the present one.

Numerical computation of collisionless drift Alfvén turbulence

An electromagnetic hybrid model of drift-kinetic electrons and cold ions in three-dimensional sheared slab geometry is constructed to treat collisionless drift Alfvén turbulence in tokamak edge plasmas. The basic nonlinear equations are solved numerically using explicit finite-difference methods on a phase-space grid rather than an ensemble of “superparticles.” Basic properties of the turbulent fluctuations such as amplitude and phase distributions, amplitude correlations, and energy spectra are investigated. The resulting turbulent particle transport by magnetic flutter is negligible compared to that by E×B convection. However, the intrinsic dynamics of the turbulence remains electromagnetic due to the influence of kinetic shear Alfvén waves and magnetic flutter. Comparisons with a companion Landau-fluid model are more successful than in similar studies of ion temperature gradient turbulence.

Numerical computation of collisionless drift wave turbulence

Collisionless drift waves are studied by means of nonlinear numerical simulations in a three-dimensional sheared slab geometry. The electron dynamics is described by a drift-kinetic equation, and the ions are treated as a cold fluid. The energy spectra of the turbulent fluctuations and the dependence of the resulting anomalous transport on various dimensionless plasma parameters are investigated. It is shown that this model resolves fundamental contradictions between experimental results and linear drift wave theory, especially the dependence of turbulent transport on radial position but also the scaling with ion mass.

Theory of drift waves in the presence of parallel and perpendicular flow curvature. II. Toroidal model

The combined effect of the perpendicular and the parallel flow curvatures on the toroidal branch of the collisionless drift waves is investigated. The full analytical stability analysis shows that the ratio of the stabilising influences of the perpendicular to the parallel flow curvature scales as α2Lv2/Ln2, where α is a numerical factor whose value is usually around 3 and Lv, Ln are respectively the velocity shear and the density variation scale length. Thus at the plasma edge (since Lv∼Ln∼ρiθ, where ρiθ is the ion poloidal gyroradius) the perpendicular flow is expected to play the major role in stabilising microinstabilities and turbulence in the improved regimes of confinement (like the high confinement-modes). However, at the plasma core (since Ln∼a≫Lv∼ρiθ, where a is the minor radius of the cross section) it is the parallel component of the flow which plays the dominant role. Furthermore, since the confinement improvement in the core is usually related to the toroidal velocity and V‖ coming from the toroidal flow is much more that V⊥ coming from the toroidal flow, our result clearly indicates that it is the parallel component of the toroidal flow and not the perpendicular component, as is usually thought, that is responsible for the core confinement improvement. This conclusion is consistent with our earlier result calculated in a sheared slab configuration [S. Sen and A. Sen, Phys. Plasmas 3, 2224 (1996)].

Collisionless drift wave instability and anomalous particle fluxes in plasmas with high-Z impurities

Collisionless drift waves and associated particle fluxes are investigated in nonuniform plasmas in the presence of stationary high-Z impurities or charged dust particulates.

The role of dissipation in the theory and simulations of homogeneous plasma turbulence, and resolution of the entropy paradox

The role of dissipation in the theory and simulations of homogeneous plasma slices is analyzed with the goal of understanding the ‘‘entropy paradox,’’ which is that a certain positive-definite functional of the perturbed distribution function increases without bound in some situations even though the potentials appear to have achieved a steady state. Confusion arises from an interchange of the limits t→∞ and η→0, where η is a measure of dissipation. It is argued that it is never strictly correct to neglect η; the averaged dissipation approaches a nonzero limit (proportional to the averaged flux) even as η→0. An exactly soluble model is worked out to illustrate the point. In collisionless particle simulations, the particle and heat fluxes may nevertheless saturate with their correct values. The relations of kinetic and fluid entropy balances are discussed with the aid of (1) the Terry–Horton model for collisionless drift waves, and (2) a simple model of the ion-temperature-gradient-driven mode. The rationale for simulations of homogeneous slices of plasma is given, with particular emphasis being placed on the relationship of dissipation in such slices to dissipation in a complete physical domain.

Collisionless drift waves in the H mode edge (plasma)

Existing theories predict that in ohmic and/or L mode discharges the drift wave is stable in a sheared slab geometry. The representative experimental values for the plasma parameters show, however, that because of the very steep density gradient the shear stabilization criteria for collisionless drift waves are not likely to be satisfied in the H mode edge plasma. Magnetic shear is, therefore, not a candidate for stabilizing the slab branch of drift waves in the H mode. However, a radially sheared transverse (to the equilibrium magnetic field) velocity field is found to play a key role in stability. Velocity profiles corresponding to those observed in a region of a few centimetres inside the separatrix of an H mode plasma stabilize drift waves. On the other hand, velocity profiles corresponding to the L mode render drift waves unstable in the experimental range of parameters, even though the magnetic shear continues to play its stabilizing role

A fluid-ion and particle-electron model for low-frequency plasma instabilities

We have developed a hybrid (particle/fluid) computer code for the study of quasi-neutral micro-instabilities for inhomogeneous plasmas that are immersed in a magnetic field. The ions are treated in the fluid approximation, retaining perpendicular E x B and polarization drifts as well as the parallel momentum and ion temperature equations. The electrons are represented as particles with perpendicular E x B drifts and parallel kinetics, thus exactly describing the effects of trapped electrons and electron-wave resonances. The code may be used in the study of low frequency (@w < @WPini, where @Wi = eB/mic) universal mode drift waves, ion-pressure-driven modes, or curvature-driven modes. At present we have implemented an electrostatic, two-dimensional, slab geometry version of the code. The model has been tested extensively for sound-wave propagation, the collisionless (universal mode) drift wave real frequency and growth rate, the @hi-mode real frequency and growth rate, and the fluctuation spectrum has been elucidated. As a nonlinear test case, we have also studied the nonlinear properties of the collisionless drift wave.

Determination of local transport coefficients by heat flux analysis and comparisons with theoretical models

The energy confinement properties of different regimes of JET plasmas are investigated. The results of local transport analysis in both L- and H-mode regimes are discussed and the properties of H-mode plasmas produced by neutral beam injection and/or ion cyclotron resonance heating are compared. Two aspects of transport analysis are addressed. Firstly, the relative importance of the electron and ion heat conductivities and a comparison with the effective particle diffusivity since this determines the nature of the turbulence responsible for the degradation in confinement. The second issue is whether theoretical models adequately describe the radial dependence of the measured heat flux. Several theoretical models are considered: the ion temperature gradient driven turbulence model, the Rebut-Lallia critical temperature gradient model, the dissipative and collisionless trapped electron drift wave mode, the Carreras-Diamond resistive ballooning model and the neoclassical pressure gradient driven turbulence model.

Determination of local transport coefficients by heat flux analysis and comparisons with theoretical models

The energy confinement properties of different regimes of JET plasmas are investigated. The results of local transport analysis in both L- and H-mode regimes are discussed and the properties of H-mode plasmas produced by neutral beam injection and/or ion cyclotron resonance heating are compared. Two aspects of transport analysis are addressed. Firstly, the relative importance of the electron and ion heat conductivities and a comparison with the effective particle diffusivity since this determines the nature of the turbulence responsible for the degradation in confinement. The second issue is whether theoretical models adequately describe the radial dependence of the measured heat flux. Several theoretical models are considered: the ion temperature gradient driven turbulence model, the Rebut-Lallia critical temperature gradient model, the dissipative and collisionless trapped electron drift wave mode, the Carreras-Diamond resistive ballooning model and the neoclassical pressure gradient driven turbulence model.