Collisionless Drift Wave Turbulence 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.

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.

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.

Effect of Nonlinear Electron Landau Damping in Collisionless Drift-Wave Turbulence

Collisionless drift-wave turbulence is studied with numerical simulations in a three-dimensional sheared slab geometry. Nonlinear electron Landau damping associated with parallel trapping is found to substantially reduce the anomalous particle transport for low magnetic shear ( $\stackrel{^}{s}<1$), whereas it plays a very weak role for higher shear ( $\stackrel{^}{s}>1$). This result has implications for the construction of transcollisional Landau-fluid models for passing electrons in the edge ( $r/a>0.8$) of a tokamak.

Renormalized dielectric function for collisionless drift wave turbulence

Earlier renormalized theories for collisionless drift wave turbulence were deficient in several respects when ω<kzvi and the principal perpendicular motion is the E×B drift. The earlier theories did not preserve the perpendicularity between the E×B ion current and the electric field E and consequently, did not conserve energy. In addition, earlier theories did not correctly treat the case ni∼eφ/T in which the nonlinear convective term -φ×B⋅-ni should be very small. These problems are analyzed and corrected in a new version. The new theory predicts that drift wave energy is converted into parallel ion energy, producing a damping rate γ∥=−(kzvi/ω)2 k⊥2D, where D is a test particle diffusion coefficient. For a fluctuating potential φ due only to drift waves, D is greater than zero only when the threshold eφ/T∼ (k⊥Ln)−1 for ion stochastic motion is exceeded. The nonlinear stabilization will occur slightly above this threshold if γe/ω< (kzvi/ω)2 (γe is the linear growth rate). For this case the density diffusion coefficient Dn (which is less than D) will be Dn∼γe/k⊥2.