Model Of Drift Wave Turbulence Research Articles

Multi-shell transport model for L-H transition

A coupled model of transport, turbulence, and mesoscale flows is proposed, including turbulence spreading. The model consists of transport equations for plasma density and pressure coupled to a shell model of drift wave turbulence, which incorporates coupling to mesoscale flows via disparate scale interactions. The model can describe the turbulent cascade and its dynamical interplay with zonal and mean shear flows as well as the profile evolution (including the profiles of turbulence intensity itself) due to these self-consistent turbulent fluxes. This simple system of equations is shown to capture the low to high confinement (L-H) transition. It is also observed that as the heating is increased, the system goes through an intermediate phase that displays oscillations between zonal flows and turbulence. The transition towards the H mode, which is characterized by the presence of a strong mean shear flow at the edge, is triggered by the mesoscale dynamics due to the action of zonal flows, with turbulence spreading playing an important role in the H to L back transition.

Transport dynamics of self-consistent, near-marginal drift-wave turbulence. I. Investigation of the ability of external flows to tune the non-diffusive dynamics

The reduction of turbulent transport across sheared flow regions has been known for a long time in magnetically confined toroidal plasmas. However, details of the dynamics are still unclear, in particular, in what refers to the changes caused by the flow on the nature of radial transport itself. In Paper II, we have shown in a simplified model of drift wave turbulence that, when the background profile is allowed to evolve self-consistently with fluctuations, a variety of transport regimes ranging from superdiffusive to subdiffusive open up depending on the properties of the underlying turbulence [D. Ogata et al., Phys. Plasmas 24, 052307 (2017)]. In this paper, we show that externally applied sheared flows can, under the proper conditions, cause the transport dynamics to be diffusive or subdiffusive.

Linear technique to understand non-normal turbulence applied to a magnetized plasma.

In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors, linear nonmodal analysis is more useful than normal mode analysis in predicting turbulent properties. However, the nontrivial time evolution of nonmodal structures makes quantitative understanding and prediction difficult. We present a technique to overcome this difficulty by modeling the effect that the advective nonlinearities have on spatial turbulent structures. The nonlinearities are taken as a periodic randomizing force with time scale consistent with critical balance arguments. We apply this technique to a model of drift wave turbulence in the Large Plasma Device [W. Gekelman etal., Rev. Sci. Instrum. 62, 2875 (1991)], where nonmodal effects dominate the turbulence. We compare the resulting growth rate spectra to the spectra obtained from a nonlinear simulation, showing good qualitative agreement, especially in comparison to the eigenmode growth rate spectra.

Predator prey oscillations in a simple cascade model of drift wave turbulence

A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separation for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.

On radial geodesic forcing of zonal modes

The elementary local and global influence of geodesic field line curvature on radial dispersion of zonal modes in magnetised plasmas is analysed with a primitive drift wave turbulence model. A net radial geodesic forcing of zonal flows and geodesic acoustic modes can not be expected in any closed toroidal magnetic confinement configuration, since the flux surface average of geodesic curvature identically vanishes. Radial motion of poloidally elongated zonal jets may occur in the presence of geodesic acoustic mode activity. Phenomenologically a radial propagation of zonal modes shows some characteristics of a classical analogon to second sound in quantum condensates.

Nonlinear Triad Interactions and the Mechanism of Spreading in Drift-Wave Turbulence

We present the results of a derivation of the fluctuation energy transport matrix for the two-field Hasegawa-Wakatani model of drift wave turbulence. The energy transport matrix is derived from a two-scale direct interaction approximation assuming weak turbulence. We examine different classes of triad interactions and show that radially extended eddies, as occurs in penetrative convection, are the most effective in turbulence spreading. We show that in the near-adiabatic limit internal energy spreads faster than the kinetic energy. Previous theories of spreading results are discussed in the context of weak turbulence theory.

Radial transport of fluctuation energy in a two-field model of drift-wave turbulence

A theory of spatial propagation of turbulence, referred to as turbulence spreading, is developed for the two-field model of drift wave turbulence. Markovian closure expressions for the flux of kinetic and internal fluctuation energies are systematically derived. Simplified closure expressions are used to obtain two coupled reaction-diffusion equations for kinetic and internal energy. The efficacy of various nonlinear interaction mechanisms for spreading is analyzed systematically. Spreading of internal energy is predicted to “lead” that of kinetic energy. The important role of zonal flow damping in spreading is identified, but zonal flows are shown not to be the dominant agents of turbulence spreading.

Turbulent particle transport in magnetized plasmas.

Particle transport in magnetized plasmas is investigated with a fluid model of drift wave turbulence. An analytical calculation shows that magnetic field curvature and thermodiffusion drive an anomalous pinch. The curvature driven pinch velocity is consistent with the prediction of turbulence equipartition theory. The thermodiffusion flux is found to be directed inward for a small ratio of electron to ion pressure gradient, and it reverses its sign when increasing this ratio. Numerical simulations confirm that a turbulent particle pinch exists. It is mainly driven by curvature for equal ion and electron heat sources. The sign and relative weights of the curvature and thermodiffusion pinches are consistent with the analytical calculation.

Bifurcation and scaling of drift wave turbulence intensity with collisional zonal flow damping

Interacting drift wave–zonal flow turbulence is examined at the spectral level of description using an extended “predator–prey” model. Analytic solutions that describe both the linear scaling of transport with ion–ion collisionality as well as the saturation regime are obtained for a simple model of drift wave turbulence. A theory of self-regulation in this system is presented. The possibility of bifurcation to a state with higher turbulence level and transport is demonstrated. This bifurcation is associated with the appearance of a condensate solution at the largest scales. The possible relevance of this phenomenon to the bursting events of turbulence and transport recently observed in gyrokinetic simulations of ITG instability is discussed.

Spectral transfer in a two-field model of drift wave turbulence

The weakly nonlinear theory of the two-field model of drift wave turbulence is outlined. It was demonstrated within the framework of this model that a double energy cascade is an element of spectral transfer due to the presence of two quadratic invariants and Poisson bracket type nonlinearities. The obtained results are illustrated by two examples of drift wave turbulence known in magnetized and unmagnetized plasmas.

Quasicrystallization of vortices in drift-wave turbulence.

The formation and dynamics of coherent vortices in the Hasegawa-Mima two-dimensional model of drift-wave turbulence is studied numerically. The effect of ``vortex shielding`` due to the presence of a characteristic length scale (ion Larmor radius {rho}{sub {ital s}}) leads to important differences between self-organization in drift-wave and Navier-Stokes fluid turbulence. While it may not be surprising that a finite deformation radius leads to the formation of coherent vortices, we show here that it also results in the appearance of long-range order in the system, i.e., the formation of a vortical ``quasicrystal.``

The dynamics of spectral transfer in a model of drift wave turbulence with two nonlinearities

The spectral transfer dynamics of two-dimensional (2-D) drift wave turbulence over a broad range incorporating long- and short-wavelength extremes is studied numerically in the context of dissipative trapped electron convective cell turbulence. The direction, locality, and isotropy of energy and enstrophy transfer in wave-number space are determined by examining energy and enstrophy transfer rates, the enstrophy generation rate, spectra, and the spectrum response to perturbative impulses. Energy transfer is characterized by two subranges, according to the dominant nonlinearity, and a dynamically complex crossover region dividing the subranges. In the long-wavelength E×B subrange, energy transfer is nonlocal and anisotropic, proceeding to shorter wavelengths with significant generation of enstrophy. In the short-wavelength polarization drift subrange, energy transfer is local and, in the absence of sources and sinks, is dominated by an inverse cascade, consistent with the near conservation of enstrophy on dynamical time scales. In the crossover region, there is isotropic nonlocal forward transfer, as well as cascading to long wavelength. A significant shift of the frequency spectrum peak in the crossover region is shown to result from the cross coupling of the two nonlinearities. The shift is in the electron diamagnetic direction and increases with increasing wave number, consistent with the behavior of the renormalized response function. The simulation model does not incorporate the effects of electron inertia, and therefore does not account for the feedback of the frequency shift on nonlinear mode stability. Nevertheless, the simulations provide numerical validation of many aspects of the accompanying analytical investigation [Liang et al., Phys. Fluids B 5, 1128 (1993)].

Statistical mechanics of a two-field model of drift wave turbulence

The absolute equilibrium statistical mechanics of a two-field model of drift wave turbulence is investigated with emphasis on predicting the direction of spectral transfer, and on exploration of the role of density-potential correlation (cross-correlation) in constraining the nonlinear transfer process. The results indicate that departure from the adiabatic relation ñ/n0=eφ̃/Te allows transfer of total energy to small scales in fully developed turbulence. This prediction is in distinct contrast to intuition based on the one-field Hasegawa–Mima model [Phys. Fluids 21, 87 (1978)].

Transport analysis of JT-60 plasma with the drift wave turbulence model

Characteristics of the JT-60 plasma in both the Ohmic heating phase and the neutral beam heating phase have been studied numerically by using a one-dimensional tokamak transport code, with the thermal conductivities based on the drift wave turbulence (DWT) model. The numerical results for the central electron temperature Te(0) and the energy confinement time τE show good agreement with the experimental data in the medium line averaged electron density range n̄e ∼ 4 × 1019 m−3, for both Ohmic heating and neutral beam'heating cases. The absorbed power degradation of is also reproduced with this model. On the other hand, the DWT model underestimates the plasma temperatures at low line averaged electron density, especially in the neutral beam heating phase, because of the strong dependence of the thermal conductivity on the electron temperature, and high temperature plasmas cannot be reproduced. This leads to a discrepancy in the n̄e dependence of τE between experiment and calculation. The current dependence of τE is not reproduced either, even when the Venetian blind model is used.