Strong Turbulence Regime Research Articles

Anisotropic electrostatic turbulence and zonal flow generation

In this paper we analyse the running and asymptotic diffusion coefficients of a plasma in the case of zonal flow generation by an anisotropic stochastic electrostatic potential. Both the weak and relatively strong turbulence regimes were analysed. The analysis of the diffusion coefficients in wave vector space provides an illustration of the fragmentation of drift wave structures in the radial direction and the generation of long-wavelength structures in the poloidal direction that are identified as zonal flows. We have shown that the fragmentation of drift wave structures is strongly influenced by the anisotropy parameter, the electrostatic Kubo number and by the initial values of the wave vector.

On spectral scaling laws for incompressible anisotropic magnetohydrodynamic turbulence

A heuristic model is given for anisotropic magnetohydrodynamics turbulence in the presence of a uniform external magnetic field B0ê‖. The model is valid for both moderate and strong B0 and is able to describe both the strong and weak wave turbulence regimes as well as the transition between them. The main ingredient of the model is the assumption of constant ratio at all scales between the linear wave period and the nonlinear turnover time scale. Contrary to the model of critical balance introduced by Goldreich and Sridhar [Astrophys. J. 438, 763 (1995)], it is not assumed, in addition, that this ratio be equal to unity at all scales. This allows us to make use of the Iroshnikov–Kraichnan phenomenology; it is then possible to recover the widely observed anisotropic scaling law k‖∝k⊥2∕3 between parallel and perpendicular wave numbers (with reference to B0ê‖) and to obtain for the total-energy spectrum E(k⊥,k‖)∼k⊥−αk‖−β the universal prediction, 3α+2β=7. In particular, with such a prediction, the weak Alfvén wave turbulence constant-flux solution is recovered and, for the first time, a possible explanation to its precursor found numerically by Galtier et al. [J. Plasma Phys. 63, 447 (2000)] is given.

Influence of weak electrostatic perturbations on the trajectories of circulating particles in a tokamak magnetic field

The influence of weak electrostatic perturbations on the trajectories of circulating particles in a tokamak magnetic field is analyzed. The parameters of the trajectories calculated in the drift approximation allow one to determine the spatial scale of diffusion. The resonant interaction between particles and waves is considered. The possibility of the emergence of collisionless diffusion in the strong turbulence regime is analyzed.

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.

Nonlinear coupling of whistler wave turbulence with magnetosonic perturbations

The coupling between the short scale whistler turbulence and the long scale magnetosonic excitations are studied in both weak and strong turbulence regimes. The coupling occurs via the following mechanism. The nonlinear interactions among the whistler waves can lead to low frequency perturbations involving ion motion. The low frequency perturbation changes the background plasma density and the magnetic field, thereby altering the whistler wave trajectories. Wave kinetic description and Fourier representation are adopted for the whistler turbulence and the magnetosonic excitations, respectively, keeping in view the disparity in their scales. It is shown that the turbulent spectrum of whistler waves is modulationally unstable to magnetosonic excitations. For the weakly turbulent case, it is shown that the long scale magnetosonic scales backreact on the whistler spectrum, leading to a diffusion of the whistler spectrum towards shorter scales. However, for a strongly turbulent case, the whistler wave trajectories can become trapped inside the magnetosonic waves, thereby leading to the formation of a variety of nonlinear coherent structures. These structures are of relevance for understanding the phenomena of intermittency in magnetofluids.

Dissipation of strong Langmuir turbulence in nonisothermal non-Maxwellian plasma

The regime of strong Langmuir turbulence characterized by the plasma nonisothermality and by the presence of an appreciable non-Maxwellian hot-electron component was experimentally studied. Turbulence was excited in the preliminary produced plasma by the relativistic electron beam. Thomson scattering of laser IR radiation served as the main diagnostic method. The spatial spectra of the Langmuir turbulence and of the attendant ion-sound turbulence were studied using Thomson collective scattering. Thomson incoherent scattering was used for studying the plasma electron distribution function and searching for the local dips of plasma density. Stark spectroscopy of turbulent microfields and the method of observation of plasma radiation at the double plasma frequency were also used. Based on the experimental data, the mechanism of Langmuir oscillation damping by plasma electrons was analyzed. The Langmuir wave conversion induced by the ion-sound turbulence is the most probable channel for energy transfer from the turbulence to plasma electrons, the low-frequency fluctuations being the direct consequence of the strong Langmuir turbulence.

Comparative study of different advective schemes: Application to the MECCA model

A 3-D version of the MECCA model (Model of Estuarine and Coastal Circulation Assessment) is used to simulate the dynamics of the Eastern part of the English Channel. This area is characterized by a strong tidal turbulent regime and a frontal zone identified near the French coast by a low-salinity band. The model uses the upwind scheme to approximate the advective terms. Results show that the model overestimates the band width of the frontal zone and that this anomaly is definitely caused by the numerical diffusion introduced by the so-called upwind scheme (first-order approximation). In this paper, we study the flux-limiter schemes as an alternative to the upwind method in order to reduce this non-physical diffusion. To illustrate the improvements provided by this type of schemes, a comparison in 2-D schematic cases is made between the upwind and centered scheme with more recent higher-order schemes combined with limiter namely Minmod, Superbee, Van Leer and Monotonized Centered (MC) (called also MUSCL scheme). Respecting the CFL condition, our numerical simulations show that the flux-limiter schemes reduce the numerical diffusion and eliminate the oscillations caused by the non-limited higher-order schemes. For the schematic and realistic cases, the Superbee limiter is a good compromise between shape preservation and computational cost.

Flux-limiter schemes for oceanic tracers: application to the English Channel tidal model

A 2-D numerical model has been used to simulate the dynamics of the Eastern part of the English Channel. This area is characterized by a strong tidal turbulent regime and a frontal zone identified near the French coast by a low-salinity band. The model uses the characteristics method with a bi-cubic interpolation to approximate the advective terms. Results show that the model overestimates the band width of the frontal zone. This anomaly is caused certainly by the numerical diffusion introduced by the interpolation procedure used with the characteristics scheme. In order to reduce this non-physical diffusion, we investigate, in this study, the flux-limiter schemes as an alternative of the characteristics method. To illustrate the improvements provided by this type of schemes, comparisons in 2-D model cases are made between the upwind and centred scheme with more recent higher order schemes combined with limiters namely Minmod, Superbee, Van Leer and Monotonized Centred (MC) (also called MUSCL scheme). Numerical simulations show that when the CFL condition is satisfied, the flux limiter schemes reduce the numerical diffusion and suppress the oscillations caused by the non-limited higher order schemes. For the model and realistic cases, the Superbee limiter was found to be a good compromise between shape preservation and computational cost.

Effect of ambient density fluctuations on Langmuir wave collapse and strong turbulence

The effect of ambient density fluctuations on Langmuir wave collapse and strong Langmuir turbulence is investigated. Hamiltonian analysis of the collapse threshold implies that fluctuations with scales near those of nucleating wave packets can disrupt them before they can accumulate enough energy to collapse, provided the ambient fluctuation level is greater than that generated ponderomotively by the Langmuir waves. If packet disruption is effective, Langmuir energy cannot be dissipated via wave collapse and burnout, but must be scattered off density fluctuations directly to high wave numbers, as predicted by previous analyses. Numerical simulations of strong Langmuir turbulence confirm these predictions, with sudden transitions occurring from a strong-turbulence regime to one dominated by scattering or one with relatively rare wave collapses as a result of disruption of nascent wave packets. A corresponding sudden drop in Langmuir energy density is observed. Simulations of individual wave packets near the threshold for collapse show that such packets are easily disrupted by fluctuations with wavelengths near their linear scale, and confirm previous analytic disruption criteria.

A test-bed for Langmuir wave turbulence modeling of stimulated Raman backscatter

Stimulated Raman backscatter (SRS) may incorporate several, qualitatively different regimes of Langmuir wave dynamics, as it grows convectively in space. These typically include a strictly linear regime at the far end of the plasma from the laser, where SRS comes up from thermal Langmuir wave fluctuations; which may progress to a regime where the primary SRS daughter Langmuir wave is unstable to the Langmuir wave decay instability (LDI); and perhaps to a regime of strong Langmuir wave turbulence (SLT). The accurate description of the spatial transition between these regimes, which may involve large Langmuir wave correlation lengths, is a great challenge for turbulence modeling. In this paper a highly idealized model of SRS in periodic geometry is introduced which allows for the presence of a unique Langmuir wave regime for a given set of physical parameters, and therefore presents the minimal challenge for a turbulence model. One- and two-dimensional simulations of this SRS model, which allows for LDI and SLT as described by Zakharov’s model of nonlinear Langmuir wave dynamics, are compared with the predictions of a recently introduced turbulence model, and quantitative agreement is obtained, without the use of any ad hoc parameters, for the SRS reflectivity and correlation length, and Langmuir and acoustic wave energy densities, over an order of magnitude variation of SRS growth rate and ion acoustic damping rate.

Asymptotic states of decaying turbulence in two-dimensional incompressible flows.

We investigate the relaxation of a strongly turbulent fluid to metastable states, in times much shorter than the dissipation time scale. Several simulations of decaying two-dimensional Navier-Stokes flows were performed, which show the relaxation to organized states dominated by coherent vortex structures of length scales comparable to the size of the system. In the case of periodic boundary conditions, the organized state is characterized by a strong correlation between vorticity and stream function, the second of which satisfies a sinh-Poisson equation quite accurately. However, in the case of free-slip boundary conditions the relaxed state does not display any significant correlation between its vorticity and its stream function. Notwithstanding, in both cases the role of nonlinearities is found to be essential even at these late stages of the evolution. However, we show that even severe truncations of a few (short wave number) nonlinearly coupled Fourier modes provide an accurate description of the long-term dynamics of the fluid. Therefore the dynamics of the flow in these metastable states is somewhere in between a strong turbulent regime and a (mostly linear) dissipative relaxation stage. \textcopyright{} 1996 The American Physical Society.

Detection of langmuir solitons: implications for type III burst emission mechanisms at 2? PE

We present the experimental verification of existing theoretical models of emission mechanisms of solar type III bursts at the second harmonic of the plasma frequency, ω pe . This study is based on the detection of Langmuir and envelope solitons by the Ulysses spacecraft inside three type III burst source regions. We show that the oscillating-two-stream instability, coherent radiation by Langmuir solitons and stochastic phase mixing of the Langmuir waves in the strong turbulence regime are the appropriate emission mechanisms at 2ω pe .

Detection of Langmuir Solitons: Implications for Type III Burst Emission Mechanisms at 2ωPE

AbstractWe present the experimental verification of existing theoretical models of emission mechanisms of solar type III bursts at the second harmonic of the plasma frequency, ωpe. This study is based on the detection of Langmuir and envelope solitons by the Ulysses spacecraft inside three type III burst source regions. We show that the oscillating-two-stream instability, coherent radiation by Langmuir solitons and stochastic phase mixing of the Langmuir waves in the strong turbulence regime are the appropriate emission mechanisms at 2ωpe.

Anomalous transport due to the ion acoustic drift mode in tokamaks

In toroidal geometry, the ion Landau resonance is suppressed by the ion magnetic drift for modes propagating in the electron diamagnetic drift, and long wavelength modes with (k⊥ρ)2 ≃ \U0001d4aa(0.01) remain unstable. Coupling to the ion acoustic transit mode becomes predominant in such long wavelength regime allowing the mode frequency to exceed the diamagnetic drift frequency by a large margin. Finite β has a destabilizing influence on the toroidal ion acoustic mode particularly in the long wavelength regime. The quasilinear electron and ion thermal fluxes both increase with β partly through finite β modification of the mode frequency and/or growth rate, and partly through magnetic fluctuations. Even the trapped electron thermal flux exhibits an increase with β. In strong turbulence regime, the thermal diffusivity scales as Bohm corrected for finite β, χ ∝ (r/R)2(cT/eB)q2β.

Electromagnetic ion acoustic ballooning mode in tokamaks

It is shown that in toroidal geometry, extremely long-wavelength modes with the ion finite Larmor radius parameter (kperpendicular to rho )2 approximately=O(10-3) and mode frequency of the order of the ion acoustic transit frequency can be strongly destabilized by a finite beta (the ratio of plasma to magnetic pressure) well below the MHD ballooning limit. Ion Landau resonance is suppressed by the ion magnetic drift for modes propagating in the electron diamagnetic drift. The quasilinear electron and ion thermal fluxes both increase with beta . In the strong turbulence regime, a Bohm-type thermal diffusivity corrected for finite beta , chi alpha (r/R)2(cT/eB)q2 beta , emerges.

Anomalous diffusion and Lévy random walk of magnetic field lines in three dimensional turbulence

The transport of magnetic field lines is studied numerically where three dimensional (3-D) magnetic fluctuations, with a power law spectrum, and periodic over the simulation box are superimposed on an average uniform magnetic field. The weak and the strong turbulence regime, δB∼B0, are investigated. In the weak turbulence case, magnetic flux tubes are separated from each other by percolating layers in which field lines undergo a chaotic motion. In this regime the field lines may exhibit Lévy, rather than Gaussian, random walk, changing from Lévy flights to trapped motion. The anomalous diffusion laws 〈Δx2i〉∝sα with α≳1 and α<1, are obtained for a number of cases, and the non-Gaussian character of the field line random walk is pointed out by computing the kurtosis. Increasing the fluctuation level, and, therefore stochasticity, normal diffusion (α≂1) is recovered and the kurtoses reach their Gaussian value. However, the numerical results show that neither the quasi-linear theory nor the two dimensional percolation theory can be safely extrapolated to the considered 3-D strong turbulence regime.

Impurity transport studies in the Texas Experimental Tokamak (TEXT)

The results of impurity transport experiments in the Texas Experimental Tokamak (TEXT) [Nucl. Technol./Fusion 1, 479 (1981)] are compared with the predictions of a turbulence-based transport model. In the experiments, Sc was injected into the plasma using laser ablation and the time-resolved profiles of critical Sc ionization stages were measured along with the potential fluctuation profile. The experiment was simulated using a one-dimensional (1-D) radial transport code with the standard transport flux Γ=−D(∂n/∂r)+nV. The diffusion coefficient D and convective velocity V parameters were varied until the time-dependent 1-D simulations reproduce the data. This representation for the empirical impurity transport is compared with the E×B turbulent diffusivities and mobility based on the fluctuation data and the measured radial electric field. The agreement is best with the E×B diffusivity taken in the strong turbulence regime, where D=cD(φ̃/BT), while the comparison with the weak turbulence diffusivity and the collisional (no fluctuations) diffusivity results in qualitative disagreements. The percolation theory diffusivity (φ̃/BT)7/10(Δω/k2⊥)3/10 is also briefly discussed.

Weak- and strong-turbulence regimes of the forced Hasegawa-Mima equation

A Kolmogorov-type analysis of the energy- and enstrophy-cascading ranges of a forced Hasegawa-Mima equation allows one to derive a criterion for the threshold of the transition between the weak-turbulence and the strong-turbulence regimes. Contrary to general belief, it is found that due to the inverse energy cascade the large-scale portion of the inertial range is in the strong-turbulence regime in the limit of infinite Reynolds-like numbers for any finite amount of forcing.

Effective plasma heat conductivity in 'braided' magnetic field-II. Percolation limit

For pt.I see ibid., vol.33, no.7, p.795-807 (1991). This paper is devoted to the problem of anomalous transport across a magnetic field that includes a small stochastic component delta B. The perturbation is assumed to be so strongly stretched along the background magnetic field B0 that the parameter R is large: R identical to b0L0/ delta >>1 (here b0 identical to delta Bperpendicular to /B0<<1, and L0 is the longitudinal and delta the transverse correlation length of the magnetic perturbation). This strong turbulence limit, which is opposite to the quasi-linear one (R<<1), has certain notable features. The principal result is that the main transport is concentrated in very thin regions, being fractal sets with the dimension df, which can range in value from 2 to 2.75, depending on the spectrum of the magnetic perturbation. These regions consist of a small fraction of magnetic lines that percolate, that is, walk from the nonperturbed magnetic flux surfaces to a distance large compared to the transverse correlation length delta . Due to such a strong inhomogeneity of the transport distribution, as well as the long correlations, the standard transport averaging techniques fail, and one should make use of the percolation theory methods. Thus the strong turbulence regime is referred to here as the percolation limit. In comparison with the quasi-linear limit, the percolation limit has several additional intermediate regimes and the expressions for the effective heat conductivity chi eff include the critical exponents of 2-D percolation theory. The estimates of chi eff are obtained both in the collisional and collisionless limits, including the case of nonstationary magnetic perturbations.

The occurrence of strong electrostatic turbulence under various experimental conditions

The Langmuir waves of a plasma can be excited through resonant interactions with a particle beam or an electromagnetic beam. For these excitations, there exist three types of phenomenology for the turbulent behavior. (1) The weak interaction regime, after a quasi-linear stage, exhibits a tendency to accumulate waves on large scales through mode couplings for which no dissipation takes place. However, intense long waves undergo a self-modulation instability, which produces a set of localized wave packets. If the beam-plasma interaction occurs along the lines of a strong magnetic field, these solitary waves are stable at some level of approximation. (2) If the interaction takes place in a moderate or negligible magnetic field, the wave packets collapse towards a point singularity in agreement with Zakharov's prediction and burn out by giving their energy to suprathermal electrons. This is the strong turbulence regime, where nonlinear self-focusing dominates over the dispersion effect. The resulting collapse produces intense spikes in the electric field at the Debye scale. This is favorable for spectroscopy involving the turbulent Stark effect. Details of the physics are reviewed, with emphasis on the various expected spectra including the distribution of suprathermal electrons that could be compared with spectroscopic data. (3) There is also an “ultrastrong” regime that has been investigated and is characterized by spikes that are so intense that the local electrostatic energy is greater than the internal energy. Spectroscopic data for this regime have recently become available from a relativistic beam-plasma experiment done at the University of California, Irvine.