Unstable Drift Waves Research Articles

Unstable drift waves in presence of dust

The well-known stability of the drift wave in a sheared slab geometry does not hold in the presence of dust particles. Due to the presence of dust particles, the magnetic shear damping is reduced drastically. As a result, collisionless drift modes become unstable under typical parameter regimes of tokamak. Consequently, drift wave must still be considered as an underlying dynamic of anomalous transport in tokamak edges, where dust particles are found to be abundant, the same physics is expected in the spacial environments as well.

Spectral transition of multiscale turbulence in the tokamak pedestal

The transition in the turbulence spectrum from ion-scale dominated regimes to multiscale transport regimes that couple ion and electron scales is studied with gyrokinetic simulations of turbulent transport. The simulations are based on DIII-D high-confinement mode (H-mode) plasma parameters in the tokamak pedestal. The transition is initiated by varying the ion temperature gradient. To our knowledge, no full multiscale simulations of pedestal-like transport have been done previously. The experimental parameters lie in a bifurcation region between the two regimes. At long wavelengths, a complex, ion-direction hybrid mode is the dominant linearly unstable drift wave, while an electron temperature gradient-driven mode is unstable at short wavelengths. In the transition from the multiscale branch to the ion-scale branch, the magnitude of the ion-scale poloidal wavenumber spectrum of the nonlinear turbulent energy flux increases and the magnitude of the high-wavenumber spectrum decreases. The decrease in the electron-scale transport is due to nonlinear mixing with ion-scale fluctuations and the ion-scale-driven zonal flows. A shift in the total energy associated with the fluctuating electrostatic potential intensity from dominantly drift kinetic energy in the multiscale regime to dominantly potential intensity in the ion-scale regime is well-correlated with the trend in the total energy flux.

Spontaneous and explicit parity-time-symmetry breaking in drift-wave instabilities.

A method of parity-time- (PT) symmetry analysis is introduced to study the high-dimensional, complicated parameter space of drift-wave instabilities. We show that spontaneous PT-symmetry breaking leads to the ion temperature gradient instability of drift waves, and the collisional instability is the result of explicit PT-symmetry breaking. A new unstable drift wave induced by finite collisionality is identified. It is also found that gradients of ion temperature and density can destabilize the ion cyclotron waves when PT symmetry is explicitly broken by a finite collisionality.

Coulomb collisions in strongly anisotropic plasmas II. Cyclotron cooling in laboratory pair plasmas

The behaviour of a strongly magnetised collisional electron–positron plasma that is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various timescales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Indeed, these are the exact conditions likely to be attained in the first laboratory electron–positron plasma experiments currently being developed, which will typically have very low densities and be confined in very strong magnetic fields. The constraint of strong magnetisation adds an additional complication in that long-range Coulomb collisions, which are usually negligible, must now be considered. A rigorous collision operator for these long-range collisions has never been written down. Nevertheless, we show that the collisional scattering can be accounted for without knowing the explicit form of this collision operator. The rate of radiation emission is calculated and it is found that the loss of energy from the plasma is proportional to the parallel collision frequency multiplied by a factor that only depends logarithmically on plasma parameters. That is, this is a self-accelerating process, meaning that the bulk of the energy will be lost in a few collision times. We show that in a simple case, that of straight field-line geometry, there are no unstable drift waves in such plasmas, despite being far from Maxwellian.

Fractional Kuramoto–Sivashinsky equation with power law and stretched Mittag-Leffler kernel

The presence of a complex spatio-temporal behavior in spatially extended systems (SES) as a result of several mechanisms that interact non-linearly with other nearby has attracted a lot of attention in recent decades. A well-known example of SES is the Kuramoto–Sivashinsky (KS) equation. In the search for a broader perspective of some unusual irregularities observed in the context of phase turbulence in the reaction–diffusion systems, the propagation of the wrinkled flame front and the unstable drift waves driven by the collision of electrons in a Tokamak, we explored the possibility of extending the analysis of the KS equation with three perturbation levels using the conceptions of fractional differentiation with non-local and non-singular kernel. We use the fractional order operator of Atangana–Baleanu in the sense of Liouville–Caputo (ABC) to set the fractional model of KS that we analyze in this article. We prove existence and uniqueness of a continuous solution to fractional KS model, using the fixed-point theorem and the Picard–Lindelöf approach, provided conditions on the perturbation parameters and the order of the fractional operator. In addion, using the theory of fixed point, we present the stability of the iterative method generated by the Picard–Lindelöf approach. Finally, we presented the approximate analytical solution of the fractional KS equation using the homotopy perturbation transform method. Some numerical simulations are carried out for illustrating the results obtained.

Global simulation of ion temperature gradient instabilities in a field-reversed configuration

We investigate the global properties of drift waves in the beam driven field-reversed configuration (FRC), the C2-U device, in which the central FRC and its scrape-off layer (SOL) plasma are connected with the formation sections and divertors. The ion temperature gradient modes are globally connected and unstable across these regions, while they are linearly stable inside the FRC separatrix. The unstable global drift waves in the SOL show an axially varying structure that is less intense near the central FRC region and the mirror throat areas, while being more robust in the bad curvature formation exit areas.

Drift wave stabilized by an additional streaming ion or plasma population.

It is shown that the universally unstable kinetic drift wave in an electron-ion plasma can very effectively be suppressed by adding an extra flowing ion (or plasma) population. The effect of the flow of the added ions is essential, their response is of the type (vph-vf0)exp[-(vph-vf0)2], where vf0 is the flow speed and vph is the phase speed parallel to the magnetic field vector. The damping is strong and it is mainly due to this ion exponential term, and this remains so for vf0<vph.

Excitation of Turbulent Fluctuations by Unstable Drift Wave in Non-uniform Plasma Flow

Excitation of Turbulent Fluctuations by Unstable Drift Wave in Non-uniform Plasma Flow

Spatiotemporal synchronization of drift waves in a magnetron sputtering plasma

A feedforward scheme is applied for drift waves control in a magnetized magnetron sputtering plasma. A system of driven electrodes collecting electron current in a limited region of the explored plasma is used to interact with unstable drift waves. Drift waves actually appear as electrostatic modes characterized by discrete wavelengths of the order of few centimeters and frequencies of about 100 kHz. The effect of external quasi-periodic, both in time and space, travelling perturbations is studied. Particular emphasis is given to the role played by the phase relation between the natural and the imposed fluctuations. It is observed that it is possible by means of localized electrodes, collecting currents which are negligible with respect to those flowing in the plasma, to transfer energy to one single mode and to reduce that associated to the others. Due to the weakness of the external action, only partial control has been achieved.

Review and limitations of 3D plasma blob modeling with reduced collisional fluid equations

Recent 3D studies on plasma blobs (coherent structures found in the edge region of magnetic confinement devices) have demonstrated that the drift wave instability can strongly limit the blob’s coherency and cross field convective nature that is predicted by 2D theory. However, the dominant unstable drift wave modes that effect plasma blobs were found to exist in parameter regimes that only marginally satisfied several of the major assumptions considered for the validity of the reduced collisional fluid equations used in the study. Namely, the neglect of electron heat flow, finite electron mean free path effects, and thermal ions. A follow up study demonstrated how the drift wave instability might change if a set of equations that does not suffer from the limitations mentioned above were considered. In the present paper, the results of this later work are used to discuss the limitations on using the collisional fluid equations for 3D studies of plasma blobs.

Effects of parallel electron dynamics on plasma blob transport

The 3D effects on sheath connected plasma blobs that result from parallel electron dynamics are studied by allowing for the variation of blob density and potential along the magnetic field line and using collisional Ohm’s law to model the parallel current density. The parallel current density from linear sheath theory, typically used in the 2D model, is implemented as parallel boundary conditions. This model includes electrostatic 3D effects, such as resistive drift waves and blob spinning, while retaining all of the fundamental 2D physics of sheath connected plasma blobs. If the growth time of unstable drift waves is comparable to the 2D advection time scale of the blob, then the blob’s density gradient will be depleted resulting in a much more diffusive blob with little radial motion. Furthermore, blob profiles that are initially varying along the field line drive the potential to a Boltzmann relation that spins the blob and thereby acts as an addition sink of the 2D potential. Basic dimensionless parameters are presented to estimate the relative importance of these two 3D effects. The deviation of blob dynamics from that predicted by 2D theory in the appropriate limits of these parameters is demonstrated by a direct comparison of 2D and 3D seeded blob simulations.

3D Blob Modelling with BOUT++

AbstractPlasma blobs found in the edge region of tokamaks are important to understand because they contribute to a large amount of the plasma particle transport in the SOL (scrape off layer). Most of the work to date is limited to 2D theory and simulations by ignoring the variation of blob parameters along the magnetic field line. 3D effects are examined in the electrostatic limit in this paper using the code BOUT++ by allowing for the variation of blob density and potential along the field line. It is demonstrated that the 3D variation of these parameters can lead to a Boltzmann potential relation that will cause the blob to spin and induce turbulent motion via unstable drift waves (© 2012 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Effect of Drift Waves on Plasma Blob Dynamics

Most of the work to date on plasma blobs found in the edge region of magnetic confinement devices is limited to 2D theory and simulations which ignore the variation of blob parameters along the magnetic field line. However, if the 2D convective rate of blobs is on the order of the growth rate of unstable drift waves, then drift wave turbulence can drastically alter the dynamics of blobs from that predicted by 2D theory. The density gradients in the drift plane that characterize the blob are mostly depleted during the nonlinear stage of drift waves resulting in a much more diffuse blob with a greatly reduced radial velocity. Sheath connected plasma blobs driven by effective gravity forces are considered in this Letter and it is found that the effects of resistive drift waves occur at earlier stages in the 2D motion for smaller blobs and in systems with a smaller effective gravity force. These conclusions are supported numerically by a direct comparison of 2D and 3D seeded blob simulations.

Gyrokinetic simulation of turbulence driven geodesic acoustic modes in edge plasmas of HL-2A tokamak

Strong correlation between high frequency microturbulence and low frequency geodesic acoustic mode (GAM) has been observed in the edge plasmas of the HL-2A tokamak, suggesting possible GAM generation via three wave coupling with turbulence, which is in turn modulated by the GAM. In this work, we use the gyrokinetic toroidal code to study the linear and nonlinear development of the drift instabilities, as well as the generation of the GAM (and low frequency zonal flows) and its interaction with the turbulence for realistic parameters in the edge plasmas of the HL-2A tokamak for the first time. The simulation results indicate that the unstable drift wave drives strong turbulence in the edge plasma of HL-2A. In addition, the generation of the GAM and its interaction with the turbulence are all observed in the nonlinear simulation. The simulation results are in reasonable agreement with the experimental observations.

Drift wave instability in the Helimak experiment

Electrostatic drift wave linear stability analysis is carried out for the Helimak configuration and compared against experimental data. Density fluctuation and cross-spectrum measurements show evidence of a coherent mode propagating perpendicular to the magnetic field which becomes unstable at k⊥ρs∼0.15. By comparing the experimental results with the wave characteristic of linear two-fluid theory, this mode is identified as an unstable resistive drift wave driven by the density gradient and magnetic grad-B/curvature present in an otherwise magnetohydrodynamic stable steady-state equilibrium.

Nonlinear saturated states of the magnetic-curvature-driven Rayleigh–Taylor instability in three dimensions

Three-dimensional electromagnetic fluid simulations of the magnetic-curvature-driven Rayleigh–Taylor instability are presented. Issues related to the existence of nonlinear saturated states and the nature of the temporal evolution to such states from random initial conditions are addressed. It is found that nonlinear saturated states arising from generation of zonal shear flows continue to exist in certain parametric domains but their spectrum and spatial characteristics have important differences from earlier two-dimensional results reported in Phys. Plasmas 4, 1018 (1997) and Phys. Plasmas 8, 5104 (2001). In particular, the three-dimensional nonlinear states possess a significant power level in short scales and the spatial structures of the potential and density fluctuations appear not to develop any functional correlations. Electromagnetic effects are found to inhibit the formation of zonal flows and thereby to considerably restrict the parametric domain of nonlinear stabilization. The role of finite k‖ and the contribution of the unstable drift wave branch are also discussed and delineated through a number of simulation studies carried out in special simplified limits.

Resistive Drift-Alfvén Instability in a Cylindrical Magnetized Plasma

Linearized eigenmode equations governing resistive drift-Alfvén modes are derived by using the two-fluid model or a cylindrical plasma with a uniform longitudinal magnetic field. The local dispersion relation shows that the shear Alfvén wave couples with the unstable resistive drift wave due to the finite Larmor radius effect measured with the electron temperature. The eigenmode equations are solved by the shooting method in the cylindrical plasma.Generally growth rates decrease with the increase of electron pressure for the larger m mode. This behavior seems consistent with a theoretical model that stabilization of drift-Alfvén wave induces the L(Low confinement)-H(High confinement) transition at the edge of tokamak plasma.

Drift waves in plasmas with sheared flows

In the standard approach to the problem of shear stabilization of drift waves the diamagnetic drift velocity v* is regarded as a constant, which is usually not satisfied at the edge of a tokamak plasma. In configurations of this type, with a steep density gradient and radially sheared transverse velocity field, the magnetic shear stabilization criteria are severely restricted, and the velocity profile curvature v0″(x) is found to play a crucial role. In the strongly nonlinear regime, unstable drift waves may saturate into stationary coherent vortex-type structures. The latter include a tripolar vortex.

Nonlinear mode competition between unstable drift waves in an rf heated ring discharge

The nonlinear wave-wave interaction between unstable drift modes of different wave numbers existing in an rf heated, magnetized plasma is studied experimentally by means of capacitive probe measurements during the evolution of the discharge towards steady state. The results are compared with theoretical calculations. Special interest is attached to the unstable growth of multiple modes arising out of the noise level, where strong suppressive interaction between different modes is observed, finally leading to a single mode spectrum.

Experiments on drift wave launching: I. Dispersion curves and damping rates

We describe experiments on the launching of drift waves in the UMIST Quadrupole GOLUX, presenting the general principles of successful launching and showing how these are applied to launch both the unstable drift waves which occur spontaneously in the device, and other stable modes representing different branches of the drift wave dispersion relation. In each case the measured dispersion curves are presented and compared with theory. All the waves appear to be spatially damped, including those known to be unstable; we propose that this is due to systematic error in the detection system. The results suggest that only if the measured decay constant exceeds about can we be certain that the waves are actually damped. This is the case at low frequencies, where the dissipation is due to ion Landau damping, and again at high wavenumbers where no suitable dissipative process has been discovered. We conjecture that the effect is due to radiative damping, associated with the breakdown of the one-dimensional propagation assumed in the theory.