Electrostatic Drift Waves Research Articles

Linear stability analysis of the electrostatic drift wave in the electron thermal internal transport barrier in EAST

An alternative local electrostatic gyrokinetic eigenvalue code is developed for the ion-temperature-gradient-driven mode, the trapped-electron mode (TEM), and the electron-temperature-gradient (ETG)-driven mode. It numerically solves the linear eigenvalue problem for the electrostatic drift waves in the Fourier transformed space and benchmarks well with the HD-7 code and FULL code. The linear ETG and TEM instabilities in the electron thermal internal transport barrier (eITB) with dominant electron heating in experimental advanced superconducting tokamak are analyzed by using this code. The linear analysis results are consistent with that from the critical electron-temperature-gradient threshold analysis. Moreover, the sensitivity of ETG and TEM instabilities to parameters during the eITB formation has been investigated. For the typical eITB discharge, it is found that the instability of ETG mode is more sensitive to the stabilizing effect of the electron–ion temperature ratio (τe), while the instability of TEM is more sensitive to the destabilizing effect of ηe. In addition, mixing length estimation of the turbulent transport in the eITB is also discussed, which suggests that the TEM may be saturated by other nonlinear effects than the resonance broadening.

Nonlinear dynamical modelling of high frequency electrostatic drift waves using fluid theoretical approach in magnetized plasma

A novel third order nonlinear evolution equation governing the dynamics of the recently observed high frequency electrostatic drift waves has been derived in the framework of a plasma fluid model in an inhomogeneous magnetized plasma. The corresponding linear dispersion relation arising out of the fluid equations has been studied in detail for the conventional low frequency as well as the recently observed high frequency electrostatic drift waves along with the electrostatic ion cyclotron waves. The derived nonlinear evolution equation of third order is then decomposed into two second order equations as the order of the equation becomes reduced after this kind of decomposition under certain conditions, and one equation becomes linear whereas the other equation becomes nonlinear. The detailed analysis of fixed points leading to bifurcations has been performed using the qualitative theory of differential equations and the bifurcation theory of planar dynamical systems for the reduced second order nonlinear equation. The bifurcation curves for the individual fixed points are also shown for the variations of different parameters in the parameter space of this reduced nonlinear equation. Then some exact as well as approximate travelling wave solutions of this reduced nonlinear equation have been derived. As the other second order reduced equation is linear in nature, its exact oscillatory and exponential solutions are obtained. The intersection of the solutions of these two reduced second order equations provides the solutions of the original third order nonlinear evolution equation; it is verified that the solutions of the reduced nonlinear second order equation are subsets of the oscillatory solution of the reduced linear second order equation in most cases whereas the intersection is different if the exponential solution of the reduced linear second order equation is considered. This further implies that the solutions of the reduced second order nonlinear equation can directly represent the solutions of the original third order nonlinear evolution equation in most cases representing the dynamics of the nonlinear high frequency electrostatic drift waves. These solutions of the novel third order nonlinear evolution equation represent certain vortex-like structures as our work is restricted to (1 + 1) dimensions only. The possible applications of our novel results on the dynamics of the high frequency electrostatic drift waves are discussed along with future directions for research in this field.

Transport analysis of NBI heating H-mode experiment on HL-2 A with integrated modeling

The physical process of tokamak plasma spans a large space-time scale, and the main physical processes differ widely in different spatial regions (such as core, pedestal, scraping-off layer, divertor region), so it is necessary to adopt the integrated modeling method to analyze the physical problems on a global multi-space-time scale. In order to study in depth the transport and confinement during the steady-state or ramp-up of the tokamak discharging experiment, it is necessary to use a variety of physical programs to carry out integrated simulation research and physical analysis. Based on the OMFIT platform, in this paper the integrated simulation verification and analysis of the shot #37012 are conducted, which is a high-<inline-formula><tex-math id="M1">\begin{document}$\beta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20211941_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20211941_M1.png"/></alternatives></inline-formula> discharge experiment on HL-2A device and verifies the reliability and applicability of those programs. In this process, the experimental parameters are checked and supplemented by selecting appropriate models. The simulation results after evolution are consistent with the experimental results. On this basis, we use the TGLF model to analyze the linear electrostatic drift wave instability in the core region. The reason for the improvement of the H-mode confinement by NBI off-axis heating is that the ETG instability in the NBI power deposition region is suppressed. The transport is dominated by ITG instability in the internal transport barrier (ITB), and the transport is reduced to the level of neoclassical transport.

Role of microtearing mode in DIII-D and future high-βp core plasmas

Excellent confinement has been routinely observed in DIII-D (J. L. Luxon, Nucl. Fusion 2002) high βp discharges, which are characterized by a strong large-radius internal transport barrier (ITB) in almost all kinetic channels. Typically, the ion thermal transport is neoclassical with conventional long-wavelength turbulence instabilities suppressed by α stabilization, while the mechanism for the anomalous electron thermal transport remains unclear [Garofalo et al., Nucl. Fusion 55(12), 123025 (2015)]. A new gyrokinetic analysis shows that while the large values of α in the ITB can stabilize all local electrostatic drift wave (ES-DW) instabilities as well as the kinetic ballooning mode, a new slab-like microtearing mode (MTM) with its eigenfunction mainly peaking on the high field slide is destabilized. This destabilization is shown to be more likely to happen in discharges with high safety factors. Nonlinear gyrokinetic simulations demonstrate that this MTM branch can reproduce the experimentally inferred electron thermal flux in the ITB region and, therefore, provide convincing evidence that the electron temperature profile in the ITB is regulated by the MTM. Extrapolations to the future scenarios, like ITER high βp plasmas, show that the dominant instability is likely to come back to ES-DW due to the lower density gradient and collisionality. However, even in this regime, some unusual features associated with MTMs predicted for DIII-D parameters, such as the high-field-side peaking and slab nature, may remain for the reactor ES-DW.

Generalized non-ideal treatment and growth rates analysis of drift waves instabilities in a collisions-free magnetized dusty plasma

Dust acoustic wave propagation in weak magnetized homogeneous dusty plasmas has been extensively and successfully studied by different authors. Here, it is analyzed the behavior of electrostatic drift waves of very low frequency, appearing as due to the motion of plasma particles across the static magnetic field and the inhomogeneity introduced by the distribution of the particles in the dusty plasma generating the well-known diamagnetic effect. To study this situation, the kinetic Vlasov model in plasmas will be used. However, these models tend to behave unstably driven by the quasi-equilibrium of the diamagnetic current arising by the heavier species of dusty plasma particles. While other authors have used a standard state equation, such as the Van der Waals one, here, a more accurate model has been chosen as the equation of Ree and Hoover, a state equation that can be considered as a new form of the state equation. Together with the multipole approximation of the dispersion function, Z53 [P. Martin et al., J. Math. Phys. 21, 280–283 (1980)] allows a new derivation to obtain the simplest form of the dispersion relation in the form of a polynomial with complex coefficients. This mathematical approach was realized successfully and allowed straightforward calculus of the growth rate due to the drift unstable mode. This problem has been extensively analyzed in this work, including the non-ideal effect of dusty plasmas. These unstable modes are well discriminated and plotted as a function of the density of the grains in dusty plasma and their radius. Temperature gradients and charge fluctuation have been ignored.

ITG mode driven vortices in spatially inhomogeneous magnetoplasma with generalized (r, q) distribution

In this paper, we have investigated the ion temperature gradient (ITG) driven electrostatic drift waves in the presence of non-thermal electrons that follow the generalized (r, q) distribution. In the linear regime, we have derived the linear dispersion relation of the coupled drift-ion acoustic wave. In the nonlinear regime, stationary solutions of the nonlinear equations have been obtained in the presence of gradients in equilibrium density, temperature and magnetic field. It has been found that the tail parameter q and the flatness parameter r strongly affect the profiles of linear and non-linear propagation characteristics of ITG driven electrostatic drift ion acoustic waves. It has been found that the flat-topped distribution augments the growth rate of the ITG driven electrostatic modes under consideration which is undesirable from the confinement stand point. It has also been shown that the double spectral indices r and q affect the structure of the nonlinear vortex structures. The comparison of the spatial scales over which vortices are formed for different distributions has also been presented.

Kappa distributed trapped electrons, drift wave instability and nonlinear structures in O–H plasma of ionosphere

Generation of drift waves by field-aligned shear flow of protons and oxygen ions is investigated in the presence of kappa distributed trapped electrons in upper ionosphere within auroral latitudes. Very low-frequency electrostatic waves having frequencies of the order of a few Hz observed by Freja satellite at altitude 1700 km can be either the ion acoustic waves (IAWs) or the electrostatic drift waves EDW depending up on density uniformity or non-uniformity in the region. Growth rate of drift wave increases in the presence of 0.4 percent hydrogen ions in oxygen plasma. Drift wave is coupled with the four branches of ion acoustic modes in this bi-ion plasma. In nonlinear regime, EDW and IAWs produce electrostatic solitary structures of a few meters width and their amplitude depends up on the density gradient scale length, non-thermality parameter and trapping of electrons.

A mechanism of neoclassical tearing modes onset by drift wave turbulence

The evolution of neoclassical tearing modes (NTMs) in the presence of electrostatic drift wave turbulence is investigated. In contrast with anomalous transport effect induced by turbulence on NTMs, a new mechanism that turbulence-driven current can affect the onset threshold of NTMs significantly is suggested. Turbulence acts as a source or sink to exchange energy with NTMs. The turbulence-driven current can change the parallel current in magnetic islands and affect the evolution of NTMs, depending on the direction of turbulence intensity gradient. When the turbulence intensity gradient is negative, the turbulence-driven current enhances the onset threshold of NTMs. When the turbulence intensity gradient is positive, it can reduce or even overcome the stabilizing effect of neoclassical polarization current, leading to a small onset threshold of NTMs. This implies that NTMs can appear without noticeable magnetohydrodynamics (MHD) events.

Electrons in regions of high phase density exhibit uncanny traits in the study of linear and nonlinear drift waves in spatially non-uniform magnetoplasmas

Linear and nonlinear waves are examined on the ion time scale in a spatially inhomogeneous plasma having electrons that follow product bi (r,q) distribution. It has been shown that the linear dispersion relation for product bi (r,q) distribution undergoes appreciable changes as opposed to the one for the Maxwellian electrons. It has been found that the drift wave frequency is highest for flat-topped distribution, whereas it is lowest for the spiky distribution. It has been found that the drift solitary wave with flat-topped distribution (i.e., r > 0) is one of a kind and exhibits peculiar characteristics. It has been shown that Maxwellian and kappa-like electrons cannot alter the nature of the electrostatic drift waves under consideration; however, the spiky electrons can. The results obtained here are general and can be applied to many regions of space plasmas where the satellite missions have reported the presence of electron distribution functions that show deviation from the Gaussian behavior.

Drift dust acoustic soliton in the presence of field-aligned sheared flow and nonextensivity effects

Low frequency electrostatic dust drift acoustic (DDA) waves are studied in an inhomogeneous dust magnetoplasma comprised of dust components of opposite polarity, Boltzmannian ions, and nonextensive distributed electrons. The magnetic-field-aligned dust sheared flow drives the electrostatic drift waves in the presence of ions and electrons. The sheared flow decreases or increases the frequency of the DDA wave, mostly depending on its polarity. The conditions of instability for this mode, with nonextensivity and dust streaming effects, are discussed. The nonlinear dynamics is then investigated for the DDA wave by deriving the Koeteweg-deVries (KdV) nonlinear equation. The KdV equation yields an electrostatic structure in the form of a DDA soliton. The relevancy of the work to laboratory four component dusty plasmas is illustrated.

Magnetospheric Multiscale Observations of an Ion Diffusion Region With Large Guide Field at the Magnetopause: Current System, Electron Heating, and Plasma Waves

AbstractWe report Magnetospheric Multiscale (MMS) observations of a reconnecting current sheet in the presence of a weak density asymmetry with large guide field at the dayside magnetopause. An ion diffusion region (IDR) was detected associated with this current sheet. Parallel current dominated over the perpendicular current in the IDR, as found in previous studies of component reconnection. Electrons were preferentially heated parallel to the magnetic field within the IDR. The heating was manifested as a flattop distribution below 400 eV. Two types of electromagnetic electron whistler waves were observed within the regions where electrons were heated. One type of whistler wave was associated with nonlinear structures in E|| with amplitudes up to 20 mV/m. The other type was not associated with any structures in E||. Poynting fluxes of these two types of whistler waves were directed away from the X‐line. We suggest that the nonlinear evolution of the oblique whistler waves gave rise to the solitary structures in E||. There was a perpendicular super‐Alfvénic outflow jet that was carried by magnetized electrons. Intense electrostatic lower hybrid drift waves were localized in the current sheet center and were probably driven by the super‐Alfvénic electron jet, the velocity of which was approximately equal to the diamagnetic drift of demagnetized ions. Our observations suggest that the guide field significantly modified the structures (Hall electromagnetic fields and current system) and wave properties in the IDR.

Formation of Nonlinear Solitary Vortical Structures by Coupled Electrostatic Drift and Ion-Acoustic Waves

Propagation of coupled electrostatic drift and ion-acoustic waves (DIAWs) is presented. It is shown that nonlinear solitary vortical structures can be formed by low-frequency coupled electrostatic DIAWs. Primary waves of distinct (small, intermediate and large) scales are considered. Appropriate set of 3D equations consisting of the generalized Hasegawa–Mima equation for the electrostatic potential (involving both vector and scalar nonlinearities) and the equation of motion of ions parallel to magnetic field are obtained. According to experiments of laboratory plasma mainly focused to large scale DIAWs, the possibility of self-organization of DIAWs into the nonlinear solitary vortical structures is shown analytically. Peculiarities of scalar nonlinearities in the formation of solitary vortical structures are widely discussed.

Fractal boundaries in chaotic hamiltonian systems

Fractal structures are typically present in the dynamics of chaotic orbits in non-integrable open Hamiltonian systems and result from the extremely complicated nature of the invariant manifolds of unstable periodic orbits. Exit basins, the set of initial conditions leading to orbits escaping through a given exit, have very frequently fractal boundaries. In this work we analyze exit basin boundaries in a dynamical system of physical interest, namely the motion of charged particles in a magnetized plasma subjected to electrostatic drift waves, and characterize in a quantitative way the fractality of these structures and their observable consequences, as the final-state uncertainty.

Drift-wave stability in the field-reversed configuration

Gyrokinetic simulations of C-2-like field-reversed configuration (FRC) find that electrostatic drift-waves are locally stable in the core. The stabilization mechanisms include finite Larmor radius effects, magnetic well (negative grad-B), and fast electron short circuit effects. In the scrape-off layer (SOL), collisionless electrostatic drift-waves in the ion-to-electron-scale are destabilized by electron temperature gradients due to the resonance with locally barely trapped electrons. Collisions can suppress this instability, but a collisional drift-wave instability still exists at realistic pressure gradients. Simulation results are in qualitative agreement with C-2 FRC experiments. In particular, the lack of ion-scale instability in the core is not inconsistent with experimental measurements of a fluctuation spectrum showing a depression at ion-scales. The pressure gradient thresholds for the SOL instability from simulations are also consistent with the critical gradient behavior observed in experiments.

Generation of zonal flows by coupled electrostatic drift and ion-acoustic waves

Generation of sheared zonal flow by low-frequency coupled electrostatic drift and ion-acoustic waves is presented. Primary waves of different (small, intermediate, and large) scales are considered, and the appropriate system of equations consisting of generalized Hasegawa-Mima equation for the electrostatic potential (involving both vector and scalar nonlinearities) and equation of parallel to magnetic field ions motion is obtained. It is shown that along with the mean poloidal flow with strong variation in minor radius mean sheared toroidal flow can also be generated. According to laboratory plasma experiments, main attention to large scale drift-ion-acoustic wave is given. Peculiarities of the Korteweg-de Vries type scalar nonlinearity due to the electrons temperature non-homogeneity in the formation of zonal flow by large-scale turbulence are widely discussed. Namely, it is observed that such type of flows need no generation condition and can be spontaneously excited.

Coupled drift and ion-acoustic cnoidal waves in an inhomogeneous plasma with field-aligned shear flow

The coupled drift and ion-acoustic cnoidal wave structures in an inhomogeneous plasma with shear flow along the magnetic field lines are investigated. The linear analysis and instability condition of the electrostatic drift and ion acoustic waves with the shear flow is also presented. The Sagdeev potential approach is employed for studying nonlinear periodic wave structures. The analytical solutions of cnoidal wave and soliton structures for coupled drift and ion-acoustic waves in the presence of field-aligned shear flow are obtained. It is found that the shear flow along the magnetic field has a significant effect on the formation of cnoidal waves and solitons in inhomogeneous plasmas. The numerical results in phase plane portraits of cnoidal and soliton structures of coupled drift and ion-acoustic waves are agreed with the satellite observations of F-region ionosphere containing shear field-aligned flows.

Generation of electrostatic drift zonal flows under the action of mean sheared flows

Generation of large-scale zonal flows by the small-scale electrostatic drift wave turbulence in the magnetized plasma under the action of mean poloidal sheared flow is considered. Attention to large-scale (compared to the ion Larmor radius) drift structures is paid. To this end, the generalized Hasegawa-Mima equation containing both vector and scalar nonlinearities is derived, and the appropriate eigenvalue problem is solved numerically. Destabilizing role of the small amplitude mean shear flow and spatial inhomogeneity of electron temperature is shown.

Effect of resonant magnetic perturbations on microturbulence in DIII-D pedestal

Vacuum resonant magnetic perturbations (RMP) applied to otherwise axisymmetric tokamak plasmas produce in general a combination of non-resonant effects that preserve closed flux surfaces (kink response) and resonant effects that introduce magnetic islands and/or stochasticity (tearing response). The effect of the plasma kink response on the linear stability and nonlinear transport of edge turbulence is studied using the gyrokinetic toroidal code GTC for a DIII-D plasma with applied n = 2 vacuum RMP. GTC simulations use the 3D equilibrium of DIII-D discharge 158103 (Nazikian et al 2015 Phys. Rev. Lett. 114 105002), which is provided by nonlinear ideal MHD VMEC equilibrium solver in order to include the effect of the plasma kink response to the external field but to exclude island formation at rational surfaces. Analysis using the GTC simulation results reveal no increase of growth rates for the electrostatic drift wave instability and for the electromagnetic kinetic-ballooning mode in the presence of the plasma kink response to the RMP. Furthermore, nonlinear electrostatic simulations show that the effect of the 3D equilibrium on zonal flow damping is very weak and found to be insufficient to modify turbulent transport in the electrostatic turbulence.

Finite amplitude nonlinear drift waves in a spatially inhomogeneous degenerate plasma with Landau quantization and electron temperature corrections

In the present investigation, linear and nonlinear electrostatic drift waves in the presence of trapped electrons with quantizing magnetic field and finite electron temperature effects in dense plasmas have been studied. The linear dispersion relation of the ion drift wave has been derived and it has been found that the Landau quantization and finite temperature effects significantly alter the linear propagation characteristics of the wave under consideration. Employing the Sagdeev potential approach, the formation of finite amplitude drift solitary structures has been investigated in the presence of a quantizing magnetic field for both fully and partially degenerate plasmas. Both compressive and rarefactive drift solitary structures have been obtained for different values of quantizing magnetic field and finite electron temperature effects. The theoretical results obtained have been analyzed numerically for the parameters typically found in white dwarfs.

A statistical study of gyro-averaging effects in a reduced model of drift-wave transport

A statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic drift-waves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K0, becomes K0J0(ρ̂), where J0 is the zeroth-order Bessel function and ρ̂ is the Larmor radius. Assuming a Maxwellian probability density function (pdf) for ρ̂, we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturbation amplitude K0J0(ρ̂). Using these results, we compute the probability of loss of confinement (i.e., global chaos), Pc, and the probability of trapping in the main drift-wave resonance, Pt. It is shown that Pc provides an upper bound for the escape rate, and that Pt provides a good estimate of the particle trapping rate. The analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.