Low-frequency Turbulence Research Articles

Electrostatic wave generation and transverse ion acceleration by Alfvénic wave components of broadband extremely low frequency turbulence

We present results here from 2.5‐dimensional particle‐in‐cell simulations showing that the electrostatic (ES) components of broadband extremely low frequency (BBELF) waves could possibly be generated by cross‐field plasma instabilities driven by the relative drifts between the heavy and light ion species in the electromagnetic (EM) Alfvénic component of the BBELF waves in a multi‐ion plasma. The ES components consist of ion cyclotron as well as lower hybrid modes. We also demonstrate that the ES wave generation is directly involved in the transverse acceleration of ions as commonly measured with the BBELF wave events. The heating is affected by ion cyclotron resonance in the cyclotron modes and Landau resonance in the lower hybrid waves. In the simulation, we drive the plasma by the transverse electric field, Ey, of the EM waves; the frequency of Ey, ωd, is varied from a frequency below the heavy ion cyclotron frequency, Ωh, to below the light ion cyclotron frequency, Ωi. We have also performed simulations for Ey having a continuous spectrum given by a power law, namely, ∣Ey∣ ∼ ωd−α, where the exponent α = , 1, and 2 in three different simulations. The driving electric field generates polarization and E × B drifts of the ions and electrons. When the interspecies relative drifts are sufficiently large, they drive electrostatic waves, which cause perpendicular heating of both light and heavy ions. The transverse ion heating found here is discussed in relation to observations from Cluster, Fast Auroral Snapshot, and Freja.

Interplanetary and interstellar plasma turbulence

Theoretical approaches to low-frequency magnetized turbulence in collisionless and weakly collisional astrophysical plasmas are reviewed. The proper starting point for an analytical description of these plasmas is kinetic theory, not fluid equations. The anisotropy of the turbulence is used to systematically derive a series of reduced analytical models. Above the ion gyroscale, it is shown rigourously that the Alfvén waves decouple from the electron-density and magnetic-field-strength fluctuations and satisfy the reduced MHD equations. The density and field-strength fluctuations (slow waves and the entropy mode in the fluid limit), determined kinetically, are passively mixed by the Alfvén waves. The resulting hybrid fluid-kinetic description of the low-frequency turbulence is valid independently of collisionality. Below the ion gyroscale, the turbulent cascade is partially converted into a cascade of kinetic Alfvén waves, damped at the electron gyroscale. This cascade is described by a pair of fluid-like equations, which are a reduced version of the electron MHD. The development of these theoretical models is motivated by observations of the turbulence in the solar wind and interstellar medium. In the latter case, the turbulence is spatially inhomogeneous and the anisotropic Alfvénic turbulence in the presence of a strong mean field may coexist with isotropic MHD turbulence that has no mean field.

A Low Frequency Coherent Structure Driven by Turbulence in a Hanbit Mirror Plasma

Ion saturation currents in a Hanbit mirror plasma have been analyzed by using the wavelet bispectral method. From this bicoherence analysis, an interesting phase coherent mode has been found at a very low frequency. This mode seems to be generated by the low frequency turbulence which could be identified as either ion drift waves or interchange modes. The wave coupling process leading to this coherent structure is found to follow the resonant three-wave coupling with an exact frequency match. A brief review is given on this coherent turbulence structure in a Hanbit mirror plasma.

Low-Frequency Turbulence and Non-Diffusive Cross-Field Plasma Transport in Mirror Systems

Low-frequency turbulence and the resultant cross-field plasma transport in mirror-based systems are studied by means of direct computer simulations of nonlinear plasma dynamics. Under the low-beta assumption the nonlinear dynamics are simulated in a frame of adiabatically reduced one-fluid MHD model. Simulations of self-consistent plasma evolutions have shown formation of large-scale flute-like stochastic vortex structures, which have broad-band frequency and wave-number spectra and are similar to the intermittent vortex-like structures observed in GAMMA 10 experiments. Simulations were performed both for the conventional tandem mirror configuration and for axisymmetric non-paraxial configuration with divertor-like separatrix. Various regimes of plasma confinement with sheared plasma rotation have been modeled and analyzed.

Electrostatic ion-temperature-gradient drift-waves and anomalous energy transport in a collisional dusty magnetoplasma

Electrostatic ion-temperature-gradient (ITG) driven drift waves are investigated by using Brangskii's model for the ions and Boltzmann distribution for the electrons in a dust-contaminated plasma with equilibrium density, temperature, and magnetic field gradients. Within the local approximation, we are able to recover the coupled ion-acoustic drift-waves in an inhomogeneous magnetic field and the Rudakov–Sagdeev (R–S) ITG instability in the presence of dust-charge fluctuations. It has been shown that the dust charging is always dissipative and the growth rate of various modes are damped. Furthermore, we also derive an expression for the anomalous ion-energy flux and transport coefficient in the presence of nonthermal fluctuations. The present investigation should be helpful in identifying the features of low-frequency turbulence and associated cross-field ion-energy transport in magnetically confined dust-contaminated tokamak plasmas.

Study of nonlinear interaction of waves through plasma-maser in magnetosphere plasma

A theoretical study is made on the generation mechanism of electrostatic Bernstein mode wave in the presence of electromagnetic Kinetic Alfven wave turbulence in magnetized inhomogeneous plasma on the basis of plasma-maser interaction. It is shown that a test high-frequency electrostatic Bernstein mode wave is unstable in the presence of low-frequency Kinetic Alfven wave turbulence. Because of the universal existence of the Kinetic Alfven waves in large-scale plasmas, the result has potential importance in space and astrophysical radiation process. The growth rate of the test high-frequency Bernstein mode wave is obtained with the involvement of spatial density gradient parameter. A comparative study on the role of density gradient in the generation of Bernstein mode on the basis of plasma-maser effect is presented.

Modeling of Stark Profiles in a Fluctuating Edge Tokamak Plasma

We present a model for the spectroscopic density diagnostic of a recombining divertor plasma, by retaining the fluctuations of charged particles due to low frequency turbulence. A Stark broadening model for hydrogen isotopes is used for the local line shape, and in accordance with our model, averaged over a density fluctuation PDF for obtaining the apparent line shape. We present the results of our model for the Balmer 10 → 2 line and compare to an experimental spectrum observed in the JET divertor.

A note on local and non-local properties of turbulence in the bora flow

On the basis of two-month measurements of the bora wind at Senj, Croatia, with a 1 s temporal resolution, properties of the bora turbulence are inspected using the records of three bora episodes. The spectrum is divided into two parts: high-frequency turbulence (periods less than 1 min) and the low-frequency part (periods between 1 and 10 min) where pulsations appear. We have found that the high-frequency turbulence is generated locally by surface roughness and local wind shear. On the other hand, the low-frequency turbulence, i.e. the pulsations, seems to be independent of the local properties and can therefore be treated as an organized non-local effect. This is in accordance with the studies of the pulsations in the Boulder downslope windstorm.

Study of plasma–maser instability in an inhomogeneous plasma

The plasma–maser, an interesting nonlinear process in plasmas, is an effective means of energy up-conversion in frequency from low-frequency turbulence to a high-frequency wave. A theoretical study is made of the amplification mechanism of an electrostatic Bernstein mode wave in presence of Langmuir wave turbulence in a magnetized inhomogeneous plasma on the basis of a plasma–maser interaction. It is shown that a test high-frequency electrostatic Bernstein mode wave is unstable in the presence of low-frequency Langmuir wave turbulence. The growth rate of a test high-frequency Bernstein mode wave is calculated with the involvement of a spatial density gradient parameter. A comparative study on the role of density gradient in the generation of the Bernstein mode on the basis of the plasma–maser effect is presented.

Spectral line shapes modeling in turbulent plasmas

In this work we investigate the influence of low frequency turbulence on Doppler spectral line shapes in magnetized plasmas. Low frequency refers here to fluctuations whose typical time scale is much larger than those characterizing the atomic processes, such as radiative decay, collisions and charge exchange. This ordering is in particular relevant for drift wave turbulence, ubiquitous in edge plasmas of fusion devices. Turbulent fluctuations are found to affect line shapes through both the spatial and time averages introduced by the measurement process. The profile is expressed in terms of the fluid fields describing the plasma. Assuming the spectrometer acquisition time to be much larger than the turbulent time scale, an ordering generally fulfilled in experiments, allows to develop a statistical formalism. We proceed by successively investigating the effects of density, fluid velocity and temperature fluctuations on the Doppler profile of a spectral line emitted by a charge exchange population of neutrals. Line shapes, and especially line wings are found to be affected by ion temperature or fluid velocity fluctuations, and can in some cases exhibit a power-law behavior. These effects are shown to be measurable with existing techniques, and their interpretation in each particular case would rely on already existing tools. From a fundamental point of view, this study gives some insights in the appearance of non-Boltzmann statistics, such as Levy statistics, when dealing with averaged experimental data.

A two-component phenomenology for homogeneous magnetohydrodynamic turbulence

A one-point closure model for energy decay in three-dimensional magnetohydrodynamic (MHD) turbulence is developed. The model allows for influence of a large-scale magnetic field that may be of strength sufficient to induce Alfvén wave propagation effects, and takes into account components of turbulence in which either the wave-like character is negligible or is dominant. This two-component model evolves energy and characteristic length scales, and may be useful as a simple description of homogeneous MHD turbulent decay. In concert with spatial transport models, it can form the basis for approximate treatment of low-frequency plasma turbulence in a variety of solar, space, and astrophysical contexts.

Plasma-maser instability of the ion acoustics wave in the presence of lower hybrid wave turbulence in inhomogeneous plasma

A theoretical study is made on the generation mechanism of ion acoustics wave in the presence of lower hybrid wave turbulence field in inhomogeneous plasma on the basis of plasma-maser interaction. The lower hybrid wave turbulence field is taken as the low-frequency turbulence field. The growth rate of test high frequency ion acoustics wave is obtained with the involvement of spatial density gradient parameter. A comparative study of the role of density gradient for the generation of ion acoustics wave on the basis of plasma-maser effect is presented. It is found that the density gradient influences the growth rate of ion acoustics wave.

Particle Acceleration and Intermittent Turbulence in Coronal Loops

A test particle numerical experiment is performed to simulate particle acceleration in low-frequency turbulence generated by footpoint motions in a coronal loop. The turbulence is modeled within the reduced MHD theory. Only the effect of the resistive electric field E|| is retained, which is mainly parallel to the axial magnetic field. In its spectrum, the contribution of small scales is dominant. The spatial structure of E|| is obtained by a synthetic turbulence method (p-model), which allows us to reproduce intermittency. By solving the relativistic motion equations, the time evolution of particle distribution is calculated. Electrons can be accelerated to energies of the order of 50 keV in less than 0.3 s, and the final energy distribution can exhibit a power-law range. A correlation is found between the heating events in the MHD turbulence and particle acceleration that is qualitatively similar to what is observed in solar flares. Spatial intermittency plays a key role in acceleration, enhancing both the extension of a power-law range and the maximum energy.

MeV acceleration processes for heliospheric heavy ions

Observations of energetic ions of solar origin in the heliosphere suggest the existence of two main energization sites with different physical mechanisms: (1) impulsive mechanism on the flaring coronal magnetic field – via resonant interaction, presumably with low-frequency electromagnetic waves; (2) gradual mechanism around the propagating, interplanetary shock – by interaction with quasi-static inhomogeneous electromagnetic structure and low-frequency Alfvenic turbulence. While the coronal process enhances a subset of rare elements, the interplanetary interaction energizes most of the elements of coronal/solar wind origin. In the impulsive events, according to recent models, a significant fraction of heavy elements which reside on the active flaring flux rope is energized; the resonant interaction operates mainly on Fe and other heavy elements with high charge states. In the gradual events main energization occurs close to the Sun at low Mach numbers; significant interplanetary enhancement of energetic ion fluxes requires a narrow scale length in the propagating shock. Coupling of both processes results in the final heliospheric distribution function of the heavy elements. The enhanced energetic heavy ion population may have a profound impact on human space exploration in the interplanetary space as well as in the resulting trapped radiation in the magnetosphere.

Nonlinear Energetic Charged Particle Transport and Energization in Enhanced Compressive Wave Turbulence near Shocks

During solar maximum, interplanetary coronal mass ejections and associated interplanetary shocks occur frequently. These structures are often accompanied by high levels of low-frequency compressive wave turbulence, which requires a nonlinear extension of standard quasi-linear theory to properly describe energetic particle transport in their vicinities. The same might be true for the solar wind termination shock. We present a nonlinear diffusive kinetic theory for suprathermal particle transport and stochastic acceleration along the background magnetic field in strong compressive dynamic wave turbulence to which small-scale Alfven waves are coupled. Our theory shows that the standard cosmic-ray transport equation must be revised for low suprathermal particle energies to accommodate fundamental changes in spatial diffusion (standard diffusion becomes turbulent diffusion), as well as modifications to particle convection and adiabatic energy changes. In addition, a momentum diffusion term, which generates accelerated suprathermal particle spectra with a hard power law, must be added. Such effective first-stage acceleration possibly leads to efficient injection of particles into second-stage diffusive shock acceleration, as described by standard theory.

Wave stimulated phenomena in inductively coupled magnetized plasmas

Linear and nonlinear wave phenomena and their influence on the discharge performance are considered in the helicon plasma (HP) and magnetized inductively coupled plasma (MICP). Magnetic field configuration is shown to result in strong variation in the efficiency of plasma production caused by alterations of the character of wave processes rather than by the particle confinement. Effects of magnetic configuration are found to be dominant in operation of the compact HP with permanent magnet. Low frequency turbulence in the megahertz range is revealed to be inherent for both the HP and MICP and to depend strongly on the magnetic configuration. Enhanced axial electric field arising in front of the metal end plate in the HP is argued to be a potential source of the nonlinear effects.

New possibilities for the mathematical modeling of turbulent transport processes in plasma

A new mathematical model is proposed for the probability distributions of the characteristics of the processes observed in turbulent plasmas. The model is based on formal theoretical considerations related to probabilistic limit theorems for a nonhomogeneous random walk and has the form of a finite mixture of Gaussian distributions. The reliability of the model is confirmed by the results of a statistical analysis of the experimental data on density fluctuations in high-temperature plasmas of the L-2M, LHD, and TJ-II stellarators and the local fluctuating flux in the TAU-1 linear device and in the edge plasma of the L-2M stellarator with the use of the estimation-maximization algorithm. It is shown that low-frequency structural turbulence in a magnetized plasma is related to non-Brownian transport, which is determined by the characteristic temporal and spatial scales of the ensembles of stochastic plasma structures. Mechanisms that could be responsible for the random nature of time samples of the local turbulent flux in TAU-1 are indicated. A new physical concept of the intermittence of plasma turbulent pulsations is developed on the basis of the statistical separation of mixtures in terms of the model proposed. The intermittence of plasma pulsations is shown to be associated with the generation of plasma structures (solitons and vortices) and their nonlinear interaction, as well as with their damping and drift.

Low-frequency instabilities driven by oxygen ion beams in plasma sheet region

Low-frequency instabilities driven by ionospheric oxygen ion beam are studied in the plasma sheet region. In three component cold and uniform plasma consisting of electrons, protons and oxygen ions, the linear dispersion relation is derived with velocity shear in each component. The dispersion relation is solved for the case of uniform as well as nonuniform oxygen ion beam with shear flow passing through stationary electron–ion plasma. It is found that uniform oxygen ion beam can excite the low-frequency instabilities provided the Mach number exceeds a critical value. For the case of nonuniform oxygen ion beam it is found that the velocity shear can give rise to Kelvin–Helmholtz type instabilities. These low-frequency waves may be responsible for the low-frequency turbulence observed in the plasma sheet region.

First principles based simulations of instabilities and turbulence

It is now widely believed that low frequency turbulence developing from small-scale instabilities is responsible for the phenomenon of anomalous transport generally observed in magnetic confinement fusion experiments. The micro-instabilities are driven by gradients of equilibrium density, ion and electron temperatures and magnetic field strength. Gyrokinetic theory is based on the Vlasov–Maxwell equations and, consistent with the ordering, averages out the fast particle gyromotion, reducing the phase space from 6 to 5 dimensions. Solving the resulting equations is a non-trivial task. Difficulties are associated with the magnetic confinement geometry, the strong disparities in space and time scales perpendicular and parallel to B, the different time scales of ion and electron dynamics, and the complex nonlinear behaviour of the system. The main numerical methods are briefly presented together with some recent developments and improvements to the basic algorithms. Recent results are shown, with emphasis on the roles of zonal E × B flows, of parallel nonlinearity and of toroidal coupling on the saturation of ion temperature gradient (ITG) driven turbulence in tokamaks.

Spectra of enhanced scattering by spontaneous density fluctuations in a tokamak

The wavenumber-resolved radar backscattering diagnostics in the upper hybrid resonance (UHR) region was used to study low-frequency short-scale turbulence in the FT-1 tokamak. The scattered spectra were measured for different delay times of the scattered signals. It is shown that the width of the spectrum of enhanced scattering by spontaneous fluctuations is proportional to the delay time. Possible mechanisms for the formation of the scattered spectra are proposed and discussed. The results of simulations and additional experiments were used to determine the dominant mechanisms governing the formation of the scattered spectra in the FT-1 tokamak. These mechanisms are related to the effect of multiple small-angle scattering of both the probing wave and the waves backscattered in the UHR region by long-scale density fluctuations and to the Doppler effect caused by the entrainment of short-scale fluctuations by the long-scale turbulent flow.