Strong Electrostatic Turbulence Research Articles

On the role of separatrix instabilities in heating the reconnection outflow region

A study of the role microinstabilities at the reconnection separatrix can play in heating the electrons during the transition from inflow to outflow is being presented. We find that very strong flow shears at the separatrix layer lead to counterstreaming electron distributions in the region around the separatrix, which become unstable to a beam-type instability. Similar to what has been seen in earlier research, the ensuing instability leads to the formation of propagating electrostatic solitons. We show here that this region of strong electrostatic turbulence is the predominant electron heating site when transiting from inflow to outflow. The heating is the result of heating generated by electrostatic turbulence driven by overlapping beams, and its macroscopic effect is a quasi-viscous contribution to the overall electron energy balance. We suggest that instabilities at the separatrix can play a key role in the overall electron energy balance in magnetic reconnection.

Poloidal rotation driven by nonlinear momentum transport in strong electrostatic turbulence

Virtually, all existing theoretical works on turbulent poloidal momentum transport are based on quasilinear theory. Nonlinear poloidal momentum flux— is universally neglected. However, in the strong turbulence regime where relative fluctuation amplitude is no longer small, quasilinear theory is invalid. This is true at the all-important plasma edge. In this work, nonlinear poloidal momentum flux in strong electrostatic turbulence is calculated using the Hasegawa–Mima equation, and is compared with quasilinear poloidal Reynolds stress. A novel property is that symmetry breaking in fluctuation spectrum is not necessary for a nonlinear poloidal momentum flux. This is fundamentally different from the quasilinear Reynold stress. Furthermore, the comparison implies that the poloidal rotation drive from the radial gradient of nonlinear momentum flux is comparable to that from the quasilinear Reynolds force. Nonlinear poloidal momentum transport in strong electrostatic turbulence is thus not negligible for poloidal rotation drive, and so may be significant to transport barrier formation.

Nonlinear parallel momentum transport in strong electrostatic turbulence

Most existing theoretical studies of momentum transport focus on calculating the Reynolds stress based on quasilinear theory, without considering the nonlinear momentum flux- ⟨ṽrñũ∥⟩. However, a recent experiment on TORPEX found that the nonlinear toroidal momentum flux induced by blobs makes a significant contribution as compared to the Reynolds stress [Labit et al., Phys. Plasmas 18, 032308 (2011)]. In this work, the nonlinear parallel momentum flux in strong electrostatic turbulence is calculated by using a three dimensional Hasegawa-Mima equation, which is relevant for tokamak edge turbulence. It is shown that the nonlinear diffusivity is smaller than the quasilinear diffusivity from Reynolds stress. However, the leading order nonlinear residual stress can be comparable to the quasilinear residual stress, and so may be important to intrinsic rotation in tokamak edge plasmas. A key difference from the quasilinear residual stress is that parallel fluctuation spectrum asymmetry is not required for nonlinear residual stress.

Trapping, Anomalous Transport, and Quasi-coherent Structures in Magnetically Confined Plasmas

Strong electrostatic turbulence in magnetically confined plasmas is characterized by trapping or eddying of particle trajectories produced by the $E\times B$ stochastic drift. Trapping is shown to produce strong effects on test particles and on test modes. It determines non-standard statistics of trajectories: non-Gaussian distribution, memory effects and coherence. Trapped trajectories form quasi-coherent structure. Trajectory trapping has strong nonlinear effects on the test modes on turbulent plasmas. We determine the growth rate of drift modes as function of the statistical characteristics of the background turbulence. We show that trapping provides the physical mechanism for the inverse cascade observed in drift turbulence and for the zonal flow generation.

A perturbative solution of the drift kinetic equation yields pinch type convective terms in the particle and energy fluxes for strong electrostatic turbulence

Approximate linearized solutions to the drift kinetic equation (DKE) can provide physical insights into turbulent transport processes in a tokamak plasma. These types of solutions can provide a useful supplement to the results of numerical solutions to either the gyrokinetic equation or to nonlinear fluid equations. Here the DKE is solved in an iterative fashion with an attempt to include the tokamak geometry in a realistic way. The gradients in the DKE are expressed in tokamak geometry, not just by the plane wave approximation. The ballooning type spatial dependence of the electrostatic turbulence is assumed to have a given poloidal dependence. There is no attempt to solve for the radial, poloidal or toroidal dependence of the turbulence. This approximate solution shows that the nonadiabatic part of the perturbed electron distribution function yields particle fluxes which have pinch-like terms proportional to the electron temperature gradient and the safety factor gradient. The terms proportional to the safety factor gradient are inward, but the terms proportional to the temperature gradient can be either inward or outward.

Identification of the wave-particles interaction in space plasma using higher-order statistics

The interaction of wave-particles and wave-wave in the space plasmas are essentially non-linear or non-Gaussian processes. Using the higher-order statistical analyses methods (higher-order moments and bi-tri correlation or bi-tri spectrum), its physical properties can be described. The question addressed in this paper is that of the usefulness of higher-order statistical analysis for identification of the wave-particles interaction in space plasmas. The signals handled are from the ARCAD-3 ISOPROBE experiment on ELF frequency range, then strong electrostatic turbulence and electron density irregularities. Second and third order statistical analyses are applied: first, on time series associated with each type of measurement, then, on the two types. All results are presented for one typical case. Correlation functions estimated over the corresponding time intervals point out the existence of a, non-linear interaction between these fluctuations and electrostatic filed.

Ion Transport in Turbulent Edge Plasmas.

Edge plasmas, such as the tokamak scrape-off layer, exist as a consequence of a balance between cross-field diffusion and parallel losses. The former is usually anomalous, and is widely thought to be driven by strong electrostatic turbulence. It is shown that the anomalous diffusion affects the parallel ion transport by giving rise to a new type of thermal force between different ion species. This force is parallel to the magnetic field, but arises entirely because of perpendicular gradients, and could be important for impurity retention in the tokamak divertor.

Generation of auroral kilometric radiation in upper hybrid wave‐lower hybrid soliton interaction

Sporadic bursts of auroral kilometric radiation (AKR) associated with strong bursty electrostatic turbulence in the vicinity of the lower hybrid frequency have been frequently recorded in the AKR source region by the Viking satellite. The variation time scale of these emissions is typically 1 s, long enough for lower hybrid waves to grow to amplitudes of several hundred millivolts per meter and to evolve nonlinearly into solitons. On the basis on these observations it is suggested that formation of lower hybrid solitons may play a role in the generation of AKR. A theoretical model is proposed which is based on the direct acceleration of electrons in the combined lower hybrid soliton and upper hybrid wave fields. The solitons act as sporadic, localized antennas allowing for efficient conversion of the electrostatic energy stored in upper hybrid waves into electromagnetic radiation at a frequency above the X mode cutoff. Excitation of lower hybrid waves is due to the presence of energetic electron beams in the auroral zone found to be associated with steep plasma density gradients. Upper hybrid waves can be excited by a population of energetic electrons with loss cone distributions. The power of the electromagnetic radiation obtained is only noticeable in regions where the plasma frequency is less than the electron gyrofrequency. The theory predicts spectral power densities of the order of 10−11 to 10−9 W m−2 Hz−1 in the source region, in good agreement with the Viking observations. The sporadic nature of the radiation derives from lower hybrid soliton collapses which occur on ∼1‐s time scales.

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.

Computer Simulation of Plasma Turbulence in Open Systems

A short review of the results of kinetic simulation of collective phenomena in open plasma systems with the variable total energy and number of particles, i.e., the particle and energy fluxes on boundary surfaces and/or their internal sources and channels is given. Three specific problems are considered in different detail for such systems in one-dimensional geometry: the generation and evolution of double layers in a currently unstable plasma: the collisionless relaxation of strongly non-equilibrium electron distributions; the Langmuir collapse and strong electrostatic turbulence in systems with parametric excitation of a plasma by an external pumping wave and with cooling the fast non-Maxwell electrons. In all these cases the non-linearity and a collective character of processes give examples of new dissipative plasma structures that essentially widen our idea about the nature of the plasma turbulence in non-homogeneous open systems.

Theory of electromagnetic waves on auroral field lines.

Intense bursts of electromagnetic radiation generated in auroral regions during substorms radiate as much as one percent of the precipitated electron energy. The generation mechanism for the intense bursts of radio noise is apparently associated with the auroral electron beam. Some processes suggested for direct generation of electromagnetic noise by the auroral electron beam are briefly reviewed but it is suggested that the electromagnetic noise bursts are created indirectly due to radiation from strong electrostatic turbulence generated by the auroral electron beam. Due to refraction of ray paths out of the spatially limited auroral electron beam, beams below a certain intensity generate low levels of electrostatic noise as commonly observed by polar orbiting satellites. However, above a certain level, the electrostatic noise generated by the beam becomes intense and forms ‘solitons’ (large ion density cavities) or ‘spiky turbulence.’ Soliton turbulence can radiate efficiently enough to account for the observed levels of electromagnetic radiation.