Low-frequency Electrostatic Turbulence Research Articles

Robust computational method for fast calculations of multicharged ions lineshapes affected by a low-frequency electrostatic plasma turbulence

Transport phenomena in plasmas, such as, e.g., resistivity, can be affected by electrostatic turbulence that frequently occurs in various kinds of laboratory and astrophysical plasmas. Transport phenomena are affected most significantly by a low-frequency electrostatic turbulence—such as, e.g., ion acoustic waves, also known as ionic sound—causing anomalous resistivity. In this case, for computing profiles of spectral lines, emitted by plasma ions, by any appropriate code for diagnostic purposes, it is necessary to calculate the distribution of the total quasistatic field. For a practically important situation, where the average turbulent field is much greater than the characteristic ion microfield, we develop a robust computational method valid for any appropriate distribution of the ion microfield at a charged point. We show that the correction to the Rayleigh distribution of the turbulent field is controlled by the behavior of the ion microfield distribution at large fields—in distinction to the opposite (and therefore, erroneous) result in the literature. We also obtain a universal analytical expression for the correction to the Rayleigh distribution based on the asymptotic of the ion microfield distribution at large fields at a charged point. By comparison with various known distributions of the ion microfield, we show that our asymptotic formula has a sufficiently high accuracy. Also exact computations are used to verify the high accuracy of the method. This robust approximate, but accurate method yields faster computational results than the exact calculations and therefore should be important for practical situations requiring simultaneous computations of a large number of spectral lineshapes (e.g., for calculating opacities)—especially for laser-produced plasmas.

Inhomogeneities of plasma density and electric field as sources of electrostatic turbulence in the auroral region

Inhomogeneities of plasma density and non-uniform electric fields are compared as possible sources of a sort of electrostatic ion cyclotron waves that can be identified with broadband extremely low frequency electrostatic turbulence in the topside auroral ionosphere. Such waves are excited by inhomogeneous energy-density-driven instability. To gain a deeper insight in generation of these waves, computational modeling is performed with various plasma parameters. It is demonstrated that inhomogeneities of plasma density can give rise to this instability even in the absence of electric fields. By using both satellite-observed and model spatial distributions of plasma density and electric field in our modeling, we show that specific details of the spatial distributions are of minor importance for the wave generation. The solutions of the nonlocal inhomogeneous energy-density-driven dispersion relation are investigated for various ion-to-electron temperature ratios and directions of wave propagation. The relevance of the solutions to the observed spectra of broadband extremely low frequency emissions is shown.

Role of Lorentz–Stark broadening of hydrogen spectral lines in magnetized plasmas: Applications to magnetic fusion and solar physics

Broadening of hydrogen spectral lines in plasmas is an important diagnostic tool for many applications (here and below by “hydrogen atoms” and “hydrogen spectral lines” we mean atoms and spectral lines of hydrogen, deuterium, and tritium). In magnetized plasmas radiating hydrogen atoms moving with the velocity v across the magnetic field B experience a Lorentz electric field EL=v×B/c in addition to other electric fields. Since the velocity v has a distribution, so does the Lorentz field, thus making an additional contribution to the broadening of spectral lines. Compared to previous studies of this contribution, we cover the following new aspects. First, we consider the Lorentz–Doppler broadening of highly-excited hydrogen lines and produce new analytical results for arbitrary strength of the magnetic field B. We show for the first time that in the high-B case, the π-components of hydrogen lines are significantly suppressed compared to the σ-components. Second, we derive analytically Lorentz-broadened profiles of highly-excited hydrogen lines. We obtain expressions for the principal quantum number nmax of the last observable hydrogen line in the spectral series. These expressions differ very significantly from the corresponding Inglis–Teller result and constitute a new diagnostic method allowing to measure the product T1/2B, where T is the atomic temperature. Third, we consider magnetized plasmas containing a low-frequency electrostatic turbulence. This kind of turbulence causes anomalous transport phenomena (e.g., the anomalous resistivity) and is therefore very important to be diagnosed. We derive analytically distributions of the total electric field and the corresponding Stark profiles of hydrogen lines. We demonstrate that our findings lead to a significantly revised interpretation of the previous and future experimental data in magnetic fusion and the observational data in solar physics.

Turbulent transport in a toroidal magnetized plasma

Turbulent plasma transport due to low-frequency electrostatic fluctuations in a toroidal plasma is studied experimentally. The data are obtained in a magnetized toroidal plasma with no toroidal transform. The plasma is generated by a discharge from a hot electron emitting filament and diagnosed by conventional Langmuir probes measuring densities by electron or ion saturation currents and floating potentials. We present results for the statistical properties of the fluctuating radial transport caused by low-frequency electrostatic turbulence in the device. The turbulent plasma flux is identified as the product of the fluctuating density and the E × B/B2-velocity. Even though the probability densities of the fluctuating electric fields and plasma densities are close to Gaussians, we find strongly intermittent features in the flux signal obtained as the product of these two fluctuating quantities. A conditional statistical analysis gives insight in detail of the turbulent transport. The intermittency studies are extended by analyzing the excess statistics, i.e. the average duration of time intervals in the flux signal spent above a given reference level. We find that this analysis offers a very effective measure for intermittency effects. In our case, the signal is characterized by an excess of temporally narrow, large amplitude bursts, when compared with an equivalent Gaussian random signal.

Structure functions and intermittency in ionospheric plasma turbulence

Abstract. Low frequency electrostatic turbulence in the ionospheric E-region is studied by means of numerical and experimental methods. We use the structure functions of the electrostatic potential as a diagnostics of the fluctuations. We demonstrate the inherently intermittent nature of the low level turbulence in the collisional ionospheric plasma by using results for the space-time varying electrostatic potential from two dimensional numerical simulations. An instrumented rocket can not directly detect the one-point potential variation, and most measurements rely on records of potential differences between two probes. With reference to the space observations we demonstrate that the results obtained by potential difference measurements can differ significantly from the one-point results. It was found, in particular, that the intermittency signatures become much weaker, when the proper rocket-probe configuration is implemented. We analyze also signals from an actual ionospheric rocket experiment, and find a reasonably good agreement with the appropriate simulation results, demonstrating again that rocket data, obtained as those analyzed here, are unlikely to give an adequate representation of intermittent features of the low frequency ionospheric plasma turbulence for the given conditions.

Observation of radial propagation of electrostatic fluctuations in toroidal plasma

There has been a great deal of activity in the area of the detection of radial propagation of electrostatic fluctuations in toroidal magnetic fusion devices. The role of radial propagation is considered extremely important in the understanding of cross field anomalous transport. Radial propagation of low frequency electrostatic turbulence in a purely toroidal device, having no rotational transform, is reported in this paper. The propagation characteristics of the turbulence has been studied using Langmuir probes. It is found that the turbulence has a finite propagation in the radial direction and the radial speed is a sizeable fraction of the poloidal speed.

Bounce-averaged kinetic equations and neoclassical polarization density

The rigorous formulation of the bounce-averaged equations is presented based upon the Poincaré–Cartan one-form and Lie perturbation methods. The resulting bounce-averaged Vlasov equation is Hamiltonian, and is thus suitable for the self-consistent simulation of low frequency electrostatic turbulence in the trapped ion mode regime. In the bounce-kinetic Poisson equation, the “neoclassical polarization density” arises from the difference between the bounce-averaged banana center and real trapped particle densities across a field line. This representation of the neoclassical polarization drift as a shielding term provides a systematic way to study the long term behavior of the turbulence driven E×B flow.

Finite Larmor radius effects and velocity correlations in two-dimensionalelectrostatic plasma turbulence

Low-frequency electrostatic turbulence in low-{beta} plasmas is studied in two spatial dimensions by direct numerical simulations. In this limit the guiding center velocity in the direction perpendicular to a homogeneous magnetic field is in a first approximation the {bold {ital E}}{times}{bold {ital B}}{sub 0}/B{sub 0}{sup 2} velocity. The electron Larmor radius can safely be set to zero for most relevant conditions, but the ion dynamics are noticeably influenced by their finite Larmor radius. In the present study we use a fluid model where these effects are included by a simple filtering operation. The equilibrium spectra are investigated and compared with known analytical results. Particular attention is given to the finite Larmor radius effect for the turbulent diffusion of charged particles across magnetic field lines. The integral time scale and the micro time scale associated with the velocity correlations for the turbulent flow are discussed with attention to their dependence on the finite Larmor radius corrections. Finally, the numerical code is generalized to a hybrid model, which incorporates many ion species with different Larmor radii simultaneously present in the flow. {copyright} {ital 1997} {ital The American Physical Society}

Velocity correlations in two-dimensional electrostatic turbulence in low-β plasmas

The Eulerian and Lagrangian correlation functions in low-frequency electrostatic turbulence in strongly magnetized plasmas are studied in two spatial dimensions. In this limit the ion velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E × B/B2velocity. For strictly flute-type fluctuations, a similar model is also used for the electron dynamics. Allowing, on the other hand, for a small B-parallel component of the perturbations, an isothermal Boltzmann distribution for the electrons can be justified while the two-dimensional ion description is retained. The present analysis is based on an approximation of the actual two-dimensional flow in terms of an autonomous system consisting of many overlapping and mutually convecting vortices. Simple analytical expressions for the full space—time-varying Eulerian correlation are derived solely in terms of plasma parameters. it is demonstrated that an extension of the arguments giving the foregoing results also allows for derivation of analytical expressions for the Lagrangian correlation function. The results are supported by a Monte Carlo simulation based on the model.

Finite Larmor Radius Effects in Two-Dimensional Electrostatic Plasma Turbulence

Low frequency electrostatic turbulence in strongly magnetized, low β-plasmas, is studied in two spatial dimensions. In this limit the guiding center velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E x B 0 /B 0 2 -velocity. The electron Larmor radius can safely be set to zero for most relevant conditions, but the ion-dynamics are noticeably influenced by finite Larmor radius effects. We analyzed the effects of finite Larmor radius corrections on the ion velocity and density by using a fluid model where these effects are included by a computationally simple filtering operation. The equilibrium spectra are investigated and compared with analytical results. The consequences of finite Larmor radius corrections for the turbulent diffusion of charged particles across magnetic field lines are studied by obtaining the Lagrangian correlation functions for passive test particles convected by the plasma flow.

Invariant measure and turbulent pinch in tokamaks.

It is shown that electron transport due to a generic low-frequency electrostatic turbulence in tokamak geometry results in the relaxation to a peaked, self-sustained plasma density profile ${n}_{0}(r)$, rather than to a diffusion-induced flat distribution. The relaxed density profile depends on the magnetic geometry and the distribution of turbulence. The associated inward pinch velocity ${\mathbf{V}}_{r}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}D\mathbf{\ensuremath{\nabla}}\mathrm{ln}{n}_{0}$ results from the competition of the turbulent diffusion of trapped electrons over the poloidal magnetic flux coordinate $\ensuremath{\psi}$ and the collisional relaxation toward a Maxwellian distribution function.

Turbulent acceleration in solar flares

Turbulent acceleration in the impulsive phase of solar flares is reviewed, with the emphasis on bulk energization of nonrelativistic electrons and prompt acceleration of the gamma-ray emitting nonrelativistic ions and relativistic electrons. The primary energy release in a flare cannot be due to collisional dissipation. Anomalous resistivity requires that the current flows in many narrow channels with the current density above threshold for current instability. The bulk energization of the electrons is due to the damping of low-frequency electrostatic turbulence generated by the current instability. This turbulence also limits the rate a nonthermal electron tail forms due to runaway acceleration. Stochastic and gyroresonant acceleration by MHD turbulence are discussed briefly, emphasizing the need for preacceleration. Stochastic acceleration is favorable for the gamma-ray emitting particles only if an adequated source of the MHD turbulence can be identified. Subject headings: acceleration of particles — MHD — Sun: flares — turbulence

Velocity correlations in two-dimensional electrostatic plasma turbulence

The Eulerian and Lagrangian correlation functions in low frequency electrostatic turbulence in strongly magnetized plasmas are studied in two spatial dimensions. In this limit the ion velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E × B/B2-velocity. For strictly flute type fluctuations a similar model is used also for the electron dynamics. Allowing, on the other hand, for a small B-parallel component of the perturbations an isothermal Boltzmann distribution for the electrons can be argued while the two dimensional ion description is retained. The present analysis is based on an approximation of the actual two-dimensional flow in terms of an autonomous flow consisting of many overlapping and mutually convecting vortices. Simple analytical expressions for the full space-time varying Eulerian correlation are derived solely in terms of plasma parameters. It is demonstrated that an extension of the arguments giving the foregoing results allows also for derivation of analytical expressions for the Lagrangian correlation function. The results are supported by a Monte Carlo simulation based on the model.

Turbulent Acceleration in Solar Flares

AbstractTurbulent acceleration in the impulsive phase of solar flares is reviewed, with the emphasis on bulk energization of nonrelativistic electrons and prompt acceleration of the gamma-ray emitting nonrelativistic ions and relativistic electrons. The primary energy release in a flare cannot be due to collisional dissipation. Anomalous resistivity requires that the current flows in many narrow channels with the current density above threshold for current instability. The bulk energization of the electrons is due to the damping of low-frequency electrostatic turbulence generated by the current instability. This turbulence also limits the rate a nonthermal electron tail forms due to runaway acceleration. Stochastic and gyroresonant acceleration by MHD turbulence are discussed briefly, emphasizing the need for preacceleration. Stochastic acceleration is favorable for the gamma-ray emitting particles only if an adequated source of the MHD turbulence can be identified.Subject headings: acceleration of particles — MHD — Sun: flares — turbulence

On energy transport equations for turbulent magnetized plasma

The Braginskii magnetohydrodynamic (MHD) equations are used to derive anomalous transport equations in the presence of electromagnetic fluctuations. The structure of convective energy fluxes and source terms in the energy balance equation is investigated in some detail. For low-frequency electrostatic turbulence, the energy flux has a unique numerical factor 3/2 in its convective part. However, for magnetic turbulence, the convective energy flux, which is proportional to the particle flux induced by magnetic fluctuations, has a numerical factor 5/2. The physical meaning of the source terms in the energy balance equation is clarified.

Conditional eddies in plasma turbulence

Low-frequency electrostatic turbulence generated by the ion–ion beam instability was investigated experimentally in a double-plasma device. Real time signals were recorded and examined by a conditional statistical analysis. Conditionally averaged potential distributions reveal the formation and propagation of structures with a relatively long lifetime. Various methods for making a conditional analysis are discussed and compared. The results are discussed with reference to ion phase space vortices and clump formation in collisionless plasmas.

Genereration of magnetospheric radiation by decay of Bernstein waves

Recent observations show that extremely narrow emission lines are present in the spectrum of the terrestrial myriametric radiation, which on the basis of earlier observations has been characterized as nonthermal continuum radiation. The occurance of these monochromatic emissions is not predicted by previously published theories for the radiation. A linear instability, exciting low frequency electrostatic turbulence, is required by theories invoking a nonlinear coalescence to produce the radiation, but there are no conclusive observations associating low frequency electrostatic waves with the sources of myriametric radiation. In this study, the possibility that the radiation is produced by a nonlinear decay of electrostatic Bernstein waves with frequency near the upper hybrid frequency is considered. This mechanism can explain the narrow spectral lines, and does not require a linear instability at low frequencies.

The influence of a turbulent region on the flux of auroral electrons

The influence of low-frequency electrostatic turbulence on the flux of precipitating magnetospheric electrons is analyzed in the framework of the quasilinear kinetic equation. It is shown that an electron population in a turbulent region, with an electric field parallel to the ambient magnetic field, can be separated into two parts by introducing a pitch angle dependent runaway velocity v r ( θ). Lower energy electrons with parallel velocity v ∥ < v r are effectively scattered by plasma waves, so that they remain in the main population and are subjected to an anomalous transport equation. A distribution function f ∞ v −4 (or the particle flux vs energy J ∞ E −1) is established in this velocity range. Faster electrons with v ∥ ≳ v r are freely accelerated by a parallel electric field, so that they contribute directly to hot electron fluxes which are observed at ionospheric altitudes. New expressions are derived for the magnetic-field aligned current and the electron energy flux implied by this model. These expressions agree well with empirical relations observed in auroral inverted-V structures.