Spectrum Of Electron Density Fluctuations Research Articles

Density wavenumber spectrum measurements, synthetic diagnostic development, and tests of quasilinear turbulence modeling in the core of electron-heated DIII-D H-mode plasmas

Measurements of the turbulent density wavenumber spectrum, δnˆe(k⊥) , using the Doppler Back-Scattering (DBS) diagnostic are reported from DIII-D H-mode plasmas with electron cyclotron heating as the only auxiliary heating method. These electron-heated plasmas have low collisionality, νe∗<1 , Te/Ti>1 , and zero injected torque—a regime expected to be relevant for future fusion devices. We probe density fluctuations in the core (ρ ≈ 0.7) over a broad wavenumber range, 0.5⩽k⊥⩽16 cm−1 ( 0.1⩽k⊥ρs⩽5 ), to characterize plasma instabilities and compare with theoretical predictions. We present a novel synthetic DBS diagnostic to relate the back-scattered power spectrum, Ps(k⊥) —which is directly measured by DBS—to the underlying electron density fluctuation spectrum, δnˆe(k⊥) . The synthetic DBS Ps(k⊥) spectrum is calculated by combining the SCOTTY beam-tracing code with a model δnˆe(k⊥) predicted either analytically or numerically. In this work we use the quasi-linear code Trapped Gyro-Landau Fluid (TGLF) to approximate the δnˆe(k⊥) spectrum. We find that TGLF, using the experimental profiles, is capable of closely reproducing the DBS measurements. Both the DBS measurements and the TGLF-DBS synthetic diagnostic show a wavenumber spectrum with variable decay. The measurements show weak decay (k −0.6) for k < 3.5 cm−1, with k −2.6 at intermediate-k ( 3.5⩽k⩽8.5 cm−1), and rapid decay (k −9.4) for k > 8.5 cm−1. Scans of physics parameters using TGLF suggest that the normalized ∇Te scale-length, R/LTe , is an important factor for distinguishing microturbulence regimes in these plasmas. A combination of DBS observations and TGLF simulations indicate that fluctuations remain peaked at ITG-scales (low k) while R/LTe -driven TEM/ETG-type modes (intermediate/high k) are marginally sub-dominant.

Simulation of transport in the FT-2 tokamak up to the electron scale with GENE

Prior experimental work on the FT-2 tokamak has observed electron density fluctuations at electron Larmor radius scales using the enhanced scattering (ES) diagnostic (Gusakov et al 2006 Plasma Phys. Control. Fusion 48 A371–6, Gurchenko and Gusakov 2010 Plasma Phys. Control. Fusion 52 124035). Gyrokinetic GENE simulations of conditions at the upper hybrid resonance layer probed by the ES diagnostic show the presence of the anticipated turbulence from the electron temperature gradient (ETG) driven instability in linear and nonlinear simulations. Ion-scale turbulence is responsible for majority of the transport via trapped electron modes, while impurities act to merge the spectrum of the ion and the electron scale instabilities into a continuum. The linear spectrum at electron scales is characterized by maximal growth rate at a significant ballooning angle θ 0, and at ion scales the turbulence is broad in the ballooning angle distribution. The neoclassical shearing rate obtained from GENE breaks symmetry in nonlinear simulations of ETG turbulence, which manifests itself as an asymmetric turbulence spectrum. The electron density fluctuation spectrum obtained with GENE corresponds well to the ES measurement at electron scales, as do the fluxes obtained from the ion-scale simulations.

Plasma fluctuations in the presence of random density and temperature irregularities

A theoretical approach for finding spectra of electrostatic fluctuations in a plasma with random density and temperature irregularities is developed. The approach is valid for nonequilibrium plasmas, in particular, when electrons and ions have different temperatures. Using these results, we calculated the spectrum of electron density fluctuations, which is necessary to interpret incoherent scattering experiments. It is shown that ignoring the random irregularities can introduce errors into the measurements of main plasma parameters, such as ambient density and temperatures. The calculated spectra are applied to experiments on the artificial ionosphere modification by high-power radio waves. A possible experimental method for estimating the intensity of random temperature irregularities in the artificially modified ionosphere is discussed.

Anisotropic Scattering of the Radio Emission of the Pulsar B0833–45 in the Vela Supernova Remnant

Very Long Baseline Interferometry (VLBI) observations of the pulsar B0833–45 have been carried out as part of the scientific program of the RadioAstron mission. Ground support was provided by the Long Baseline Array, which includes radio telescopes in Australia and other countries in the southern hemisphere. The VLBI observations of the pulsar are analyzed in order to derive the parameters characterizing the scattering of the pulsar radio emission: the angular size of the scattering disk, the spatial scale of the diffraction pattern, the drift velocity of this pattern relative to the observer, the pulse scattering time scale, and the characteristic scintillation time and frequency scales, as well as the index of the electrondensity fluctuation spectrum. Comparison of these values with the predictions of the theory of scattering on a thin screen enables the determination of the position of the effective screen along the line of sight. Estimates made using various methods give distances to the screen from the observer of 0.79 to 0.87 times the total distance to the pulsar. Although the position of the screen is beyond the boundary of the Vela supernova remnant, this object may play the dominant role in the scattering. The scattering disk is an ellipse with a 2:1 axis ratio and with the inferred position angle of the major axis being ≈ 50°, based on the changes in the visibility-function amplitude for various orientations of the projected baseline. This conclusion is supported by the shape of the visibility-function amplitude as a function of the delay.

INTERPRETATION OF THE STRUCTURE FUNCTION OF ROTATION MEASURE IN THE INTERSTELLAR MEDIUM

ABSTRACT The observed structure function (SF) of rotation measure (RM) varies as a broken power-law function of angular scales. The systematic shallowness of its spectral slope is inconsistent with the standard Kolmogorov scaling. This motivates us to examine the statistical analysis on RM fluctuations. The correlations of RM constructed by Lazarian &amp; Pogosyan are demonstrated to be adequate in explaining the observed features of RM SFs through a direct comparison between the theoretically obtained and observationally measured SF results. By segregating the density and magnetic field fluctuations and adopting arbitrary indices for their respective power spectra, we find that when the SFs of RM and emission measure have a similar form over the same range of angular scales, the statistics of the RM fluctuations reflect the properties of density fluctuations. RM SFs can be used to evaluate the mean magnetic field along the line of sight, but cannot serve as an informative source on the properties of turbulent magnetic field in the interstellar medium. We identify the spectral break of RM SFs as the inner scale of a shallow spectrum of electron density fluctuations, which characterizes the typical size of discrete electron density structures in the observed region.

Applications of large eddy simulation methods to gyrokinetic turbulence

The large eddy simulation (LES) approach—solving numerically the large scales of a turbulent system and accounting for the small-scale influence through a model—is applied to nonlinear gyrokinetic systems that are driven by a number of different microinstabilities. Comparisons between modeled, lower resolution, and higher resolution simulations are performed for an experimental measurable quantity, the electron density fluctuation spectrum. Moreover, the validation and applicability of LES is demonstrated through a series of diagnostics based on the free energetics of the system.

“Bloch wave” modification of stimulated Raman by stimulated Brillouin scattering

Using the reduced-description particle-in-cell (RPIC) method, we study the coupling of backward stimulated Raman scattering (BSRS) and backward stimulated Brillouin scattering (BSBS) in regimes where the reflectivity involves the nonlinear behavior of particles trapped in the daughter plasma waves. The temporal envelope of a Langmuir wave (LW) obeys a Schrödinger equation where the potential is the periodic electron density fluctuation resulting from an ion-acoustic wave (IAW). The BSRS-driven LWs in this case have a Bloch wave structure and a modified dispersion due to the BSBS-driven spatially periodic IAW, which includes frequency band gaps at kLW∼kIAW/2∼k0 (kLW, kIAW, and k0 are the wave number of the LW, IAW, and incident pump electromagnetic wave, respectively). This band structure and the associated Bloch wave harmonic components are distinctly observed in RPIC calculations of the electron density fluctuation spectra and this structure may be observable in Thomson scatter. Bloch wave components grow up in the LW spectrum, and are not the result of isolated BSRS. Self-Thomson scattered light from these Bloch wave components can have forward scattering components. The distortion of the LW dispersion curve implies that the usual relationship connecting the frequency shift of the BSRS-scattered light and the density of origin of this light may become inaccurate. The modified LW frequency results in a time-dependent frequency shift that increases as the IAW grows, detunes the BSRS frequency matching condition, and reduces BSRS growth. A dependence of the BSRS reflectivity on the IAW Landau damping results because this damping determines the levels of IAWs. The time-dependent reflectivity in our simulations is characterized by bursts of sub-picosecond pulses of BSRS alternating with multi-ps pulses of BSBS, and BSRS is observed to decline precipitously as soon as SBS begins to grow from low levels. In strong BSBS regimes, the Bloch wave effects in BSRS are strong and temporal anti-correlation with BSRS is due to pump depletion in addition to frequency detuning. In most cases studied, BSBS suppressed the time-averaged reflectivity of BSRS compared to the levels obtained with fixed ions (and therefore no BSBS). The strong spatial modulation of the Bloch Langmuir waves appears to weaken electron trapping and thereby lowers the inflated reflectivity levels of BSRS.

Experimental study of the relationship between micro-turbulence and magnetohydrodynamics on the HT-7 tokamak

Electron density fluctuations were measured by a CO2 laser collective scattering diagnostic system on the HT-7 tokamak. The relationship between electron density fluctuations and magnetohydrodynamics has been studied under three ohmic plasma discharge conditions (kθ = 12 cm−1): (i) only Mirnov activities, (ii) only big sawtooth activities and (iii) Mirnov activities, sawtooth activities and slight disruptions coexisting. It has been shown that electron density fluctuations obviously increase during sawtooth activities or Mirnov activities. A periodic burst in the frequency spectrum of electron density fluctuations has been observed during case (iii); detailed investigations suggest magnetic energy, the equilibrium current gradient and the heat pulse may supply sources of free energy to micro-turbulence, leading to the micro-turbulence growing rapidly and significantly.

Particle dynamics description of “BGK collisions” as a Poisson process

[1] The Gordeyev integral for plasma particles colliding with neutrals is obtained using a particle dynamics formalism in which the collisions are modeled as a discrete Poisson process. The result leads to an electron density fluctuation spectrum model for partially ionized plasmas which is identical with the spectral model obtained from BGK plasma kinetic equations. This isomorphism between the Poisson process and the BGK operator is analogous to a similar relation between the Brownian motion process and the Fokker-Planck operator with constant coefficients. We take advantage of this analogy to derive a collisional ISR spectrum model that takes into account collisions with both neutrals and charged species.

Diagnostics of Near-Solar Plasma Turbulence Parameters Using the Radio Sounding Technique at Small Heliocentric Distances

We investigate the temporal correlation function and the mean intensity of monochromatic radio emission in the neighborhood of a regular caustic produced by radio sounding of near-solar plasma. Using asymptotic analysis and numerical simulation, we determine conditions under which the temporal correlation function is related to the temporal structure function by a relation similar to that used for the solar wind diagnostics (Coles and Harmon, Astrophys. J.337, 1023, 1989) in the case of weak refraction of radio waves. Information on the correlation function and on the mean intensity in the caustic shadow region can be used to determine the parameters of the electron density fluctuation spectrum at small heliocentric distances.

Folded Fields as the Source of Extreme Radio-Wave Scattering in the Galactic Center

A strong case has been made that radio waves from sources within about half a degree of the Galactic center undergo extreme diffractive scattering. However, problems arise when standard (Kolmogorov) models of electron density fluctuations are employed to interpret the observations of scattering in conjunction with those of free-free radio emission. Specifically, the outer scale of a Kolmogorov spectrum of electron density fluctuations is constrained to be so small that it is difficult to identify an appropriate astronomical setting. Moreover, an unacceptably high turbulent heating rate results if the outer scale of the velocity field coincides with that of the density fluctuations. We propose an alternative model based on folded magnetic field structures that have been reported in numerical simulations of small-scale dynamos. Nearly isothermal density variations across thin current sheets suffice to account for the scattering. There is no problem of excess turbulent heating, because the outer scale for the velocity fluctuations is much larger than the widths of the current sheets. We speculate that interstellar magnetic fields could possess geometries that reflect their origins: fields maintained by the Galactic dynamo could have large correlation lengths, whereas those stirred by local energetic events might exhibit folded structures.

Some properties of the angular power distribution of electromagnetic waves multiply scattered in a collisional magnetized turbulent plasma

A study is made of oblique incidence of a small-amplitude plane electromagnetic wave on a semi-infinite slab of a collisional turbulent plasma in an external uniform magnetic field. In the small-angle scattering approximation, the condition for neutralizing the effects of oblique incidence and plasma anisotropy on the statistical properties of radiation multiply scattered in the absorbing plasma medium is determined by using the methods of geometrical optics. The validity of this condition was confirmed by numerical calculations based on the statistical modeling technique. The effect of the shape of the spectrum of the electron density fluctuations on the shape of the angular power distribution of a multiply scattered radiation is investigated.

Long-term scintillation observations of five pulsars at 1540 MHz

From 2001 January to 2002 June, we monitored PSRs B0329+54, B0823+26, B1929+10, B2020+28 and B2021+51 using the Nanshan 25-m radio telescope of Urumqi Observatory to study their diffractive interstellar scintillation (DISS). The average interval between observations was about 9 days and the observation duration ranged between 2 and 6 hours depending on the pulsar. Wide variations in the DISS parameters were observed over the 18-month data span. Despite this, the average scintillation velocities are in excellent agreement with the proper motion velocities. The average two-dimensional autocorrelation function for PSR B0329+54 is well described by a thin-screen Kolmogorov model, at least along the time and frequency axes. Observed modulation indices for the DISS time scale and bandwidth and the pulsar flux density are greater than values predicted for a Kolmogorov spectrum of electron density fluctuations. Correlated variations over times long compared to the nominal refractive scintillation time are observed, suggesting that larger-scale density fluctuations are important. For these pulsars, the scintillation bandwidth as a function of frequency has a power-law index (~3.6) much less than expected for Kolmogorov turbulence (~4.4). Sloping fringes are commonly observed in the dynamic spectra, especially for PSR B0329+54. The detected range of fringe slopes are limited by our observing resolution. Our observations are sensitive to larger-scale fringes and hence smaller refractive angles, corresponding to the central part of the scattering disk.

The frequency evolution of interstellar pulse broadening from radio pulsars

In this paper we report multi-frequency measurements of pulse broadening times (tau_d) for nine medium dispersion measure (DM $\approx 150-400$ pc cm$^{-3}$) pulsars observed over a wide frequency range. The low frequency data at 243, 325 and 610 MHz are new observations done with the Giant Metrewave Radio Telescope (GMRT). The frequency dependence of tau_d for all but one (PSR B1933+16) of our sources is consistent with the Kolmogorov spectrum of electron density fluctuations in a turbulent medium. PSR B1933+16, however, shows a very flat spectrum as previously observed for high DM pulsars. Our observations combined with earlier published results enable us to study the spectral index of tau_d over the whole observed DM range. While the spectral properties are generally consistent with a Kolmogorov spectrum, pulsars seen along line-of-sights towards the inner Galaxy or complex regions often show deviations from this expected behaviour.

Pulsars and the ISM

Radio signals from pulsars are significantly affected by propagation effects such as dispersion, faraday rotation and scintillations in the interstellar medium (ISM). In this paper, I review some aspects of our understanding about pulsars and interstellar scintillations (ISS). The study of pulsar scintillation has dual benefits in that it allows us to learn about the properties of the ISM using pulsars as probes, as well as to infer some properties about pulsars, using the ISM as a tool. Both these aspects are addressed in this paper. The main emphasis is on recent developments in the following topics : (i) the shape of the spectrum of electron density fluctuations in the interstellar medium (ii) the distribution of scattering plasma in the local ISM and (iii) resolving pulsar emission regions using ISS.

Spectrum of electron density fluctuations in the interstellar medium from pulsar observations

Abstract We present here our new results about the shape of the turbulent spectrum based on pulsar observations.

Anisotropic Interstellar Scattering toward the Cygnus Region

We report on multifrequency VLBA observations of interstellar scattering (ISS) toward four extragalactic sources seen through the Cygnus region, 2005+403, 2008+332, 2021+317, and 2048+312. We are able to successfully determine scattering disk parameters at frequencies up to 5.0 GHz for 2005+403 and 2008+332 and up to 2.3 GHz for 2048+312. We were unable to reliably determine scattering disk parameters for 2021+317 at frequencies from 8.5 GHz down to 1.67 GHz because of its complex intrinsic source structure. The scattering disks are elliptical with axial ratios of about 0.75:1 with little measurable variation between these sources. We interpret our measurements as due to the effects of anisotropic interstellar turbulence. The anisotropy parameters, axial ratio and position angle, for those sources for which we have data at multiple frequencies appear to be frequency-independent making refractive distortions of isotropic turbulence an unlikely explanation. Our estimates of β, the power-law index of the power spectrum of electron density fluctuations, based upon direct model fits to the data on a source-by-source and frequency-by-frequency basis, are consistent with β = 4 for most of the data but are strongly affected by our estimate of the intrinsic structure of the sources. Two of these sources, 2005+403 and 2021+317, exhibit significant intrinsic source structure at frequencies as low as 1.67 GHz, while the other two, 2008+332 and 2048+312, lack discernible source structure at frequencies lower then 2.3 GHz. The frequency scalings of the scattered angular sizes are also consistent with β = 4. We discuss the implications of our measurements for the inner and outer scales of the turbulence.

Pulsar Scintillation: Overview and Some Recent Results

Radio signals from pulsars are significantly affected by scattering in the interstellar medium. A review of this phenomenon of pulsar scintillation forms the main objective of this paper. The basic concepts are described and some new results related to the following aspects are presented: (i) understanding of refractive scintillation effects and (ii) constraining the spectrum of electron density fluctuations in the interstellar medium.

Pulsar Scintillation: Overview and Some Recent Results

AbstractRadio signals from pulsars are significantly affected by scattering in the interstellar medium. A review of this phenomenon of pulsar scintillation forms the main objective of this paper. The basic concepts are described and some new results related to the following aspects are presented: (i) understanding of refractive scintillation effects and (ii) constraining the spectrum of electron density fluctuations in the interstellar medium.

Radio wave scattering in the outer heliosphere

The Voyager 1 and 2 plasma wave instruments have observed low‐frequency (1.5–4 kHz) radio waves apparently generated near the heliopause. The waves are found in two distinct bands. Power at the lower frequencies centered on 1.78 kHz shows no modulation when the spacecraft is rolled about the Earth‐spacecraft line, indicating that the radiation is isotropic. Power in the higher band centered on 3.11 kHz shows roll modulation as high as 60%, indicating that the source of the radiation is quite compact, subtending an angle &lt;1 rad at the spacecraft. Simple estimates of the scattering of 3.11 kHz radiation from electron density fluctuations indicate that, if the radiation had originated from the distance of the heliopause, the scattering would be so large that no roll modulation should be observed. Here we show that these earlier scattering estimates were too high because they ignored the latitude variation of scattering and the inner scale of the electron density fluctuation spectrum. With these two effects properly included, the expected scattering is consistent with the observations and the postulate that the radiation originates from near the nose of the heliosphere.