Magnetic Fluctuation Spectrum Research Articles

Experimental study of the electromagnetic component of drift-wave turbulence

The magnetic turbulent fluctuation spectrum is investigated in the core of a toroidally confined plasma with parameters similar to those in the fusion edge plasma. The measured spectra show fully developed turbulence over almost 6 decades down to the range of nano-Tesla field amplitudes. The magnetic fluctuations are interpreted as being due to the parallel dynamics of drift-wave turbulence. The predicted strong β dependence of the magnetic fluctuations is experimentally confirmed. For the present parameters, anomalous transport due to the magnetic turbulence can be neglected compared with the electrostatic contribution.

Solar wind vs magnetosheath turbulence and Alfvén vortices

Abstract. In this paper we give firstly a broad review of the space plasma turbulence around the ion characteristic space and temporal scales within two natural laboratories, the solar wind and the Earth magnetosheath. In both regions power law spectra of magnetic fluctuations are observed. In both regions these spectra have a break in the vicinity of the ion cyclotron frequency. A distinctive feature of the magnetosheath turbulence is the presence of Alfvén vortices at scales of the spectral break. The Alfvén vortices are multi-scale nonlinear structures. We give a review of the main theoretical features of incompressible Alfvén vortsices in the second part of the paper. Finally, we analyze the spectral properties of the Alfvén vortex solution and of the network of such vortices. We show that the observed magnetosheath spectrum in presence of the Alfvén vortices can be described, at least partially, by the vortex network model.

Cascade of whistler turbulence: Particle‐in‐cell simulations

A two‐dimensional electromagnetic particle‐in‐cell simulation in a magnetized, homogeneous, collisionless plasma of electrons and protons has been carried out, demonstrating a forward cascade of whistler turbulence. Enhanced magnetic fluctuation spectra are initially imposed with −0.2 < k∥c/ωe < 0.2 and −0.2 < k⊥c/ωe < 0.2 where the directional subscripts denote directions relative to the background magnetic field Bo and c/ωe is the electron inertial length. The late‐time evolution of the simulation shows a cascade of magnetic fluctuation energy to shorter wavelengths; furthermore, the spectrum is anisotropic with more fluctuation energy at a given wavenumber perpendicular to Bo than at the same wavenumber parallel to the background field. The late‐time electron velocity distribution shows a magnetic‐field aligned signature due to the Landau resonance of the obliquely propagating whistlers.

Role of stochastic anisotropy and shear on magnetic field lines diffusion

Anisotropy in the magnetic fluctuation spectrum (stochastic anisotropy) and magnetic shear induce variations of global averaged quantities such as the running and the asymptotic diffusion tensors that can be investigated using a semi-analytical method. The study considers ranges for the anisotropy parameter, magnetic Kubo number and shear parameter leading to contrasting dynamical behaviors. In particular, the trapping of the stochastic magnetic field lines is analyzed. An asymptotic ‘poloidal’ velocity larger for stronger anisotropy is obtained for the wandering of the magnetic field lines for different values of the parameters.

Solar wind Cluster observations: Turbulent spectrum and role of Hall effect

Turbulent spectrum of magnetic fluctuations in the solar wind nearly follows Kolmogorov's law ∼ f - 5 / 3 below the ion cyclotron frequency f ci . Above this frequency, the observed steeper power law is believed to be a ‘dissipative range’ of the solar wind turbulence. In this paper we analyze magnetic field fluctuations measured onboard Cluster, lasting two decades above f ci . Well-defined power law and a strong increase of intermittency with frequency in this range indicates that turbulence cannot be characterized by a ‘dissipative range’. Rather we conjecture that above f ci the turbulence is generated by a different nonlinear cascade. We suggest that the presence of dispersive effects is responsible for a steepening of the spectral energy density, simply because a cascade can be realized in a time that is shorter than the usual eddy-turnover time. In the Hall MHD formulation, the magnetic power follows a law ∼ f - 7 / 3 + 2 α , which depends on the degree of plasma compressibility α .

Ion thermalization and wave excitation downstream of Earth's bow shock: A theory for Cluster observations of He2+ acceleration

It has been well documented that the plasma immediately downstream of Earth's quasi‐perpendicular bow shock, which consists of reflected protons and directly transmitted ions with large temperature anisotropies (T⊥/Tz), is unstable to the excitation of ion cyclotron waves. These waves in turn scatter the protons and ions to marginal stability. Using Cluster data following the inbound shock crossing at 1717:48 UT on 31 March 2001, we investigate the joint evolution of the proton and helium distribution functions. Within a short distance downstream of the shock the perpendicular heating of helium is faster than the parallel heating, so that the temperature anisotropy of helium first increases near the shock before decreasing farther downstream. The observed spectra of magnetic fluctuations, which are dominated by left‐hand circularly polarized waves, display one peak at < gα (He2+ gyrofrequency), just downstream of the shock, and two peaks with a slot near ≈ gα, farther downstream, where is wave frequency in hertz. We present a quasi‐linear theory that accounts for the observed long‐time decrease of the He2+ temperature anisotropy and the excited wave spectrum. The predicted temperature anisotropy and the general shape of the excited wave spectrum match the observations remarkably well. Nevertheless, certain features of the observations, such as the large amplitude of the lower‐frequency peak and very low amplitude of the higher‐frequency peak just downstream of the shock, require further work.

Multiscale Hall‐Magnetohydrodynamic Turbulence in the Solar Wind

The spectra of solar wind magnetic fluctuations exhibit a significant power-law steepening at frequencies f > 1 Hz. The origin of this multiple scaling is investigated through dispersive Hall magnetohydrodynamics. We perform three-dimensional numerical simulations in the framework of a highly turbulent shell model and show that the large-scale magnetic fluctuations are characterized by a k-5/3-type spectrum that steepens at scales smaller than the ion inertial length di, to k-7/3 if the magnetic energy overtakes the kinetic energy, or to k-11/3 in the opposite case. These results are in agreement both with a heuristic description a la Kolmogorov and with the range of power-law indices found in the solar wind.

Wave-Number Spectra and Intermittency in the Terrestrial Foreshock Region

Wave-number spectra of magnetic field fluctuations are directly determined in the terrestrial foreshock region (upstream of a quasiparallel collisionless shock wave) using four-point Cluster spacecraft measurements. The spectral curve is characterized by three ranges reminiscent of turbulence: energy injection, inertial, and dissipation range. The spectral index for the inertial range spectrum is close to Kolmogorov's slope, -5/3. On the other hand, the fluctuations are highly anisotropic and intermittent perpendicular to the mean magnetic field direction. These results suggest that the foreshock is in a weakly turbulent and intermittent state in which parallel propagating Alfvén waves interact with one another, resulting in the phase coherence or the intermittency.

Power spectrum of small‐scale turbulent velocity fluctuations in the solar wind

It is well known that the power spectrum of magnetic field fluctuations in the solar wind exhibits a Kolmogorov spectrum f−α in the inertial range of the turbulence with a power law exponent α near 5/3. The power spectrum of velocity fluctuations has not been as well studied, partly because of the lack of high time resolution measurements needed to resolve a significant fraction of the inertial range. In situ measurements in the ecliptic plane at 1 AU acquired by the 3DP instrument on board the Wind spacecraft near solar minimum in 1995 are used to determine power spectra of the proton bulk velocity fluctuations between 10−5 and 10−1 Hz. The spectrum for the proton kinetic energy (the sum of the spectra for the individual components Vx, Vy, and Vz) obtained using 3‐s velocity data is found to possess the spectral exponent α = 1.50 in the inertial range of the turbulence. A similar calculation of the magnetic energy spectrum yields the exponent α = 1.67. The Alfvén ratio, the ratio of the kinetic to magnetic energy spectrum, is a slowly increasing function of frequency throughout the inertial range increasing from approximately 0.5 to 1 in the frequency interval from 10−4 to 10−2 Hz. This indicates that the partition of energy between small‐scale velocity and magnetic field fluctuations is frequency‐dependent, contrary to some theories. The total energy spectrum (kinetic plus magnetic) has the power law exponent 3/2. A brief investigation of high‐ and low‐speed solar wind streams is also performed, which shows that different spectral exponents for velocity and magnetic field fluctuations are observed in both high‐ and low‐speed wind.

Thermodynamic structure of collision‐dominated expanding plasma: Heating of interplanetary coronal mass ejections

We investigate the thermodynamic structure of interplanetary coronal mass ejections (ICMEs) using combined surveys of the ejecta between 0.3 and 20 AU. ICMEs are shown to have a moderate expansion in the solar wind compared with theoretical predictions. The expansion seems to be governed by a polytrope with γ ∼ 1.3 in this distance range. We find that Coulomb collisions are important contributors to the ion‐ion equilibration process in the ICME plasma. The alpha‐proton differential speed quickly drops to below 10 km s−1 due to strong Coulomb collisions. However, the two species of particles are far from thermal equilibrium with a temperature ratio Tα/Tp = 4–6, suggestive of a preferential heating of alpha particles. The plasma heating rate as a function of heliocentric distance required for the temperature profile is deduced by taking into account the expansion and energy transfer between protons and alphas via Coulomb collisions. The turbulence dissipation rate is also inferred from the inertial range power spectrum of magnetic fluctuations within ICMEs. Comparison of the turbulence dissipation rate with the required heating rate shows that turbulence dissipation seems sufficient to explain the ICME heating. Sources powering the turbulence are also investigated by examining the instabilities induced by temperature anisotropies and energy deposition by pickup ions.

Low-frequency electromagnetic fluctuations in thermal-equilibrium, multi-ion-species plasmas

Low-frequency electromagnetic thermal fluctuations propagating perpendicular to a magnetic field are theoretically studied with attention to the effect of multiple ion species. In the frequency regime lower than the lower hybrid frequency, there exist three types of modes; magnetosonic mode with ω≃kvA, ion cyclotron modes with ω≃nΩi, and heavy-ion cutoff modes with frequencies slightly higher than the ion-ion hybrid resonance frequencies. The power spectra of magnetic fluctuations due to these modes are obtained analytically and numerically. In a single-ion-species plasma, the magnetosonic mode is an overwhelmingly dominant mode. The autocorrelation function Ck(τ) is thus given by a cosine function with a constant amplitude. In a multi-ion-species plasma, however, the amplitudes of the heavy-ion cutoff modes can be comparable to that of the magnetosonic mode. Therefore, Ck(τ) is initially damped, and its recurrence time is extremely long.

Measurement of the Electric Fluctuation Spectrum of Magnetohydrodynamic Turbulence

Magnetohydrodynamic (MHD) turbulence in the solar wind is observed to show the spectral behavior of classical Kolmogorov fluid turbulence over an inertial subrange and departures from this at short wavelengths, where energy should be dissipated. Here we present the first measurements of the electric field fluctuation spectrum over the inertial and dissipative wave number ranges in a Beta > or approximately = 1 plasma. The k(-5/3) inertial subrange is observed and agrees strikingly with the magnetic fluctuation spectrum; the wave phase speed in this regime is shown to be consistent with the Alfvén speed. At smaller wavelengths krho(i) > or = 1 the electric spectrum is enhanced and is consistent with the expected dispersion relation of short-wavelength kinetic Alfvén waves. Kinetic Alfvén waves damp on the solar wind ions and electrons and may act to isotropize them. This effect may explain the fluidlike nature of the solar wind.

Modeling of short scale turbulence in the solar wind

Abstract. The solar wind serves as a laboratory for investigating magnetohydrodynamic turbulence under conditions irreproducible on the terra firma. Here we show that the frame work of Hall magnetohydrodynamics (HMHD), which can support three quadratic invariants and allows nonlinear states to depart fundamentally from the Alfvénic, is capable of reproducing in the inertial range the three branches of the observed solar wind magnetic fluctuation spectrum - the Kolmogorov branch f -5/3 steepening to f -α1 with on the high frequency side and flattening to f -1 on the low frequency side. These fluctuations are found to be associated with the nonlinear Hall-MHD Shear Alfvén waves. The spectrum of the concomitant whistler type fluctuations is very different from the observed one. Perhaps the relatively stronger damping of the whistler fluctuations may cause their unobservability. The issue of equipartition of energy through the so called Alfvén ratio acquires a new status through its dependence, now, on the spatial scale.

Hall-MHD Turbulence in the Solar Wind

The solar wind is a great paradigm for investigating magnetohydrodynamic turbulence. It is shown that the frame work of Hall magnetohydrodynamics (HMHD), which can support three quadratic invariants and allows nonlinear states to depart fundamentally from the Alfvénic, is capable of reproducing in the inertial range the three branches of the observed solar wind magnetic fluctuation spectrum – the Kolmogorov branch f–5/3 steepening to f–α1 with α1 ≃ 3–4 on the high frequency side and flattening to f–1 on the low frequency side. These fluctuations are found to be associated with the nonlinear Hall-MHD Shear Alfvén waves. The spectrum of the concomitant whistler type fluctuations is very different from the observed one. Perhaps the relatively stronger damping of the whistler fluctuations may cause their unobservability. The issue of the anisotropy of the turbulence is addressed briefly.

Magnetic fluctuations and Hall magnetohydrodynamic turbulence in the solar wind

It is shown that the framework of Hall magnetohydrodynamics (Hall‐MHD), which can support three quadratic invariants and allows nonlinear states to depart fundamentally from the Alfvénic, is capable of reproducing in the inertial range the three branches of the observed solar wind magnetic fluctuation spectrum: the Kolmogorov branch f−5/3, steepening to with α1 ≃ 3–4 on the high‐frequency side and flattening to f−1 on the low‐frequency side. These fluctuations are found to be associated with the nonlinear Hall‐MHD shear Alfvén waves. The spectrum of the concomitant whistler‐type fluctuations is very different from the observed one. Perhaps the relatively stronger damping of the whistler fluctuations may cause their unobservability. The issue of the anisotropy of the turbulence is addressed briefly.

On the Generation, Propagation, and Reflection of Alfven Waves from the Solar Photosphere to the Distant Heliosphere

We present a comprehensive model of the global properties of Alfven waves in the solar atmosphere and fast solar wind. Linear non-WKB wave transport equations are solved from the photosphere to 4 AU, and for wave periods ranging from 3 seconds to 3 days. We derive a radially varying power spectrum of kinetic and magnetic energy fluctuations for waves propagating in both directions along a superradially expanding magnetic flux tube. This work differs from previous models in 3 major ways. (1) In the chromosphere and low corona, the successive merging of flux tubes on granular and supergranular scales is described using a 2D magnetostatic model of a network element. Below a critical merging height the waves are modeled as thin-tube kink modes, and we assume that all of the kink-mode wave energy is transformed into volume-filling Alfven waves above the merging height. (2) The frequency spectrum of horizontal motions is specified only at the photosphere based on prior analyses of G-band bright point kinematics. Everywhere else the amplitudes of outward and inward propagating waves are computed with no free parameters. We find that the wave amplitudes in the corona agree well with off-limb nonthermal line widths. (3) Nonlinear turbulent damping is applied to the results of the linear model using a phenomenological loss term. A single choice for the normalization of the turbulent outer-scale length produces both the right amount of damping at large distances (to agree with in situ measurements) and the right amount of heating in the extended corona (to agree with empirical wind acceleration models). In the corona, the modeled heating rate differs by more than an order of magnitude from a rate based on isotropic Kolmogorov turbulence.

Scanning internal probe for plasma particle, fluctuation, and LIF tomographic measurements

An internal scanning probe capable of spatially resolved measurements throughout a horizontal (r,z) cross section of the expansion region between a helicon plasma source and an expansion chamber is described. For complete diagnosis of the expanding magnetoplasma, the probe is designed to simultaneously measure the electron temperature, the electron density, the plasma potential, the magnetic fluctuation spectrum in three dimensions, and the two-dimensional ion velocity distribution function (through a tomographic inversion method). The probe design and operational characteristics as well as representative measurements are presented.

Self-organization towards helical states in the Toroidal Pinch Experiment reversed-field pinch

In this paper results of an experimental study of magnetic fluctuations in the Toroidal Pinch Experiment (TPE–RX) [Y. Yagi, S. Sekine, H. Sakakita et al., Fus. Eng. Design 45, 409 (1999)] are reported. This study has permitted the identification of the experimental conditions under which the usually turbulent spectrum of magnetic fluctuations in TPE–RX turns into a single tearing mode, in the so-called quasi-single helicity (QSH) state. The large data set has allowed us to provide a complete two dimensional map of QSH probability in the current F plane, being F=Bφ(a)/〈Bφ〉. Two main basins of high QSH probability have been found. The first one, at high current and low |F|, confirms previous results on QSH in other machines; the second one is completely new, and is found at low current and high |F|. These studies show that QSH is a robust, device-independent phenomenon, and a significant step towards a laminar type of dynamo in the reversed-field pinch configuration.

A model and observations of the multifractal spectrum of the heliospheric magnetic field strength fluctuations near 40 AU

The Voyager 1 (V1) observations of the magnetic field strength as a function of time during 1989, between 36.3 and 38.8 AU, have a multifractal structure in the range of scales from 2 to 32 days. We show that a 1‐D multi‐fluid MHD model with observations made at 1 AU during 1999 as input predicts the multifractal structure at 40 AU. The multifractal spectrum determined from the time series at 40 AU predicted by the model agrees with that observed by V1. The observed multifractal scaling symmetry can be explained by a deterministic model.

Laser polarimetric measurement of equilibrium and fluctuating magnetic fields in a reversed field pinch (invited)

New developments in Faraday rotation polarimetry have provided the first measurements of current density profile and core magnetic fluctuations in the core of a high-temperature reversed field pinch. This has been achieved by a fast-polarimeter system with time response up to 1 μs and phase resolution <1 mrad. Recent experiments on Madison Symmetric Torus have directly measured radial magnetic field fluctuations in the plasma interior with amplitude 33 G, ∼1%. A broad spectrum of magnetic fluctuations is observed up to 100 kHz. Relaxation of the current density profile at the sawtooth crash occurs on the timescale of 100 μs. Reversed-field pinch behavior is determined in large part by magnetic fluctuations driven by the radial gradient in the parallel current density. Hence, measurement of magnetic fluctuations and the current density profile is essential to understand the link between the current density profile, fluctuations, and transport.