Magnetic Power Spectra Research Articles

Power Spectra of Solar Network and Non-Network Fields

We report new properties of solar magnetic fields in a quiet region as found from their magnetic power spectra. The power spectra of network and intranetwork fields (non-network fields) are separately calculated from a Big Bear magnetogram obtained with moderately high spatial resolution of 1.5 arc sec and a high sensitivity reaching 2 Mx cm-2. The effect of seeing on the power spectrum has been corrected using Fried's (1966) Modulation Transfer Function with the seeing parameter determined in our previous analysis of the magnetogram. As a result, it is found that the two-dimensional power spectra of network and non-network fields appear in a form: Γ( $$k_0 $$ ≲ $$k $$ ≲ $$k $$ 1) ∼ $$k $$ -1 and Γ( $$k $$ ≳ $$k $$ 1) ∼ $$k $$ -3.5. Here $$k $$ 0 ≈ 0.47 Mm-1 for network fields and $$k $$ 0 ≈ 0.69 Mm-1 for non-network fields, the latter of which corresponds to the size of mesogranulation; $$k $$ 1 ≈ 3.0 Mm-1 for both, which is about the size of a large granule. The network field spectrum below $$k $$ 0 appears nearly flat, whereas that of non-network fields instead decreases towards lower wave numbers as Γ( $$k $$ ) ∼ $$k $$ 1.3. The turnover behavior of magnetic field spectra around $$k $$ 1 coincides with that found for the velocity power spectrum, which may justify the kinetic approach taken in previous theoretical studies of the solar magnetic power spectra.

Generation of Density Perturbations by Primordial Magnetic Fields

We study the generation and evolution of density perturbations and peculiar velocities due to primordial magnetic fields. We assume that a random magnetic field was present before recombination and follow the field's effect on the baryon fluid starting at recombination. We find that magnetic fields generate growing density perturbations on length scales larger than the magnetic Jeans length, $\lambda_B$, and damped oscillations for scales smaller than $\lambda_B$. For small wavenumbers $k$ (large length scales), we find the magnetic field-induced density power spectrum generally scales as $k^4$. We derive the magnetic Jeans length explicitly by including the back--reaction of the velocity field onto the magnetic field by decomposing the magnetic field into a force-free background field and perturbations about it. Depending on the strength of the magnetic field and the ultraviolet cutoff of its spectrum, structure can be generated on small or intermediate scales early in the history of the universe. For a present {\it rms} magnetic field of $10^{-10}$ G on intergalactic scales, we find that perturbations on galactic scales could have gone non--linear at $z \simeq 6$. Finally, we discuss how primordial magnetic fields affect scenarios of structure formation with non--baryonic dark matter.

Palaeosecular variation recorded by lava flows over the past five million years

We present a new global palaeomagnetic database, comprising lava flows and thin intrusive bodies, suitable for studying palaeosecular variation and the time-averaged field. The database is presented in some detail in the appendix and is available on-line from the authors. We review palaeosecular variation models to date, emphasizing the assumptions required and the rather arbitrary construction of many of these models. Preliminary studies of the statistical properties of the new database suggest that existing palaeosecular variation models are inadequate to explain the long-term temporal variations in the field. It is increasingly apparent that data distribution and quality are pivotal in determining the characteristics of the secular variation. The work presented here demonstrates the need for revised models of the time-averaged field structure for both normal and reverse polarities before reliable models for palaeosecular variation can be made.

Magnetohydrodynamic and hybrid simulations of broadband fluctuations near interplanetary shocks

We present results of a theoretical study of evolution of a spectrum of finite amplitude right‐hand elliptically polarized magnetohydrodynamic (MHD) waves. The analysis includes use of one‐and‐a‐half‐dimensional solutions of the equations that describe compressible MHD together with one‐and‐a‐half‐dimensional hybrid simulation of the phenomenon. The motivation of the study is to understand the origin and properties of finite amplitude waves often observed in the vicinity of collisionless shocks in the heliosphere. The solutions of the MHD equations are compared with both the results of the hybrid simulations and observations previously reported by Viñas et al. (1984) in the vicinity of a quasi‐parallel interplanetary shock. The initial conditions of the MHD solutions were constructed to model the observed spectrum of magnetic and velocity fluctuations; plasma parameters were also chosen to replicate the observed parameters. For the typical parameters of β = 0.5, δB/B0 = 0.25 and a spectrum of parallel propagating, circularly polarized dispersive waves, initially the density and magnetic energy density correlations grow due to the (nonlinear) ponderomotive effect. The spectral features below the ion cyclotron frequency are established quickly on the Alfvénic timescale but then persist and match closely the observed fluctuations. The parametric decay instabilities that subsequently appear further enhance the density fluctuations and produce a high‐frequency magnetic power spectrum consistent with the spacecraft observation. The MHD and hybrid simulations extend the previous picture of wave generation by a beam‐driven ion cyclotron instability to the fully nonlinear stage.

Evolution of the particle injection at propagating interplanetary shocks

For 16 proton events in the 10 MeV energy range associated with interplanetary shocks we guesstimated the particle mean free paths (mfp) and the radial development of the particle injection at the shock using a numerical solution of the focused transport equation. The particle mfps derived by this method typically are larger than the mfps derived from the magnetic field power spectra and are comparable to the ones found in previous studies of solar energetic particle events. The evolution of the shocks acceleration efficiency can be highly variable with efficiencies varying as τ α where α is between −2 and 2. In some cases α can be as large as 5 or more. These latter events show distinct features, in particular quasi-exponential particle increases and extremely weak proton spectra with spectral indices around −5 for protons with energies of a few to a few tens of MeV. In the 7 events with sufficient quality of the magnetic field data we find no indication of an increase of turbulence in the upstream medium at wave numbers in resonance with the particles.

Statistical Treatment of Crustal Magnetization

We present a general statistical theory for relating magnetic fields to the magnetization of their source region, when the geometry of the source is spherical and the magnetization is a realization of a stationary, isotropic random process. For the case of Gaussian statistics, considered here, the second-order statistics are sufficient to determine the process uniquely. Observed high-degree coefficients from a spherical-harmonic expansion of the field appear to be consistent with this model. We find simple models of crustal magnetization that are compatible with observational constraints, namely the values of the magnetic power spectra believed to be derived from the crust, and the total crustal power. Any statistical model of the crust can be used to ‘pre-whiten’ observations prior to modelling the core field in a way described previously by Jackson.

Crustal structure of the eastern part of the Maya Terrane from magnetic anomalies and magnetic power spectrum inversion

Se interpreta una compilación reciente de anomalías magnéticas de campo total de la porción oriental del Terreno Maya, que incluye datos aeromagnéticos de la Península de Yucatán y datos magnéticos marinos de su margen continental hacia el norte y oriente. Con base en la amplitud, forma y extensión horizontal de las anomalías magnéticas y su correlación con información geológica y geofísica disponible se infiere que la porción oriental del Terreno Maya está constituida por al menos cuatro bloques tectónicos. Modelamos el espectro de potencia radial de las anomalías magnéticas de la margen continental al norte de la Penín­sula mediante la superposición de funciones que en forma estadística describen la profundidad a la cima, el espesor y las dimen­siones horizontales de una colección de prismas verticales uniformemente magnetizados. Los resultados se exhiben en forma de mapas de contornos que muestran la profundidad a la cima y a la base de la corteza. El relieve del basamento promedia 1.8 km bajo el nivel del mar y está de acuerdo tanto con el carácter de las anomalías gravimétricas y magnéticas como con la interpreta­ción de datos sísmicos y con información de pozos. La profundidad a la base de la corteza magnetizada varía de 15 a 35 km bajo el nivel del mar según la presencia o ausencia de anomalías magnéticas y gravimétricas de gran longitud de onda. Esta interpre­tación sugiere que localmente el Moho es la frontera magnética. PALABRAS CLAVE: Anomalías magnéticas, inversión del espectro de potencia, estructura de la corteza, Terreno Maya, Blo­que Yucatán, México.

Interplanetary transport of solar electrons and protons: Effect of dissipative processes in the magnetic field power spectrum

Quasi‐linear theory describing charged particle transport in interplanetary space within the framework of a slab turbulence picture was for a long time confronted with the problem that the theoretically predicted mean free path for scattering at magnetic field fluctuations was too small when compared with the corresponding parameter derived from fits to observed intensity and anisotropy profiles of solar energetic particles. The theory up to now has neglected the dispersiveness of some of the scattering plasma waves and the effects resulting from the finite temperature of the plasma through which the particles propagate. We have therefore attempted to give a more realistic model of an observed interplanetary turbulence spectrum. The most simple picture we find requires the dissipation range to be constituted by parallel dispersive whistler, electron and ion cyclotron waves in a warm plasma (β ≈ 1). The dispersion relation of heavily thermally affected ion cyclotron waves needed in this model is calculated for the first time. The model is fitted to the turbulence spectrum measured on June 7, 1980, by ISEE 3 (ICE). The derived model parameters are used in a quasi‐linear calculation of both proton and electron mean free paths. As a first step resonance broadening due to wave damping is neglected. The results are compared with typical empirical proton mean free paths and with electron mean free paths obtained from fits to electron intensity and anisotropy profiles observed simultaneously by the same satellite. In both cases the theoretical values seem to be systematically larger than the empirical ones. Thus scattering enhancements by nonlinear or thermal resonance broadening or oblique waves now bear the hope to remove the discrepancy between theory and observation.

Magnetic pulsations from 0.1 to 4.0 Hz and associated plasma properties in the Earth's subsolar magnetosheath and plasma depletion layer

Dynamic spectral analysis covering frequencies 0.1 to 4.0 Hz has been applied to analyze Active Magnetospheric Particle Tracer Explorers CCE magnetic field data during periods of magnetospheric compressions when the spacecraft sampled the magnetosheath. Ion (H+, He2+) and electron data are used to identify regions, to monitor the upstream shock geometry, and to evaluate moments of the proton distribution. A total of 14 encounters representing 46 hours of observations are analyzed. For quasi‐perpendicular shock conditions, two distinctive band limited spectral types are found to characterize the majority of magnetosheath observations: (1) purely compressional fluctuations with F < 0.2 FH+ which are attributed to mirror waves (F and FH+ denote the wave frequency and proton gyrofrequency, respectively); and (2) 0.25–1.0 FH+ frequency purely transverse fluctuations that are often left hand polarized from 0.5–1.0 FH+ and are attributed to electromagnetic ion cyclotron (EMIC) waves. The plasma characteristics for these two pulsations are different. Mirror waves are associated with βp>5 and T⊥p/T∥p of 1.5 whereas EMIC waves occur for βp≤1 and T⊥p/T∥p = 2.5 ‐ 5 (the subscript p denotes quantities evaluated for protons). EMIC waves also occur for higher field strength and lower plasma densities than mirror waves, indicative of EMIC wave occurrence in the plasma depletion layer (PDL). The increased T⊥p/T∥p during EMIC waves relative to periods of mirror waves is due to a decrease in T∥p suggesting that the EMIC wave region has suffered a loss of particles in the parallel direction. A compilation of the temporal sequence of spectral structures shows that EMIC waves occur next to the magnetopause while mirror waves occur outside the region of EMIC waves. We conclude that there is a close relationship between EMIC waves in the sheath and the PDL. Both the density depletion and the increase in temperature anisotropy, Ap = T⊥p/T∥p ‐ 1, are attributed to extrusion of plasma along the draped field lines as plasma flows into the PDL. For quasi‐parallel upstream conditions, the magnetic field power spectra often exhibit no band limited structures but only broadband noise. The absence of EMIC wave emissions during quasi‐parallel conditions is consistent with predictions that the PDL does not form for radial IMF conditions.

On low frequency magnetic field turbulence upstream of earth's bow shock

Low frequency magnetic field turbulence is described in terms of an ideal gas of circularly polarized Alfvén solitons. This approach leads to a magnetic field power spectrum with a broad local maximum and an exponential decay and is able to reproduce a special power spectrum obtained by the AMPTE/IRM spacecraft mission upstream of Earth's bow shock.

Generation of low‐frequency waves at comet Halley

In this paper we investigate the extent to which the properties of the waves observed at comet Halley during the Giotto encounter can be understood within the context of linearized Vlasov theory. In the region that is magnetically connected to the comet, fluctuations in the plasma frame of reference are detected near 4 and 10 mHz, close to the water cyclotron frequency, as well as at 20–60 mHz, which is well above the water cyclotron frequency. Using a variety of approximations for the ion distribution function, we show that waves having properties similar to those observed can then be generated with appropriate choices of plasma parameters. In the region that is magnetically disconnected from the comet, distinct peaks are observed in the magnetic power spectrum at 7, 21, 29, and 35 mHz, with a hint of a peak at 14 mHz. We show that an anisotropic distribution of pickup water group ions is able to generate unstable waves at as many as 6 harmonics in wave number in the observed range of frequencies. When Doppler shifted into the frame of the Giotto spacecraft, these harmonics in wave number will be observed as harmonics of the water ion cyclotron frequency.

The distribution function of diffuse ions and the magnetic field power spectrum upstream of Earth's bow shock

During two diffuse energetic ion events upstream of the Earth's bow shock with radial interplanetary magnetic field conditions comprehensive energy spectra of the protons and power spectra of the magnetic field fluctuations were obtained with the instrumentation on AMPTE/IRM. For diffuse ions a continuous distribution from ≈ 5 keV (starting above the solar wind energy) to the instrumental limit (230 keV/e) is found upstream and downstream of the shock. This strongly indicates a single source for the upstream diffuse ion population over the total energy range. Assuming that the ions are shock accelerated, an efficiency for the production of upstream energetic ions of ≈ 4 to 11% is found by comparing the energy flux densities of the energetic ions and of the incoming solar wind. The lower value is observed during the period with a low interplanetary magnetic field strength. The measured energy densities of the particles and the waves are compared with the self‐consistent model of Fermi acceleration by Lee (1982) which includes the coupled wave and particle behaviour. The theoretically predicted wave energy density is in excellent agreement with the observed wave energy density.

Spin-glass dynamics from magnetic noise, relaxation, and susceptibility measurements (invited)

We present a quantitative comparison between dynamic measurements on spin glasses. The case of CdIn0.3Cr1.7S4 is discussed in detail and references are made to CsNiFeF6 and Ag:Mn (2.6%). The measured quantities are the relaxation of the thermoremanent magnetization MTRM(t) in the range of observation times 1–105 s, the out-of-phase susceptibility χ″(ω) in the range 10−3–5×104 Hz, and the magnetic noise power spectrum M2(ω) between 10−2 and 103 Hz. The aging of the thermoremanent magnetization relaxation is analyzed on the basis of a phenomenological theory of time scaling which allows to derive the form of the equilibrium relaxation. It is shown that the measured values of χ″ and ∼(M2(ω)) are related according to the fluctuation dissipation theorem (FDT). The consequences of the applicability of the FDT in the frequency domain are discussed, with reference to the expected violation of the theorem in the spin-glass phase at ω=0. An important modification of the frequency dependence of χ″(ω) is observed at Tg, supporting a previous dynamic scaling approach. There is good agreement between the low-temperature stationary behaviors of MTRM(t) and χ″(ω), but they show an unexplained discrepancy close to Tg.

Beam‐driven ion cyclotron harmonic resonances in the terrestrial foreshock

We report an observation of low‐frequency terrestrial upstream waves which exhibit enhancements in the magnetic field power and polarization spectra at harmonics of the proton cyclotron resonance. These magnetic fluctuations exist concurrent with a “diffuse” suprathermal proton population, but a field rotation immediately following the wave observation reveals a “reflected” suprathermal distribution. We also compute instability growth rates due to this highly anisotropic “reflected” component and find relative maxima at frequencies corresponding to the enhancements in the observed spectra. We thus infer that the multiple spectral peaks are due to resonant, electromagnetic ion beam instabilities and conclude that the observed ion beam is the source of the observed upstream waves. Spectral analysis of the polarization, magnetic helicity, and minimum variance directions supports this interpretation. We find observational and theoretical evidence for both right‐hand polarized waves propagating parallel to the mean magnetic field and left‐hand polarized waves propagating oblique to the mean field.

Spectral analysis of magnetohydrodynamic fluctuations near interplanetary shocks

Evidence for the presence of relatively large amplitude right‐hand elliptically polarized MHD waves upstream and downstream of quasi‐parallel (θBn < 45°) forward and reverse interplanetary shocks is presented. The mode is observed with frequencies in the range of 0.025–0.17 Hz (in the spacecraft frame) and propagates along the magnetic field. The MHD modes have rest frame frequencies in the range 3.8–31 mHz, with typical wavelengths about 1.5×108 to 4.7×108 cm. The magnetic field power spectrum in the vicinity of these interplanetary shocks is much steeper than f−5/3 at high frequencies. The observed spectra have a high frequency dependence of f−2.5 to f−4. A peculiar feature of the fast mode identification in one event is the large correlation observed between |B| and proton density ρ for field‐aligned propagation. This appears to be a nonlinear effect, second order in the wave amplitude. The properties of the MHD waves can be understood in terms of the electromagnetic ion‐cyclotron instability. Both resonant and nonresonant interactions need be considered to account for the polarization and spectral content of the observed fluctuations. In association with one event, a distinct suprathermal component was observed in the solar wind proton distribution. The parameters of this distribution are adequate to drive a resonant instability with a maximum growth rate that coincides with the observed range of frequencies.

A soliton gas model for astrophysical magnetized plasma turbulence

Plasma turbulence is considered as an ensemble of solitons. The derivation of the Alfven soliton by Spangler and Sheering (1981) is reviewed, and expressions are derived for the magnetic irregularity spectrum and the relationship between the magnetic and density irregularity power spectra. A derived expression also provides the answer to the question of the correlation between magnetic field and density enhancements. The properties of the turbulence model are compared with observations of plasma turbulence in the solar wind, and are found to reasonably account for them.

Transport coefficients of low‐energy cosmic rays in interplanetary space

The propagation of energetic particles along and across the interplanetary magnetic field is governed by the large‐scale field geometry and by scattering in small‐scale turbulent fields. Values of the scattering mean free path parallel to the field, λ∥(R), are reviewed in prompt solar bursts and nonimpulsive (corotating) events. Analysis of intensity and anisotropy profiles in combination is a powerful tool for elucidating λ∥(R). A consensus is found: at 1 AU, λ∥ = 0.08–0.3 AU over a wide range of rigidity, R = 5 × 10−4 to 5 GV. Efforts to explain the discrepancy between empirical values of λ∥ and scattering theory are discussed. Quantitative measures of λ∥ in rare scatter‐free events, where λ∥ ≳ 1 AU, are discussed because they can provide important details of the scattering process and the magnetic power spectra. Cross‐field diffusion due to random walk of field lines is revisited. Recent values deduced from magnetic power spectra in interplanetary space, magnetic diffusion at the sun, Jovian electron propagation, and cosmic ray events are evaluated. Again, a consensus is sought, and a reasonable mean is K⊥r/β = 1021 cm² s−1. Previous arguments against a significant K⊥r are reassessed, including the problem of the persistence of intensity fluctuations in cosmic ray events. Combining the consensus for K⊥r/β with that for λ∥ gives K⊥r/K∥ < 0.1 at 1 AU, and thus neglect of K⊥r in the modeling of solar cosmic ray events appears justified (although account needs to be taken of coronal propagation). The outlook for the future includes better empirical values of λ∥ down to Ep ∼ 10 keV and Ee ∼ 1 keV, comparison with scattering theories at these energies, and comparison between empirical and theoretical λ∥ in other regions such as the magnetosheath and upstream solar wind.

Valence fluctuations between two magnetic configurations: An exactly solvable model

We propose an exactly solvable Hamiltonian that describes intermediate valence systems fluctuating between two magnetic configurations. It consists of a set of localized, highly correlated states hybridized through a conduction band. From it, we derive the spectral density of localized states, valence, static and dynamic magnetic susceptibilities and charge power spectrum. We also describe the results for specific heat and magnetic field dependence of electrical conductivity. We briefly discuss its relevance to the understanding of intermediate valence Tm compounds.

Intermediate wavelength magnetic anomalies over ocean basins

We have examined three very long magnetic field profiles taken over ocean basins for the presence of intermediate wavelength magnetic anomalies. One profile was from the Atlantic Ocean in the Transatlantic Geotraverse area, one ran along latitude 35°S in the SE Pacific, and one ran along 150°W in the Pacific. All three profiles show the presence of intermediate wavelength (65–1500 km) magnetic anomalies generated in the crust or upper mantle. The analysis of magnetic field power spectra shows that the core field becomes unimportant at about a wavelength of 1500 km. Sea floor spreading anomalies should produce a maximum in power at about a wavelength of 65 km. Between these two wavelengths there should be a minimum in power which is not seen on observed records. Inverting the anomalous field to obtain some idea of the magnetization necessary to explain these intermediate wavelength magnetic anomalies shows that values of magnetization in excess of 1 A m−1 are needed if the magnetized layer is as thick as the oceanic crust. Alternatively, rather large thicknesses of upper mantle material with lower intensities of magnetization need to be used. The reason why such magnetization variations exist is not known. It can be shown that upward continuation of the magnetic anomaly signature to an altitude of 350 km (about the perihelion altitude of MAGSAT) will produce anomalies up to 10 nT in amplitude. These should be capable of being seen by MAGSAT, and thus allow us to determine the spatial arrangement of the intermediate wavelength anomalies and hence, hopefully, a clue as to their origin.

Propagation of energetic electrons in the magnetosheath and upstream solar wind

The propagation of relativistic electrons through the magnetosheath and solar wind is investigated in the two extremes of scatter‐free motion and diffusive motion. For a source which is assumed on a field line close to the magnetopause, predictions are made of density U (or omnidirectional intensity) and anisotropy ξ at different points on the field line in the magnetosheath and upstream solar wind. Both extremes of motion predict in the solar wind a lower U than in the magnetosheath. However, while scatter‐free motion always gives greater anisotropy in the solar wind, in the diffusion case it depends on the locations of the comparison stations. The theory has been applied to observations of >200 keV electrons, and derived mean free paths in the magnetosheath are 3.8±0.6 RE and 8.7±0.6 RE on two separate traversals, while the average results over a 4‐year period give ≈ 1.0 RE. The latter value agrees with λ=1 RE obtained by an independent analysis of the same data set. The mean free path has also been computed from quasi‐linear theory and measured magnetic power spectra. These give λ varying from 0.27 RE for a typical high to 4.6 RE for a typical low level of disturbance in the magnetosheath, respectively. A particularly ‘quiet’ period gave λ=42.7 RE. The empirical results of λ=3.8 and 8.7 RE, obtained when Kp ≈ 2, are consistent with the low level of disturbance, while the average result of λ ≈ 1.0 RE lies right between the low and the high.