Magnetic Power Spectra Research Articles

Effect of intermittent structures on the spectral index of the magnetic field in the slow solar wind

Abstract. Intermittent structures are ubiquitous in the solar wind turbulence, and they can significantly affect the power spectral index (which reflects the cascading process of the turbulence) of magnetic field fluctuations. However, to date, an analytical relationship between the intermittency level and the magnetic spectral index has not been shown. Here, we present the continuous variation in the magnetic spectral index in the inertial range as a function of the intermittency level. Using the measurements from the Wind spacecraft, we find 42 272 intervals with different levels of intermittency and with a duration of 5–6 min from 46 slow-wind streams between 2005 and 2013. Among them, each of the intermittent intervals is composed of one dominant intermittent structure and background turbulent fluctuations. For each interval, a magnetic spectral index αB is determined for the Fourier spectrum of the magnetic field fluctuations in the inertial range between 0.01 and 0.3 Hz. A parameter Imax, which corresponds to the maximum of the trace of the partial variance increments of the intermittent structure, is introduced as an indicator of the intermittency level. Our statistical result shows that, as Imax increases from 0 to 20, the magnetic spectrum becomes gradually steeper and the magnetic spectral index αB decreases from −1.63 to −2.01. Accordingly, for the first time, an empirical relation is established between αB and Imax: αB=0.4exp⁡(-Imax/5)-2.02. The result will help us to uncover more details about the contributions of the intermittent structures to the magnetic power spectra and, furthermore, about the physical nature of the energy cascade taking place in the solar wind. It will also help to improve turbulence theories that contain intermittent structures.

Theory of magnetic turbulence and shock formation induced by a collisionless plasma instability

Magnetic fields are ubiquitous in universe, space, and laboratory plasmas. Especially, self-generated magnetic fields are important to know the mind of nature. The formation of Weibel-mediated collisionless shock is studied theoretically as a structure formation by the linear plasma wave growth, nonlinear saturation, and mode–mode coupling. Following a series of computer simulations and experimental studies of the physics, a simple model equation is proposed here to describe the time evolution of magnetic turbulence. Weibel instability is saturated by magnetic pressure, and thicker filaments continue to be generated by current coalescence (magnetic reconnection) mechanism. The model equation concludes the fact that the filament spacing increases linearly in time, and the magnetic energy power spectrum is given as Bk2 ∝ k−2. The time evolution of the turbulence is characterized with the cascade toward smaller k. Such inverse cascade is well-known in 2D hydrodynamic turbulence such as a typhoon or hurricane formation and is known to have Kolmogorov spectrum k−5/3. Although only a small difference in power, the physics of inverse cascades is very different as shown in the present paper. With use of Alfvén current limit condition, the criteria of collisionless shock formation are evaluated. The present theory is compared to corresponding experiments done with Omega and NIF lasers and a variety of PIC simulations. The theory is also applied to evaluate the strength of magnetic field near the shock front of the supernova remnant SN1006. The enhancement of magnetic field of about 25 μG is concluded in the present theory. Finally, a universality of the model equation is shown by applying the theory to the turbulent mixing due to Rayleigh–Taylor instability at the contact surface of two fluids in a gravitational or inertial force, which is very important in compressing plasma such as inertial confinement fusion by implosion. It is shown that the well-known evolution physics, mixing layer of the two fluids grows in proportion to (time)2, can be explained with the same model equation.

Inflationary and Phase-transitional Primordial Magnetic Fields in Galaxy Clusters

Primordial magnetic fields (PMFs) are possible candidates for explaining the observed magnetic fields in galaxy clusters. Two competing scenarios of primordial magnetogenesis have been discussed in the literature: inflationary and phase-transitional. We study the amplification of both large- and small-scale correlated magnetic fields, corresponding to inflation- and phase transition–generated PMFs, in a massive galaxy cluster. We employ high-resolution magnetohydrodynamic cosmological zoom-in simulations to resolve the turbulent motions in the intracluster medium. We find that the turbulent amplification is more efficient for the large-scale inflationary models, while the phase transition–generated seed fields show moderate growth. The differences between the models are imprinted on the spectral characteristics of the field (such as the amplitude and the shape of the magnetic power spectrum) and therefore also on the final correlation length. We find a one order of magnitude difference between the final strengths of the inflation- and phase transition–generated magnetic fields, and a factor of 1.5 difference between their final coherence scales. Thus, the final configuration of the magnetic field retains information about the PMF generation scenarios. Our findings have implications for future extragalactic Faraday rotation surveys with the possibility of distinguishing between different magnetogenesis scenarios.

Magnetogenesis in Higgs-Starobinsky inflation

In the framework of mixed Higgs-Starobinsky inflation, we consider the generation of Abelian gauge fields due to their nonminimal coupling to gravity (in two different formulations of gravity -- metric and Palatini). We couple the gauge-field invariants $F_{\mu\nu}F^{\mu\nu}$ and $F_{\mu\nu}\tilde{F}^{\mu\nu}$ to an integer power of the scalar curvature $R^n$ in Jordan frame and, treating these interactions perturbatively, switch to the Einstein frame where they lead to effective kinetic and axial couplings between gauge fields and inflaton. We determine the power spectra, energy densities, correlation length, and helicality of the generated gauge fields for different values of the nonminimal coupling constants and parameter $n$. We analytically estimate the spectral index $n_{B}$ of the magnetic power spectrum and show that for $n>1$ it is possible to get the scale-invariant or even red-tilted spectrum for a wide range of modes that implies larger correlation length of the generated fields. On the other hand, the magnitude of these fields typically decreases in time becoming very small in the end of inflation. Thus, it is difficult to obtain both large magnitude and correlation length of the gauge field in the frame of this model.

Correlation Between Bandwidth and Frequency of Plasmaspheric Hiss Uncovered With Unsupervised Machine Learning

AbstractPrevious statistical studies of plasmaspheric hiss investigated the averaged shape of the magnetic field power spectra at various points in the magnetosphere. However, this approach does not consider the fact that very diverse spectral shapes exist at a given L‐shell and magnetic local time. Averaging the data together means that important features of the spectral shapes are lost. In this paper, we use an unsupervised machine learning technique to categorize plasmaspheric hiss. In contrast to the previous studies, this technique allows us to identify power spectra that have “similar” shapes and study their spatial distribution without averaging together vastly different spectral shapes. We show that strong negative correlations exist between the hiss frequency and bandwidth.

Low Frequency ULF Waves in the Earth's Inner Magnetosphere: Power Spectra During High Speed Streams and Quiet Solar Wind and Seeding of EMIC Waves.

Here, we extend the scope of the Gamayunov and Engebretson (2021, hereinafter Paper 1), https://doi.org/10.1029/2021JA029247 work by analyzing the low frequency ultra-low-frequency (ULF) wave power spectra in the Earth's inner magnetosphere during high speed stream (HSS) and quiet solar wind (QSW) driving conditions in the upstream solar wind (SW) and comparing our results to the results of Paper 1, where the statistics of ULF wave power spectra during coronal mass ejections (CMEs) are presented. The most important results of our statistical and comparative analyses are as follows. (a) During CMEs, HSSs, and QSW, the magnetic field power spectra of the transverse and compressional fluctuations are well approximated by power laws in the ∼mHz-Hz frequency range, where on average the parameters of power law fits during CMEs and HSSs are close, and those during QSW differ considerably from the respective parameters during CMEs and HSSs. (b) The dominance of the average compressional power over the average transverse power for the low frequency ULF waves during the 0<SYM/H≲25nT geomagnetic conditions may serve as a proxy of HSSs in the upstream SW, whereas the opposite relation between the average powers is an indication of CMEs. (c) Independently of the SW driving conditions, a turbulent energy cascade from low frequencies in the ULF wave frequency range into the higher frequency range exists in the Earth's inner magnetosphere, supplying the nonthermal electromagnetic seed fluctuations needed for the growth of electromagnetic ion cyclotron waves (∼Hz) due to relaxation of unstable distributions of energetic magnetospheric ions.

Rotation measure structure functions with higher-order stencils as a probe of small-scale magnetic fluctuations and its application to the Small and Large Magellanic Clouds

ABSTRACTMagnetic fields and turbulence are important components of the interstellar medium (ISM) of star-forming galaxies. It is challenging to measure the properties of the small-scale ISM magnetic fields (magnetic fields at scales smaller than the turbulence driving scale). Using numerical simulations, we demonstrate how the second-order rotation measure (RM, which depends on thermal electron density, ne, and magnetic field, b) structure function can probe the properties of small-scale b. We then apply our results to observations of the Small and Large Magellanic Clouds (SMC and LMC). First, using Gaussian random b, we show that the characteristic scale, where the RM structure function flattens is approximately equal to the correlation length of b. We also show that computing the RM structure function with a higher-order stencil (more than the commonly-used two-point stencil) is necessary to accurately estimate the slope of the structure function. Then, using Gaussian random b and lognormal ne with known power spectra, we derive an empirical relationship between the slope of the power spectrum of b, ne, and RM. We apply these results to the SMC and LMC and estimate the following properties of small-scale b: correlation length (160 ± 21 pc for the SMC and 87 ± 17 pc for the LMC), strength (14 ± 2 $\mu {\rm G}$ for the SMC and 15 ± 3 $\mu {\rm G}$ for the LMC), and slope of the magnetic power spectrum (−1.3 ± 0.4 for the SMC and −1.6 ± 0.1 for the LMC). We also find that ne is practically constant over the estimated b correlation scales.

Multispacecraft Analysis of the Properties of Magnetohydrodynamic Fluctuations in Sub-Alfvénic Solar Wind Turbulence at 1 au

We present observations of three-dimensional magnetic power spectra in wavevector space to investigate the anisotropy and scalings of sub-Alfvénic solar wind turbulence at magnetohydrodynamic (MHD) scale using the Magnetospheric Multiscale spacecraft. The magnetic power distributions are organized in a new coordinate determined by wavevectors () and background magnetic field () in Fourier space. This study utilizes two approaches to determine wavevectors: the singular value decomposition method and multispacecraft timing analysis. The combination of the two methods allows an examination of the properties of magnetic field fluctuations in terms of mode compositions without any spatiotemporal hypothesis. Observations show that fluctuations (δ B ⊥1) in the direction perpendicular to and prominently cascade perpendicular to , and such anisotropy increases with wavenumbers. The reduced power spectra of δ B ⊥1 follow Goldreich–Sridhar scalings: and . In contrast, fluctuations within the plane show isotropic behaviors: perpendicular power distributions are approximately the same as parallel distributions. The reduced power spectra of fluctuations within the plane follow the scalings and . Comparing frequency–wavevector spectra with theoretical dispersion relations of MHD modes, we find that δ B ⊥1 are probably associated with Alfvén modes. On the other hand, magnetic field fluctuations within the plane more likely originate from fast modes based on their isotropic behaviors. The observations of anisotropy and scalings of different magnetic field components are consistent with the predictions of current compressible MHD theory. Moreover, for the Alfvénic component, the ratio of cascading time to the wave period is found to be a factor of a few, consistent with critical balance in the strong turbulence regime. These results are valuable for further studies of energy compositions of plasma turbulence and their effects on energetic particle transport.

Patches of Magnetic Switchbacks and Their Origins

Parker Solar Probe (PSP) has shown that the solar wind in the inner heliosphere is characterized by the quasi omnipresence of magnetic switchbacks (“switchback” hereinafter), local backward bends of magnetic field lines. Switchbacks also tend to come in patches, with a large-scale modulation that appears to have a spatial scale size comparable to supergranulation on the Sun. Here we inspect data from the first 10 encounters of PSP focusing on different time intervals when clear switchback patches were observed by PSP. We show that the switchbacks modulation, on a timescale of several hours, seems to be independent of whether PSP is near perihelion, when it rapidly traverses large swaths of longitude remaining at the same heliocentric distance, or near the radial-scan part of its orbit, when PSP hovers over the same longitude on the Sun while rapidly moving radially inwards or outwards. This implies that switchback patches must also have an intrinsically temporal modulation most probably originating at the Sun. Between two consecutive patches, the magnetic field is usually very quiescent with weak fluctuations. We compare various parameters between the quiescent intervals and the switchback intervals. The results show that the quiescent intervals are typically less Alfvénic than switchback intervals, and the magnetic power spectrum is usually shallower in quiescent intervals. We propose that the temporal modulation of switchback patches may be related to the “breathing” of emerging flux that appears in images as the formation of “bubbles” below prominences in the Hinode/SOT observations.

Power spectra of the Sun’s large-scale magnetic field during solar cycles 23 and 24

AbstractThe magnetic power spectrum analysis provides an effective way to understand the observed distribution of the photospheric magnetic fields and their interaction with plasma motions. We aim to investigate the power spectra using spherical harmonic decomposition of SOHO/MDI and SDO/HMI synoptic magnetograms for cycles 23 and 24. We find that the calibration factor between MDI and HMI power spectral density is spatial scale-dependent. The magnetic power spectra show two peaks at the AR scale (l≈30) and supergranular scale (l≈120). The power law indices between these show a good anti-correlation with the amplitude of magnetic activity.

On the Small-scale Turbulent Dynamo in the Intracluster Medium: A Comparison to Dynamo Theory* * Released on August, 19th, 2021.

We present non-radiative, cosmological zoom-in simulations of galaxy-cluster formation with magnetic fields and (anisotropic) thermal conduction of one massive galaxy cluster with M vir ∼ 2 × 1015 M ⊙ at z ∼ 0. We run the cluster on three resolution levels (1×, 10×, 25×), starting with an effective mass resolution of 2 × 108 M ⊙, subsequently increasing the particle number to reach 4 × 106 M ⊙. The maximum spatial resolution obtained in the simulations is limited by the gravitational softening reaching ϵ = 1.0 kpc at the highest resolution level, allowing one to resolve the hierarchical assembly of the structures in fine detail. All simulations presented are carried out with the SPMHD code gadget3 with an updated SPMHD prescription. The primary focus of this paper is to investigate magnetic field amplification in the intracluster medium. We show that the main amplification mechanism is the small-scale turbulent dynamo in the limit of reconnection diffusion. In our two highest resolution models we start to resolve the magnetic field amplification driven by the dynamo and we explicitly quantify this with the magnetic power spectra and the curvature of the magnetic field lines, consistent with dynamo theory. Furthermore, we investigate the ∇ · B = 0 constraint within our simulations and show that we achieve comparable results to state-of-the-art AMR or moving-mesh techniques, used in codes such as enzo and arepo. Our results show for the first time in a cosmological simulation of a galaxy cluster that dynamo action can be resolved with modern numerical Lagrangian magnetohydrodynamic methods, a study that is currently missing in the literature.

Quantum control of two critically dressed spin-1/2 species in magnetic fluctuations

The neutron electric dipole moment experiment at the Spallation Neutron Source (nEDM@SNS experiment) proposes to measure the nEDM using the spin-dependent capture cross section of neutrons on $^{3}\mathrm{He}$. The critical dressing mode of this experiment uses an oscillating magnetic field to dress the gyromagnetic ratios of neutrons and $^{3}\mathrm{He}$ to the same value. While this technique grants increased sensitivity to the nEDM by improving the signal-to-noise ratio, this mode of measurement also introduces additional noise from the power supply used to drive the dressing field. This can lead to randomly fluctuating magnetic fields which cause the spins of neutrons and $^{3}\mathrm{He}$ to drift apart over time. Here we use second-order time-dependent perturbation theory to compute relaxation and frequency shifts due to fluctuations in the dressing field in terms of the magnetic field noise power spectrum and compare these calculations to numerical solutions obtained by integrating the Bloch equations. We then use these results to develop mitigation strategies for this type of noise. Furthermore, we report on spin dressing modulation techniques that significantly amplify coherence times for the critically dressed system, and attempt to quantify the achievable coherence time.

Fundamental scales in the kinematic phase of the turbulent dynamo

ABSTRACT The turbulent dynamo is a powerful mechanism that converts turbulent kinetic energy to magnetic energy. A key question regarding the magnetic field amplification by turbulence, is, on what scale, kp, do magnetic fields become most concentrated? There has been some disagreement about whether kp is controlled by the viscous scale, kν (where turbulent kinetic energy dissipates), or the resistive scale, kη (where magnetic fields dissipate). Here, we use direct numerical simulations of magnetohydrodynamic turbulence to measure characteristic scales in the kinematic phase of the turbulent dynamo. We run 104-simulations with hydrodynamic Reynolds numbers of 10 ≤ Re ≤ 3600, and magnetic Reynolds numbers of 270 ≤ Rm ≤ 4000, to explore the dependence of kp on kν and kη. Using physically motivated models for the kinetic and magnetic energy spectra, we measure kν, kη, and kp, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations $k_\nu = (0.025^{+0.005}_{-0.006})\, k_\text{turb}\, \mbox{Re}^{3/4}$ and $k_\eta = (0.88^{+0.21}_{-0.23})\, k_\nu \, \mbox{Pm}^{1/2}$, where kturb is the turbulence driving wavenumber and Pm = Rm/Re is the magnetic Prandtl number. We demonstrate that the principle dependence of kp is on kη. For plasmas, where Re ≳ 100, we find that $k_p= (1.2_{-0.2}^{+0.2})\, k_\eta$, with the proportionality constant related to the power-law ‘Kazantsev’ exponent of the magnetic power spectrum. Throughout this study, we find a dichotomy in the fundamental properties of the dynamo where Re &amp;gt; 100, compared to Re &amp;lt; 100. We report a minimum critical hydrodynamic Reynolds number, Recrit = 100 for bonafide turbulent dynamo action.

Measurement and suppression of magnetic field noise of trapped ion qubit

Magnetic field noise is an important factor causing quantum decoherence in quantum systems. In order to suppress the decoherence effect, magnetic field noise needs to be properly measured and controlled. Magnetic field noise power spectrum measurement using a single trapped ion based quantum spectrum analyzer is a very effective way. In this paper, the magnetic field noise measurement based on dynamic decoupling technique is analyzed theoretically. Furthermore, we use magnetically insensitive transition to measure the magnetic field noise, which has the potential to measure stronger magnetic field noise and speed up the measurement process. In our experiment, we suppress the magnetic field noise by using active feedback control and passive compensation, where the required passive compensation amplitude is obtained by measuring the magnetic field noise spectrum of a single 25Mg+ ion. With the magnetic field noise suppressed, the expected contribution of the magnetic field noise to the stability of the 25Mg+–27Al+ ion optical clock can be decreased from to .

A depolarizing H I tidal tail in the western lobe of Fornax A

Recent MeerKAT neutral hydrogen (H I) observations of Fornax A reveal tidal material intersecting in projection the western lobe of this radio galaxy. We found a spatial coincidence between the northern H Itail and a depolarized structure observed for the first time with the Australian Square Kilometre Array Pathfinder (ASKAP) at 1.2 GHz. We analyzed the properties of the rotation measure (RM) image obtained with ASKAP data at the location of the H Itail and in its neighborhood. We modeled the observed RM structure function to investigate the magnetic field power spectrum at the location of the H Itail and in a nearby control region. We found that the observed RM, in the control region and in a region enclosing the H Itail, cannot be due to the intracluster Faraday screen caused by the Fornax cluster. An intragroup magnetized medium with a central magnetic field strength of 18.5 μG can explain the control region RM, but it is clear that there is an excess in correspondence with the H Itail region. We evaluated several scenarios in which the H Itail is either in the lobe foreground or embedded in the lobe. We determined a magnetic field strength on the order of ∼9.5−11 μG in the H Itail, a value consistent with constraints derived from narrowband Hαimaging of the ionized gas. The spatial coincidence between H Itail and depolarization analyzed in this paper could be the first observed evidence of a magnetic field that either has passed through a radio galaxy lobe or has survived the lobe expansion.

High-latitude Observations of Inertial-range Turbulence by the Ulysses Spacecraft During the Solar Minimum of 1993–96

Abstract We have examined Ulysses magnetic field measurements for the years 1993 through 1996 as the spacecraft moved sunward from 5 au at high southern latitudes, passing through perihelion during the first fast-latitude scan to achieve high northern latitudes, and finally returning to 5 au. These years represent near-solar-minimum activity, providing a clear measure of high-latitude solar-wind turbulence. We apply a series of tests to the data, examining both the magnetic variance anisotropy and the underlying wavevector anisotropy, finding them to be consistent with past 1 au observations. The variance anisotropy depends upon both the thermal proton temperature parameter and the amplitude of the magnetic power spectrum, while the underlying wavevector anisotropy is dominated by the component perpendicular to the mean magnetic field. We also examine the amplitude of the magnetic power spectrum as well as the associated turbulent transport of energy to small scales that results in the heating of the thermal plasma. The measured turbulence is found to be stronger than that seen at low latitudes by the Voyager spacecraft as it traverses the distance from 1 to 5 au during the years approaching solar maximum. If the high- and low-latitude sources are comparable, this would indicate that while the heating processes are active in both regions, the turbulence has had less decay time in the transport of energy to small scales. Alternatively, it may also be that the high-latitude source is stronger.

Hilltop Inflation and Generation of Helical Magnetic Field

Primordial magnetic field generated in the inflationary era can act as a viable source for the present day intergalactic magnetic field of sufficient strength. We present a fundamental origin for such a primordial generation of the magnetic field, namely through anomaly cancellation of U(1) gauge field in quantum electrodynamics in the context of hilltop inflation. We have analysed at length the power spectrum of the magnetic field, thus generated, which turns out to be helical in nature. We have also found that magnetic power spectrum has significant scale-dependence giving rise to a non-trivial magnetic spectral index, a key feature of this model. Interestingly, there exists a large parameter space, where magnetic field of significant strength can be produced.

Large-scale gauge spectra and pseudoscalar couplings

It is shown that the slopes of the superhorizon hypermagnetic spectra produced by the variation of the gauge couplings are practically unaffected by the relative strength of the parity-breaking terms. A new method is proposed for the estimate of the gauge power spectra in the presence of pseudoscalar interactions during inflation. To corroborate the general results, various concrete examples are explicitly analyzed. Since the large-scale gauge spectra also determine the late-time magnetic fields, it turns out that the pseudoscalar contributions have little impact on the magnetogenesis requirement. Conversely the parity-breaking terms crucially affect the gyrotropic spectra that may seed, in certain models, the baryon asymmetry of the Universe. In the most interesting regions of the parameter space, the modes reentering prior to symmetry breaking lead to a sufficiently large baryon asymmetry while the magnetic power spectra associated with the modes reentering after symmetry breaking may even be of the order of a few hundredths of a nG over typical length scales comparable with the Mpc prior to the collapse of the protogalaxy. From the viewpoint of the effective field theory description of magnetogenesis scenarios, these considerations hold generically for the whole class of inflationary models where the inflaton is not constrained by any underlying symmetry.

A Novel Machine Learning Technique to Identify and Categorize Plasma Waves in Spacecraft Measurements

AbstractThe available magnetic field data from the terrestrial magnetosphere, solar wind and planetary magnetospheres exceeds over hours. Identifying plasma waves in these large data sets is a time consuming and tedious process. In this Paper, we propose a solution to this problem. We demonstrate how self‐organizing maps (SOMs) can be used for rapid data reduction and identification of plasma waves in large data sets. We use 72,000 fluxgate and 110,000 search coil magnetic field power spectra from the Magnetospheric Multiscale Mission () and show how the SOM sorts the power spectra into groups based on their shape. Organizing the data in this way makes it very straightforward to identify power spectra with similar properties and therefore this technique greatly reduces the need for manual inspection of the data. We suggest that SOMs offer a time effective and robust technique, which can significantly accelerate the processing of magnetic field data and discovery of new wave forms.

Spacetime Hall-MHD Turbulence at Sub-ion Scales: Structures or Waves?

Abstract Spatiotemporal properties of two-dimensional (2D) Hall-magnetohydrodynamic (MHD) turbulence at intermediate plasma β = 2 are studied by means of Fast Iterative Filtering (FIF), a new technique for the decomposition of nonstationary nonlinear signals. Results show that the magnetic energy at sub-ion scales is concentrated in perturbations with frequencies smaller than the ion-cyclotron (IC) frequency and with polarization properties that are incompatible with both kinetic Alfvén waves (KAWs) and IC waves. At higher frequencies, we clearly identify signatures of both whistler waves and KAWs; however, their energetic contribution to the magnetic power spectrum is negligible. We conclude that the dynamics of 2D Hall-MHD turbulence at sub-ion scales is mainly driven by localized intermittent structures, with no significant contribution of wavelike fluctuations.