Magnetic Field Spectrum Research Articles

Precise numerical estimation of the magnetic field generated around recombination

We investigate the generation of magnetic fields from non-linear effects around recombination. As tight-coupling is gradually lost when approaching $z\simeq 1100$, the velocity difference between photons and baryons starts to increase, leading to an increasing Compton drag of the photons on the electrons. The protons are then forced to follow the electrons due to the electric field created by the charge displacement; the same field, following Maxwell's laws, eventually induces a magnetic field on cosmological scales. Since scalar perturbations do not generate any magnetic field as they are curl-free, one has to resort to second-order perturbation theory to compute the magnetic field generated by this effect. We reinvestigate this problem numerically using the powerful second-order Boltzmann code SONG. We show that: i) all previous studies do not have a high enough angular resolution to reach a precise and consistent estimation of the magnetic field spectrum; ii) the magnetic field is generated up to $z\simeq 10$; iii) it is in practice impossible to compute the magnetic field with a Boltzmann code for scales smaller than $1\,{\rm Mpc}$. Finally we confirm that for scales of a few ${\rm Mpc}$, this magnetic field is of order $2\times 10^{-29}{\rm G}$, many orders of magnitude smaller than what is currently observed on intergalactic scales.

Study of electric and magnetic field fluctuations from lower hybrid drift instability waves in the terrestrial magnetotail with the fully kinetic, semi-implicit, adaptive multi level multi domain method

The newly developed fully kinetic, semi-implicit, adaptive multi-level multi-domain (MLMD) method is used to simulate, at realistic mass ratio, the development of the lower hybrid drift instability (LHDI) in the terrestrial magnetotail over a large wavenumber range and at a low computational cost. The power spectra of the perpendicular electric field and of the fluctuations of the parallel magnetic field are studied at wavenumbers and times that allow to appreciate the onset of the electrostatic and electromagnetic LHDI branches and of the kink instability. The coupling between electric and magnetic field fluctuations observed by Norgren et al. [“Lower hybrid drift waves: Space observations,” Phys. Rev. Lett. 109, 055001 (2012)] for high wavenumber LHDI waves in the terrestrial magnetotail is verified. In the MLMD simulations presented, a domain (“coarse grid”) is simulated with low resolution. A small fraction of the entire domain is then simulated with higher resolution also (“refined grid”) to capture smaller scale, higher frequency processes. Initially, the MLMD method is validated for LHDI simulations. MLMD simulations with different levels of grid refinement are validated against the standard semi-implicit particle in cell simulations of domains corresponding to both the coarse and the refined grid. Precious information regarding the applicability of the MLMD method to turbulence simulations is derived. The power spectra of MLMD simulations done with different levels of refinements are then compared. They consistently show a break in the magnetic field spectra at k⊥di∼30, with di the ion skin depth and k⊥ the perpendicular wavenumber. The break is observed at early simulated times, Ωcit<6, with Ωci the ion cyclotron frequency. It is due to the initial decoupling of electric and magnetic field fluctuations at intermediate and low wavenumbers, before the development of the electromagnetic LHDI branch. Evidence of coupling between electric and magnetic field fluctuations in the wavenumber range where the fast and slow LHDI branches develop is then provided for a cluster magnetotail crossing.

Fast acquisition of high-resolution 2D NMR spectroscopy in inhomogeneous magnetic fields

High-resolution nuclear magnetic resonance (NMR) spectroscopy plays an important role in chemical and biological analyses. In this study, we combine the J-coupling coherence transfer module with the echo-train acquisition technique for fast acquisition of high-resolution 2D NMR spectra in magnetic fields with unknown spatial variations. The proposed method shows satisfactory performance on a 5mM ethyl 3-bromopropionate sample, under a 5-kHz (10ppm at 11.7T) B0 inhomogeneous field, as well as under varying degrees of pulse-flip-angle deviations. Moreover, a simulative ex situ NMR measurement is also conducted to show the effectiveness of the proposed pulse sequence.

A 4 T HTS Magnetic Field Generator, Conduction Cooled, for Neutron Physics Spectrometry

This paper is concerned with the analysis of thermal and magnetic design of a high-uniformity magnetic field (HUMF) electromagnet using high temperature superconducting (HTS) coils in Helmholtz arrangement, for nuclear physics experiments. The sample, exposed to a neutron pulse, is placed in the HUMF, and detectors are registering the emerging radiation. The 4-T dipole HUMF electromagnet system is conduction cooled using a closed-cycle Gifford-McMahon cryocooler. A second cryocooler is used to keep the sample temperature in the 4.2-300 K range. The Helmholtz coils are made of high temperature superconductor (HTS) tape of YBCO type, and are mounted in a special-shaped cryostat. Numerical experiments are performed to assess the magnetic field uniformity. This paper relies on a 3-D computer-aided design model of the electromagnet prototype. They unveil the magnetic field spectrum and the heat paths within the aggregate structure of the magnet system. The "warm” channel crosses the magnet axially and the HTS field winding must be kept within safe temperature limits or the HTS may exit the superconductive state. Therefore, cryocooling is used to remove the heat influx from the ambient. The numerical modeling of the heat transfer phenomena inside the magnet system reveals the temperature distribution and thermal loads for cryocoolers.

Theory of electron spin resonance in bulk topological insulators Bi2Se3, Bi2Te3 and Sb2Te3

We report a theoretical study of electron spin resonance in bulk topological insulators, such as Bi2Se3, Bi2Te3 and Sb2Te3. Using the effective four-band model, we find the electron energy spectrum in a static magnetic field and determine the response to electric and magnetic dipole perturbations, represented by oscillating electric and magnetic fields perpendicular to the static field. We determine the associated selection rules and calculate the absorption spectra. This enables us to separate the effective orbital and spin degrees of freedom and to determine the effective g factors for electrons and holes.

Low-Temperature Studies of CuFe $$_{2}$$ 2 S $$_{3}$$ 3 and CuFeS $$_{2}$$ 2 by $$^{63,65}$$ 63 , 65 Cu NMR in the Internal Magnetic Field

The resonance $$^{63,65}$$ Cu NMR spectra in the internal magnetic field in cubanite CuFe $$_{2}$$ S $$_{3}$$ and chalcopyrite CuFeS $$_{2}$$ were studied experimentally at 77 K. Using a cluster approach, ab initio evaluation of the electric field gradient (EFG) at the nuclei of copper in both compounds was performed. The calculations were carried out by the self-consistent restricted method of Hartree–Fock with open shells (SCF-LCAO-ROHF). The largest clusters for which calculations were made had a formula of Cu $$_{7}$$ Fe $$_{14}$$ S $$_{29}^\mathrm{n}$$ for cubanite and Cu $$_{9}$$ Fe $$_{10}$$ S $$_{28}^\mathrm{n}$$ for chalcopyrite, where n is the cluster charge. The best-fit values of the quadrupole parameters (quadrupole frequency $$\nu _\mathrm{Q}$$ and the asymmetry parameter of the EFG tensor $$\eta $$ )—determined experimentally ( $$\nu _\mathrm{Q} \approx $$ 7.30 MHz and $$\eta \approx $$ 0.82) and by calculation ( $$\nu _\mathrm{Q} \approx $$ 7.38 MHz and $$\eta \approx $$ 0.87)—were obtained for a cluster Cu $$_{7}$$ Fe $$_{14}$$ S $$_{29}^{10}$$ for cubanite. Similarly, the best-fit values of the quadrupole parameters—determined experimentally ( $$\nu _\mathrm{Q} \approx $$ 1.29 MHz and $$\eta \approx $$ 0.34) and by calculation ( $$\nu _\mathrm{Q} \approx $$ 1.40 MHz and $$\eta \approx $$ 0.50)—were obtained for a cluster Cu $$_{9}$$ Fe $$_{10}$$ S $$_{28}^{-4}$$ for chalcopyrite. For these clusters, maps of the electron density distribution in the neighborhood of quadrupole nucleus of copper were built. Based on the analysis of the resulting electron density distribution, it is supposed that the bond in these compounds is not quite covalent. Evaluations of the hyperfine interaction constants were made and maps of the spin density distribution in the neighborhood of quadrupole nucleus of copper were built. The energy level diagram calculated in the high-spin ROHF approximation defined chalcopyrite as a compound with a very narrow LUMO–HOMO gap rather well and is consistent with the notion of this compound as a semiconductor.

A heteronuclear intermolecular single-quantum coherence scheme for high-resolution 2D J-resolved 1H NMR spectra in inhomogeneous magnetic fields

ABSTRACTBased on heteronuclear intermolecular single-quantum coherences between proton (1H) and quadrupolar nuclei (i.e. deuterium 2H), a three-dimensional nuclear magnetic resonance (NMR) pulse sequence is proposed for recovering high-resolution two-dimensional J-resolved NMR spectra from samples mixed with a deuterated solvent in the presence of large magnetic field inhomogeneities. Benefitting from excitation of spins via two different radio frequency (RF) transmit channels, this sequence is suitable for applications in randomly large inhomogeneous fields and the solvent suppression generally required in homonuclear intermolecular multiple-quantum coherence approaches is no longer necessary. Systematic theoretical analyses are given based on the distant dipolar field treatment. Experiment on a sample of corn oil in deuterated acetone and ethyl 3-bromopropionate and acetone dissolved in DMSO-d6 in a deshimmed field with severe inhomogeneous broadening is performed to show the feasibility and applicability of this sequence.

Spatially resolved spectroscopy using tapered stripline NMR

Magnetic field B0 gradients are essential in modern Nuclear Magnetic Resonance spectroscopy and imaging. Although RF/B1 gradients can be used to fulfill a similar role, this is not used in common practice because of practical limitations in the design of B1 gradient coils. Here we present a new method to create B1 gradients using stripline RF coils. The conductor-width of a stripline NMR chip and the strength of its radiofrequency field are correlated, so a stripline chip can be tapered to produce any arbitrary shaped B1 field gradient. Here we show the characterization of this tapered stripline configuration and demonstrate three applications: magnetic resonance imaging on samples with nL–μL volumes, reaction monitoring of fast chemical reactions (10−2–101s) and the compensation of B0 field gradients to obtain high-resolution spectra in inhomogeneous magnetic fields.

Ionopause‐like density gradients in the Martian ionosphere: A first look with MAVEN

AbstractFor unmagnetized planets, the top of the ionosphere is often marked by a sharp change in electron density and other plasma properties, called an ionopause. Here we present a statistical study of dayside ionopause‐like density gradients observed in 54% of ion density profiles from the Mars Atmosphere and Volatile EvolutioN (MAVEN) mission spacecraft at Mars. Prior studies of the Martian ionopause have lacked simultaneous comprehensive measurements of plasma and magnetic field properties. Therefore, we use MAVEN observations of the electron density, magnetic field, and ion and electron energy spectra to study the factors that influence properties of the ionopause. On average, profiles with an ionopause are accompanied by a higher energy flux of protons at high altitudes and stronger magnetic field at low altitude than profiles without an ionopause. At altitudes above ~300 km, the O+/O2+ ratio is significantly larger for profiles with an ionopause than those without an ionopause. These findings enhance our understanding of this important plasma boundary at Mars.

Cosmic ray transport and anisotropies to high energies

Abstract. A model is introduced, in which the irregularity spectrum of the Galactic magnetic field beyond the dissipation length scale is first a Kolmogorov spectrum k-5/3 at small scales λ = 2 π/k with k the wave-number, then a saturation spectrum k-1, and finally a shock-dominated spectrum k-2 mostly in the halo/wind outside the Cosmic Ray disk. In an isotropic approximation such a model is consistent with the Interstellar Medium (ISM) data. With this model we discuss the Galactic Cosmic Ray (GCR) spectrum, as well as the extragalactic Ultra High Energy Cosmic Rays (UHECRs), their chemical abundances and anisotropies. UHECRs may include a proton component from many radio galaxies integrated over vast distances, visible already below 3 EeV.

Gamma-ray observations of blazars and the intergalactic magnetic field spectrum

Very-high energy observations of blazars can be used to constrain the strength of the intergalactic magnetic field. A simplifying assumption which is often made is that of a magnetic field of constant strength composed by randomly oriented and identical cells. In this paper, we demonstrate that a more realistic description of the structure of the intergalactic magnetic field is indeed needed. If such a description is adopted, the observational bounds on the field strength are significantly affected in the limit of short field correlation lengths: in particular, they acquire a dependence on the magnetic field power spectrum. In the case of intergalactic magnetic fields which are generated causally, for which the magnetic field large scale spectral index is $n_B\geq 2$ and even, the observational lower bound becomes more constraining by about a factor 3. If instead $-3<n_B<-2$, the lower bound is significantly relaxed. Such magnetic fields with very red spectra can in principle be produced during inflation, but remain up to now speculative.

Magnetic field spectrum at cosmological recombination revisited

If vector type perturbations are present in the primordial plasma before recombination, the generation of magnetic fields is known to be inevitable through the Harrison mechanism. In the context of the standard cosmological perturbation theory, nonlinear couplings of first-order scalar perturbations create second-order vector perturbations, which generate magnetic fields. Here we reinvestigate the generation of magnetic fields at second-order in cosmological perturbations on the basis of our previous study, and extend it by newly taking into account the time evolution of purely second-order vector perturbations with a newly developed second-order Boltzmann code. We confirm that the amplitude of magnetic fields from the product-terms of the first-order scalar modes is consistent with the result in our previous study. However, we find, both numerically and analytically, that the magnetic fields from the purely second-order vector perturbations partially cancel out the magnetic fields from one of the product-terms of the first-order scalar modes, in the tight coupling regime in the radiation dominated era. Therefore, the amplitude of the magnetic fields on small scales, $k\ensuremath{\gtrsim}10\text{ }\text{ }h{\mathrm{Mpc}}^{\ensuremath{-}1}$, is smaller than the previous estimates. The amplitude of the generated magnetic fields at cosmological recombination is about ${B}_{\text{rec}}=5.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\text{ }\text{ }\text{Gauss}$ on $k=5.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}1}\text{ }\text{ }h{\mathrm{Mpc}}^{\ensuremath{-}1}$. Finally, we discuss the reason for the discrepancies that exist in estimates of the amplitude of magnetic fields among other authors.

Helical cosmological magnetic fields from extra-dimensions

We study the inflationary generation of helical cosmological magnetic fields in a higher-dimensional generalization of the electromagnetic theory. For this purpose, we also include a parity breaking piece to the electromagnetic action. The evolution of extra-dimensional scale factor allows the breaking of conformal invariance of the effective electromagnetic action in $1+3$ dimensions required for such generation. Analytical solutions for the vector potential can be obtained in terms of Coulomb wave-functions for some special cases. We also present numerical solutions for the vector potential evolution in more general cases. In the presence of a higher-dimensional cosmological constant there exist solutions for the scale factors in which both normal and extra dimensional space either inflate or deflate simultaneously with the same rate. In such a scenario, with the number of extra dimensions $D=4$, a scale invariant spectrum of helical magnetic field is obtained. The net helicity arises, as one helical mode comes to dominate over the other at the superhorizon scales. A magnetic field strength of the order of $10^{-9}$ $G$ can be obtained for the inflationary scale $H\simeq 10^{-3}$ $M_{pl}$. Weaker fields will be generated for lower scales of inflation. Magnetic fields generated in this model respects the bounds on magnetic fields by Planck and $\gamma$-ray observations (i.e. $10^{-16}$ $G$ $<$ $B_{obs}<3.4\times 10^{-9}$ $G$).

Intergalactic magnetic field spectra from diffuse gamma-rays

Non-vanishing parity-odd correlators of gamma ray arrival directions observed by Fermi-LAT indicate the existence of a helical intergalactic magnetic field (Tashiro et al.2013). We successfully test this hypothesis using more stringent cuts of the data, Monte Carlo simulations with Fermi-LAT time exposure information, separate analyses for the northern and southern galactic hemispheres, and confirm predictions made in Tashiro & Vachaspati (2014). With some further technical assumptions, we show how to reconstruct the magnetic helicity spectrum from the parity-odd correlators.

Line broadening interference for high-resolution nuclear magnetic resonance spectra under inhomogeneous magnetic fields.

Nuclear magnetic resonance spectroscopy serves as an important tool for analyzing chemicals and biological metabolites. However, its performance is subject to the magnetic-field homogeneity. Under inhomogeneous fields, peaks are broadened to overlap each other, introducing difficulties for assignments. Here, we propose a method termed as line broadening interference (LBI) to provide high-resolution information under inhomogeneous magnetic fields by employing certain gradients in the indirect dimension to interfere the magnetic-field inhomogeneity. The conventional spectral-line broadening is thus interfered to be non-diagonal, avoiding the overlapping among adjacent resonances. Furthermore, an inhomogeneity correction algorithm is developed based on pattern recognition to recover the high-resolution information from LBI spectra. Theoretical deductions are performed to offer systematic and detailed analyses on the proposed method. Moreover, experiments are conducted to prove the feasibility of the proposed method for yielding high-resolution spectra in inhomogeneous magnetic fields.

Primordial magnetic fields from self-ordering scalar fields

A symmetry-breaking phase transition in the early universe could have led to the formation of cosmic defects. Because these defects dynamically excite not only scalar and tensor type cosmological perturbations but also vector type ones, they may serve as a source of primordial magnetic fields. In this study, we calculate the time evolution and the spectrum of magnetic fields that are generated by a type of cosmic defects, called global textures, using the non-linear sigma (NLSM) model. Based on the standard cosmological perturbation theory, we show, both analytically and numerically, that a vector-mode relative velocity between photon and baryon fluids is induced by textures, which inevitably leads to the generation of magnetic fields over a wide range of scales. We find that the amplitude of the magnetic fields is given by B∼10−9((1+z)/103)−2.5(v/mpl)2(k/Mpc−1)3.5/√N Gauss in the radiation dominated era for k≲ 1 Mpc−1, with v being the vacuum expectation value of the O(N) symmetric scalar fields. By extrapolating our numerical result toward smaller scales, we expect that B∼ 10−14.5((1+z)/103)1/2(v/mpl)2(k/Mpc−1)1/2/√N Gauss on scales of k≳ 1 Mpc−1 at redshift 0z≳ 110. This might be a seed of the magnetic fields observed on large scales today.

Studying the Effect of the Local Thunderstorm Cells on the Background ULF Magnetic Noise Parameter Spectra

We study the effect of the masking factor from the local thunderstorm cells on ULF magnetic field spectra with the inhomogeneous electron-density structures existing in the local ionosphere (ionospheric and lower ionospheric Alfven resonators). Using an original data-processing technique for recording of horizontal magnetic components at the midlatitude reception point Novaya Zhizn’, we have examined the contribution of the sources located at different distances from the reception point to the formation of the background noise spectra. The ULF signal processing technique permitted us to reduce the pulse component of magnetic noise in amplitude above a certain threshold and thus rule out the effect of a local thunderstorm activity. Frequency dependences of the azimuthal angle of the principal axis of the magnetic noise polarization ellipse are also analyzed. It is shown that the presence of the lower ionospheric Alfven resonator leads to a nonmonotonic dependence of the azimuthal angle on the frequency. It was found that the local thunderstorms within 60–80 km from the reception point completely mask the manifestation of the lower ionospheric Alfven resonator in the ULF noise polarization parameters. To spot the local thunderstorm cells, we used the data from the meteorological radar facility MRL-4 in Nizhny Novgorod.

A statistical spatial power spectrum of the Earth's lithospheric magnetic field

A statistical spatial power spectrum of the Earth's lithospheric magnetic field

Landau quantization in graphene monolayer, Bernal bilayer, and Bernal trilayer on graphite surface

Electronic properties of surface areas decoupled from graphite are studied using scanning tunnelling microscopy and spectroscopy. We show that it is possible to identify decoupled graphene monolayer, Bernal bilayer, and Bernal trilayer on graphite surface according to their tunnelling spectra in high magnetic field. The decoupled monolayer and bilayer exhibit Landau quantization of massless and massive Dirac fermions, respectively. The substrate generates a sizable band gap, ~35 meV, in the Bernal bilayer, therefore, the eightfold degenerate Landau level at the charge neutrality point is split into two valley-polarized quartets polarized on each layer. In the decoupled Bernal trilayer, we find that both massless and massive Dirac fermions coexist and its low-energy band structure can be described quite well by taking into account only the nearest-neighbor intra- and interlayer hopping parameters. A strong correlation between the Fermi velocity of the massless Dirac fermions and the effective mass of the massive Dirac fermions is observed in the trilayer. Our result demonstrates that the surface of graphite provides a natural ideal platform to probe the electronic spectra of graphene layers.

Source of seed fluctuations for electromagnetic ion cyclotron waves in Earth’s magnetosphere

We consider a nonlinear wave energy cascade from the low frequency range into the higher frequency domain of electromagnetic ion cyclotron (EMIC) wave generation as a possible source of seed fluctuations for EMIC wave growth due to the ion cyclotron instability in Earth’s magnetosphere. The presented theoretical analysis shows that energy cascade from the Pc 4–5 frequency range (2–22mHz) into the range of Pc 1–2 pulsations (0.1–5Hz), i.e. into the frequency range of EMIC waves, is able to supply the needed level of seed fluctuations that guarantees growth of EMIC waves up to the observable level during one pass through the near equatorial region where the ion cyclotron instability takes place. We also analyze the magnetic field data from the Polar and Van Allen Probes spacecraft to test the suggested nonlinear mechanism. In this initial study we restrict our analysis to magnetic fluctuation spectra only. We do not analyze the third-order structure function, but judge whether a nonlinear energy cascade is present or whether it is not by only analyzing the appearance of power-law distributions in the low-frequency part of the magnetic field spectra. While the power-law spectrum alone does not guarantee that a nonlinear cascade is present, the power-law distribution is a strong indication of the possible development of a nonlinear cascade. Our analysis shows that a nonlinear energy cascade is indeed observed in both the outer and inner magnetosphere data, and EMIC waves are growing from this nonthermal background. All the analyzed data are in good agreement with the theoretical model presented in this study. Overall, the results of this study support a nonlinear energy cascade in Earth’s magnetosphere as a mechanism which is responsible for supplying seed fluctuating energy in the higher frequency domain where EMIC waves grow due to the ion cyclotron instability.