Magnetic Field Fluctuations Research Articles

Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a large-scale magnetic field

ABSTRACT Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. In this study, we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, $\delta {\boldsymbol{B}}$ , and large-scale, ${\boldsymbol{B}}_0$, fields, ${\left\langle (\delta \mathrm{{\boldsymbol {\mathit {B}}}}\cdot {\mathrm{{\boldsymbol {\mathit {B}}}}_0})^{2} \right\rangle ^{1/2}_{\mathcal {V}}}$. By considering the second moments of the energy balance equations we show that the rms coupling term is in energy equipartition with the volume-averaged turbulent kinetic energy for turbulence with a sub-Alfvénic large-scale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameter-free agreement with time-averaged data from 280 numerical simulations of compressible magnetohydrodynamic (MHD) turbulence. Furthermore, we explore the relation between the turbulent mean field and total Alfvén Mach numbers, and demonstrate that sub-Alfvénic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfvénic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfvénic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetized ISM.

Protected Hybrid Superconducting Qubit in an Array of Gate-Tunable Josephson Interferometers

We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers. The individual interferometers realize effective $\cos2\phi$ elements that exchange `pairs of Cooper pairs' between the superconducting islands when gate-tuned into balance and frustrated by a half flux quantum. If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset charge and magnetic field fluctuations for a sizable window around zero offset charge and half flux quantum. This protection window broadens upon increasing the number of interferometers if the individual elements are balanced. We use an effective spin model to describe the system and show that a quantum phase transition point sets the critical flux value at which protection is destroyed.

Turbulent magnetic field in the H II region Sh 2–27

Context. Magnetic fields in the turbulent interstellar medium (ISM) are a key element in understanding Galactic dynamics, but there are many observational challenges. One useful probe for studying the magnetic field component parallel to the line of sight (LoS) is Faraday rotation of linearly polarized radio synchrotron emission, combined with Hα observations. H ii regions are the perfect laboratories to probe such magnetic fields as they are localized in space, and are well-defined sources often with known distances and measurable electron densities. We chose the H ii region Sharpless 2–27 (Sh 2–27) as it is located at intermediate latitudes (b ~ 23°), meaning that it suffers from little LoS confusion from other sources. In addition, it has a large angular diameter (~10°), enabling us to study the properties of its magnetic field over a wide range of angular scales. Aims. By using a map of the magnetic field strength along the LoS (B‖)for the first time, we investigate the basic statistical properties of the turbulent magnetic field inside Sh 2–27. We study the scaling of the magnetic field fluctuations, compare it to the Kolmogorov scaling, and attempt to find an outer scale of the turbulent magnetic field fluctuations. Methods. We used the polarized radio synchrotron emission data from the S-band Polarization All-Sky Survey (S-PASS) at 2.3 GHz, which allowed us to test the impact of Sh 2–27 on diffuse Galactic synchrotron polarization. We estimated the rotation measure (RM) caused by the H ii region, using the synchrotron polarization angle. We used the Hα data from the Southern Hα Sky Survey Atlas to estimate the free electron density (ne) in the H ii region. Using an ellipsoid model for the shape of Sh 2–27, and with the observed RM and emission measure (EM), we estimated the LoS averaged B‖for each LoS within the ellipsoid. To characterize the turbulent magnetic field fluctuations, we computed a second-order structure function of B‖ We compared the structure function to Kolmogorov turbulence, and to simulations of Gaussian random fields processed in the same way as the observations. Results. We present the first continuous map of B‖ computed using the diffuse polarized radio emission in Sh 2–27. We estimate the median value of ne as 7.3 ± 0.1 cm−3, and the median value of B‖ as −4.5 ± 0.1 µG, which is comparable to the magnetic field strength in diffuse ISM. The slope of the structure function of the estimated B‖-map is found to be slightly steeper than Kolmogorov, consistent with our Gaussian-random-field B‖simulations revealing that an input Kolmogorov slope in the magnetic field results in a somewhat steeper slope in B‖.These results suggest that the lower limit to the outer scale of turbulence is 10 pc in the H ii region, which is comparable to the size of the computation domain. Conclusions. The structure functions of B‖ fluctuations in Sh 2–27 show that the magnetic field fluctuations in this H ii region are consistent with a Kolmogorov-like turbulence. Comparing the observed and simulated B‖ structure functions results in the estimation of a lower limit to the outer scale of the turbulent magnetic field fluctuations of 10 pc, which is limited by the size of the field of view under study. This may indicate that the turbulence probed here could actually be cascading from the larger scales in the ambient medium, associated with the interstellar turbulence in the general ISM, which is illuminated by the presence of Sh 2–27.

Magnetospheric Multiscale Mission Observations of Lower-hybrid Drift Waves in Terrestrial Magnetotail Reconnection with Moderate Guide Field and Asymmetric Plasma Density

Utilizing high-resolution data from the Magnetospheric Multiscale mission, we present new observations of lower-hybrid drift waves (LHDWs) in terrestrial magnetotail reconnection with guide field levels of ∼70% and asymmetric plasma density (N high/N low ∼ 2.5). The LHDWs, driven by lower-hybrid drift instability, were observed in correlation with magnetic field and density gradients at separatrices on both sides of the reconnection current sheet. The properties of the LHDWs at both sides of the separatrices are different: (1) At high-density side separatrices, the LHDWs with wavelength kρ e ∼ 0.41 propagated away from the X-line mainly in the L–M plane; (2) at the low-density side separatrices, the LHDWs with wavelengths kρ e ∼ 0.76 and kρ e ∼ 0.35 propagated mainly along the outflow direction and current sheet normal. It is also found that the perpendicular magnetic field fluctuations were comparable to the parallel component. Wave potential of the LHDWs was 20% ∼ 35% of the electron temperature. The LHDWs contributed to electron demagnetization and energy dissipation. Our study can promote understanding of properties of LHDWs during magnetic reconnection.

Geomagnetic pulsations in 1–4 mHz frequency range (Pc5/Pi3) in the magnetotail at different levels of disturbances in the interplanetary medium

In this paper, we study parameters of geomagnetic pulsations in the 1–4 mHz frequency range (Pc5/Pi3) in the magnetotail, utilizing data obtained by Cluster satellites at different levels of fluctuations in the interplanetary magnetic field (IMF) and the solar wind dynamic pressure in 2016. Particular attention is given to the conditions of “zero” disturbance when amplitudes of fluctuations in the interplanetary medium are smaller compared to their typical values. Both under quiet and disturbed conditions, waves of different spatial scales are recorded, with the occurrence rate of large-scale waves increasing under undisturbed conditions. Amplitudes of the large-scale waves occurring in the magnetotail under low intensity of fluctuations outside the magnetosphere are from few tenths to a few nanoteslas (nT), and their power is approximately equal in longitudinal and transverse components. Presumably, these waves are magnetotail eigen-modes.

Геомагнитные пульсации диапазона 1–4 мГц (Pc5/Pi3) в магнитосферном хвосте при разном уровне возмущенности в межпланетной среде

In this paper, we study parameters of geomagnetic pulsations in the 1–4 mHz frequency range (Pc5/Pi3) in the magnetotail, utilizing data obtained by Cluster satellites at different levels of fluctuations in the interplanetary magnetic field (IMF) and the solar wind dynamic pressure in 2016. Particular attention is given to the conditions of “zero” disturbance when amplitudes of fluctuations in the interplanetary medium are smaller compared to their typical values. Both under quiet and disturbed conditions, waves of different spatial scales are recorded, with the occurrence rate of large-scale waves increasing under undisturbed conditions. Amplitudes of the large-scale waves occurring in the magnetotail under low intensity of fluctuations outside the magnetosphere are from few tenths to a few nanoteslas (nT), and their power is approximately equal in longitudinal and transverse components. Presumably, these waves are magnetotail eigen-modes.

Shape of spectrum of galactic cosmic ray intensity fluctuations

The impact of solar wind plasma on fluxes of galactic cosmic rays (CR) penetrating from the outside into the heliosphere with energies above ~1 GeV leads to temporal variations in the CR intensity in a wide frequency range. Cosmic rays being charged particles, their modulation occurs mainly under impacts of the interplanetary magnetic field.
 It is well known that the observed spectrum of interplanetary magnetic field (IMF) fluctuations in a wide frequency range ν from ~10–7 to ~10 Hz has a pronounced falling character and consists of three sections: energy, inertial, and dissipative. Each of them is described by the power law PIMF(ν)~ν–α, while the IMF spectrum index α increases with increasing frequency. The IMF fluctuations in each of these sections are also characterized by properties that depend on their nature.
 Also known are established links between fluctuation spectra of the interplanetary magnetic field and galactic cosmic rays in the case of modulation of the latter by Alfvén or fast magnetosonic waves. The theory predicts that fluctuation spectra of cosmic rays should also be described by the power law PCR(ν)~ν–γ. However, the results of many years of SHICRA SB RAS research into the nature and properties of cosmic ray intensity fluctuations based on data from neutron monitors at stations with different geomagnetic cut-offs RC from 0.5 to 6.3 GV show that the observed spectrum of fluctuations in galactic cosmic ray intensity in the frequency range above 10–4 Hz becomes flat, i.e. it is similar to white noise. This fact needs to be realized and explained.
 This paper reports the results of research into the shape of the spectrum of galactic cosmic ray intensity fluctuations within a frequency range ν from ~10–6 to ~1 Hz and compares them with model calculations of white noise spectra, using measurement data from the neutron monitor of the Apatity station. A possible physical explanation has been given for the observed shape of the cosmic ray fluctuation spectrum on the basis of the known mechanisms of their modulation in the heliosphere.

О форме спектра флуктуаций интенсивности галактических космических лучей

The impact of solar wind plasma on fluxes of galactic cosmic rays (CR) penetrating from the outside into the heliosphere with energies above ~1 GeV leads to temporal variations in the CR intensity in a wide frequency range. Cosmic rays being charged particles, their modulation occurs mainly under impacts of the interplanetary magnetic field.
 It is well known that the observed spectrum of interplanetary magnetic field (IMF) fluctuations in a wide frequency range ν from ~10–7 to ~10 Hz has a pronounced falling character and consists of three sections: energy, inertial, and dissipative. Each of them is described by the power law PIMF(ν)~ν–α, while the IMF spectrum index α increases with increasing frequency. The IMF fluctuations in each of these sections are also characterized by properties that depend on their nature.
 Also known are established links between fluctuation spectra of the interplanetary magnetic field and galactic cosmic rays in the case of modulation of the latter by Alfvén or fast magnetosonic waves. The theory predicts that fluctuation spectra of cosmic rays should also be described by the power law PCR(ν)~ν–γ. However, the results of many years of SHICRA SB RAS research into the nature and properties of cosmic ray intensity fluctuations based on data from neutron monitors at stations with different geomagnetic cut-offs RC from 0.5 to 6.3 GV show that the observed spectrum of fluctuations in galactic cosmic ray intensity in the frequency range above 10–4 Hz becomes flat, i.e. it is similar to white noise. This fact needs to be realized and explained.
 This paper reports the results of research into the shape of the spectrum of galactic cosmic ray intensity fluctuations within a frequency range ν from ~10–6 to ~1 Hz and compares them with model calculations of white noise spectra, using measurement data from the neutron monitor of the Apatity station. A possible physical explanation has been given for the observed shape of the cosmic ray fluctuation spectrum on the basis of the known mechanisms of their modulation in the heliosphere.

Correlation between ST-elevation myocardial infarction, non-ST-elevation myocardial infarction and the local Earth’s magnetic field changes

Stronger oscillations in the local Earth magnetic field may have an impact on the course of ischemic heart disease. This effect is individual for every person and depends on the sex, age, living territory, season, capability to adjust to magnetic field fluctuations and health status. Individuals who already have cardiovascular disease are more sensitive to magnetic field fluctuations, therefore further research is needed to make conclusions. Aim: To identify correlations between changes in local Earth magnetic field frequencies and patients with ST segment elevation myocardial infarction (STEMI) and non-ST segment elevation myocardial infarction (NSTEMI) cases per week, cases by sex per week and patients’ blood laboratory parameters (low-density lipoprotein cholesterol and Troponin I level). Methods: A retrospective study of 1667 patients, who were admitted to the Hospital of Lithuanian University of Health Sciences Kaunas Clinics between 1st January and 31st December 2019 due to acute coronary syndrome (STEMI and NSTEMI), were included in the study. Local Earth's time varying magnetic field (TVMF) was measured by a magnetometer located in Baisogala, Lithuania. Data from the magnetometer was collected daily, and weekly averaged. We assessed the correlations between average weekly geomagnetic field strength in six different frequency ranges (Hz) and average number of STEMI and NSTEMI cases per week, cases by sex per week and patients’ blood laboratory parameters (low-density lipoprotein cholesterol and Troponin I level). Results: The presence of a stronger magnetic field in the frequency range of 32-65 Hz was significantly related to the number of cases in the STEMI group during the winter season (r= 0.583, p= 0.036). Tendency towards a positive correlation was found during the winter in the men's group with STEMI in the high frequency range of 32-65 Hz. Low-density lipoprotein cholesterol level correlated positively in the winter STEMI group with the magnetic field in the 32-65 Hz range, and in the autumn STEMI group with the magnetic field in the frequency range of 0-7 Hz. Conclusion: Increased geomagnetic field strength in the high frequency range of 32-65 Hz is associated with a higher number of cases in the STEMI group.

Contrasting Scaling Properties of Near-Sun Sub-Alfvénic and Super-Alfvénic Regions

Scale-invariance has rapidly established itself as one of the most used concepts in space plasmas to uncover underlying physical mechanisms via the scaling-law behavior of the statistical properties of field fluctuations. In this work, we characterize the scaling properties of the magnetic field fluctuations in a sub-alfvénic region in contrast with those of the nearby super-alfvénic zone during the ninth Parker Solar Probe perihelion. With our observations, (i) evidence of an extended self-similarity (ESS) for both the inertial and the sub-ion/kinetic regimes during both solar wind intervals is provided, (ii) a multifractal nature of field fluctuations is observed across inertial scales for both solar wind intervals, and (iii) a mono-fractal structure of the small-scale dynamics is reported. The main novelty is that a universal character is found at the sub-ion/kinetic scale, where a unique rescaling exponent describes the high-order statistics of fluctuations during both wind intervals. Conversely, a multitude of scaling symmetries is observed at the inertial scale with a similar fractal topology and geometrical structures between the magnetic field components in the ecliptic plane and perpendicular to it, in contrast with a different level of intermittency, more pronounced during the super-alfvénic interval rather than the sub-alfvénic one, along the perpendicular direction to the ecliptic plane. The above features are interpreted in terms of the possible underlying heating and/or acceleration mechanisms in the solar corona resulting from turbulence and current sheet formation.

Direct kinetic Alfvén wave energy cascade in the presence of imbalance

A two-field Hamiltonian gyrofluid model for kinetic Alfvén waves retaining ion finite Larmor radius corrections and parallel magnetic field fluctuations is used to study direct turbulent cascades from the magnetohydrodynamic to the sub-ion scales. For moderate energy imbalance and weak enough magnetic fluctuations, the spectrum of the transverse magnetic field and that of the most energetic wave display a steep transition zone near the ion scale, while the parallel transfer (and thus the parallel dissipation) remains weak. In this regime, the perpendicular flux of generalized cross-helicity displays a significant decay past the ion scale, while the perpendicular energy flux remains almost constant. A phenomenological model suggests that the interactions between co-propagative waves present at the sub-ion scales can play a central role in the development of a transition zone in the presence of a helicity barrier.

Comparing Quasi-Parallel and Quasi-Perpendicular Configuration in the Terrestrial Magnetosheath: Multifractal Analysis

The terrestrial magnetosheath is characterized by large-amplitude magnetic field fluctuations. In some regions, and depending on the bow-shock geometry, these can be observed on several scales, and show the typical signatures of magnetohydrodynamic turbulence. Using Cluster data, magnetic field spectra and flatness are observed in two intervals separated by a sharp transition from quasi-parallel to quasi-perpendicular magnetic field with respect to the bow-shock normal. The multifractal generalized dimensions Dq and the corresponding multifractal spectrum f(α) were estimated using a coarse-graining method. A p-model fit was used to obtain a single parameter to describe quantitatively the strength of multifractality and intermittency. Results show a clear transition and sharp differences in the intermittency properties for the two regions, with the quasi-parallel turbulence being more intermittent.

Photon echo, spectral hole burning, and optically detected magnetic resonance inYb3+171:LiNbO3bulk crystal and waveguides

Recent progress in the realization of high-quality optical resonators and waveguides along with the possibility to incorporate rare-earth ions, make lithium niobate a promising material to build integrated platforms for quantum information processing. $^{171}\mathrm{Yb}^{3+}$ is a particularly attractive system because it can show long coherence lifetimes at zero magnetic field thanks to transitions insensitive to magnetic field fluctuations. In this paper, we investigate the optical and spin properties of $^{171}\mathrm{Yb}^{3+}$ ions in ${\mathrm{LiNbO}}_{3}$ bulk crystals as well as implanted waveguides. Using hole-burning spectroscopy and optically detected magnetic resonance, we studied ground and excited state hyperfine structures and probed optical and spin spectral holes. Importantly, the hole linewidths suggest that part of the ions in the waveguides are in a similar environment as in the bulk sample. We furthermore characterized spin population relaxation and coherence lifetimes of $^{171}\mathrm{Yb}^{3+}$ ions in the bulk crystal at temperatures between 50 mK and 9 K. At low temperatures, ${T}_{2}$ up to 9.5 $\ensuremath{\mu}\mathrm{s}$ (34 kHz homogeneous linewidth) and spin relaxation rates as long as $\ensuremath{\approx}100$ ms were measured. Our results show that $^{171}\mathrm{Yb}^{3+}$:$\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_{3}$ is a system that exhibits narrow optical homogeneous linewidths over a 50 GHz bandwidth together with an electron spin degree of freedom. This is of interest for a variety of applications in integrated quantum photonics such as quantum memories or quantum processors.

On the Possibility of Modeling the IMF By-Weather Coupling through GEC-Related Effects on Cloud Droplet Coalescence Rate

The meteorological response to the fluctuation of the interplanetary magnetic field (IMF), known as the Mansurov effect, is well established. It is hypothesized that the IMF By fluctuation can modulate the atmospheric global electric circuit (GEC) over the polar regions and affect surface meteorology. The influence of electric charges on the rate of droplet coalescence in fair-weather clouds is one of several cloud microphysical mechanisms that have been hypothesized to be involved. However, although meteorological effects associated with IMF By have been observed, the role of cloud droplet coalescence in this solar–weather coupling mechanism has not yet been confirmed. In addition, studies demonstrating the solar wind-driven effects are based on observations without using global climate models to support the IMF By-weather linkage. In this study, we investigate the Mansurov effect over the period 1999–2002 using ensemble experiments modeled with the chemistry-climate model (CCM) SOCOLv3 (SOlar Climate Ozone Links, version 3.0). Using observed IMF By, we model its effect on ground-level air pressure and temperature to examine one of the proposed GEC-cloud hypotheses: that surface meteorology response on IMF By fluctuations occurs through the Jz-associated intensification of cloud droplet coalescence rate. The results showed that we cannot explain and confirm the hypothesis that the rate of cloud droplet coalescence is an intermediate link for the IMF By-weather coupling. Anomalies in surface air pressure and temperature from the control run, where IMF By is omitted, do not robustly differ from experiments in which the dependence of cloud droplet coalescence rate on IMF By is included. In addition, the standard deviation of anomalies in surface air pressure and temperature between ensemble members is consistent with the magnitude of the observed effect even in the control run, suggesting that the model has a strong internal variability that prevents the IMF By effect from being properly detected in the model.

Selective measurement of the longitudinal electron spin relaxation timeT1ofCe3+ions in a YAG lattice: Resonant spin inertia

Electron spin oriented along an external magnetic field is subject to longitudinal spin relaxation with characteristic time $T_1$. The corresponding decay is nonoscillating, so one cannot readily ascribe $T_1$ to a certain $g$ factor. This becomes a problem when several electronic states with different $g$ factors are present in the system, e.g. electrons and holes. We solve this problem by optically pumping spin polarization and then selectively depolarizing it using a radio frequency (rf) field. By modulating the rf field one can observe the retarded modulation of spin polarization which depends on the relation between the modulation period and $T_1$. Using this selective spin inertia method, we unveil the strong anisotropy of $T_1$ for rare-earth Ce$^{3+}$ ions in a YAG crystal at low temperatures and low magnetic fields. We also show that the spread of Larmor frequencies within the electron ensemble in this system is not static, but results from the fluctuations of internal magnetic fields on a timescale much shorter than $T_1$.

Cross helicity of interplanetary coronal mass ejections at 1 au

ABSTRACT Interplanetary coronal mass ejections (ICMEs) contain magnetic field and velocity fluctuations across a wide range of scales. These fluctuations may be interpreted as Alfvénic wave packets propagating parallel or antiparallel to the background magnetic field, with the difference in power between counterpropagating fluxes quantified by the cross helicity. We have determined the cross helicity of inertial range fluctuations at 10−3 to 10−2 Hz in 226 ICME flux ropes and 176 ICME sheaths observed by the Wind spacecraft at 1 au during 1995–2015. The flux ropes and sheaths had mean, normalized cross helicities of 0.18 and 0.24, respectively, with positive values here indicating net antisunward fluxes. While still tipped towards the antisunward direction on average, fluxes in ICMEs tend to be more balanced than in the solar wind at 1 au, where the mean cross helicity is larger. Superposed epoch profiles show cross helicity falling sharply in the sheath and reaching a minimum inside the flux rope near the leading edge. More imbalanced, solar wind-like cross helicity was found towards the trailing edge and laterally further from the rope axis. The dependence of cross helicity on flux rope orientation and the presence of an upstream shock are considered. Potential origins of the low cross helicity in ICMEs at 1 au include balanced driving of the closed-loop flux rope at the Sun and ICME–solar wind interactions in interplanetary space. We propose that low cross helicity of fluctuations is added to the standard list of ICME signatures.

Estimating Inner Magnetospheric Radial Diffusion Using a Hybrid-Vlasov Simulation

Radial diffusion coefficients quantify non-adiabatic transport of energetic particles by electromagnetic field fluctuations in planetary radiation belts. Theoretically, radial diffusion occurs for an ensemble of particles that experience irreversible violation of their third adiabatic invariant, which is equivalent to a change in their Roederer L* parameter. Thus, the Roederer L* coordinate is the fundamental quantity from which radial diffusion coefficients can be computed. In this study, we present a methodology to calculate the Lagrangian derivative of L* from global magnetospheric simulations, and test it with an application to Vlasiator, a hybrid-Vlasov model of near-Earth space. We use a Hamiltonian formalism for particles confined to closed drift shells with conserved first and second adiabatic invariants to compute changes in the guiding center drift paths due to electric and magnetic field fluctuations. We investigate the feasibility of this methodology by computing the time derivative of L* for an equatorial ultrarelativistic electron population travelling along four guiding center drift paths in the outer radiation belt during a 5 minute portion of a Vlasiator simulation. Radial diffusion in this simulation is primarily driven by ultralow frequency waves in the Pc3 range (10–45 s period range) that are generated in the foreshock and transmitted through the magnetopause to the outer radiation belt environment. Our results show that an alternative methodology to compute detailed radial diffusion transport is now available and could form the basis for comparison studies between numerical and observational measurements of radial transport in the Earth’s radiation belts.

Reconciling cosmic ray transport theory with phenomenological models motivated by Milky-Way data

ABSTRACT Phenomenological models of cosmic ray (CR) transport in the Milky Way can reproduce a wide range of observations assuming that CRs scatter off of magnetic-field fluctuations with spectrum ∝ k−δ and δ ∼ [1.4, 1.67]. We study the extent to which such models can be reconciled with current microphysical theories of CR transport, specifically self-confinement due to the streaming instability and/or extrinsic turbulence due to a cascade of magnetohydrodynamic (MHD) fast modes. We first review why it is that on their own neither theory is compatible with observations. We then highlight that CR transport is a strong function of local plasma conditions in the multiphase interstellar medium, and may be diffusive due to turbulence in some regions and streaming due to self-confinement in others. A multiphase combination of scattering mechanisms can in principle reproduce the main trends in the proton spectrum and the boron-to-carbon ratio. However, models with a combination of scattering by self-excited waves and fast-mode turbulence require significant fine-tuning due to fast-mode damping, unlike phenomenological models that assume undamped Kolmogorov turbulence. The assumption that fast modes follow a weak cascade is also not well justified theoretically, as the weak cascade is suppressed by wave steepening and weak-shock dissipation even in subsonic turbulence. These issues suggest that there may be a significant theoretical gap in our understanding of MHD turbulence. We discuss a few topics at the frontier of MHD turbulence theory that bear on this (possible) gap and that may be relevant for CR scattering.

Detecting deep axisymmetric toroidal magnetic fields in stars

Context. Asteroseismology has revealed small core-to-surface rotation contrasts in stars in the whole Hertzsprung–Russell diagram. This is the signature of strong transport of angular momentum (AM) in stellar interiors. One of the plausible candidates to efficiently carry AM is magnetic fields with various topologies that could be present in stellar radiative zones. Among them, strong axisymmetric azimuthal (toroidal) magnetic fields have received a lot of interest. Indeed, if they are subject to the so-called Tayler instability, the accompanying triggered Maxwell stresses can transport AM efficiently. In addition, the electromotive force induced by the fluctuations of magnetic and velocity fields could potentially sustain a dynamo action that leads to the regeneration of the initial strong axisymmetric azimuthal magnetic field. Aims. The key question we aim to answer is whether we can detect signatures of these deep strong azimuthal magnetic fields. The only way to answer this question is asteroseismology, and the best laboratories of study are intermediate-mass and massive stars with external radiative envelopes. Most of these are rapid rotators during their main sequence. Therefore, we have to study stellar pulsations propagating in stably stratified, rotating, and potentially strongly magnetised radiative zones, namely magneto-gravito-inertial (MGI) waves. Methods. We generalise the traditional approximation of rotation (TAR) by simultaneously taking general axisymmetric differential rotation and azimuthal magnetic fields into account. Both the Coriolis acceleration and the Lorentz force are therefore treated in a non-perturbative way. Using this new formalism, we derive the asymptotic properties of MGI waves and their period spacings. Results. We find that toroidal magnetic fields induce a shift in the period spacings of gravity (g) and Rossby (r) modes. An equatorial azimuthal magnetic field with an amplitude of the order of 105 G leads to signatures that are detectable in period spacings for high-radial-order g and r modes in γ Doradus (γ Dor) and slowly pulsating B (SPB) stars. More complex hemispheric configurations are more difficult to observe, particularly when they are localised out of the propagation region of MGI modes, which can be localised in an equatorial belt. Conclusions. The magnetic TAR, which takes into account toroidal magnetic fields in a non-perturbative way, is derived. This new formalism allows us to assess the effects of the magnetic field in γ Dor and SPB stars on g and r modes. We find that these effects should be detectable for equatorial fields thanks to modern space photometry using observations from Kepler, TESS CVZ, and PLATO.

Analysis of the Magnetic Signature of Surface Waves Measured in a Laboratory Experiment

Abstract A magnetic signature is created by secondary magnetic field fluctuations caused by the phenomenon of seawater moving in Earth’s magnetic field. A laboratory experiment was conducted at the Surge Structure Atmosphere Interaction (SUSTAIN) facility to measure the magnetic signature of surface waves using a differential method: a pair of magnetometers, separated horizontally by one-half wavelength, were placed at several locations on the outer tank walls. This technique significantly reduced the extraneous magnetic distortions that were detected simultaneously by both sensors and additionally doubled the magnetic signal of surface waves. Accelerometer measurements and local gradients were used to identify magnetic noise produced from tank vibrations. Wave parameters of 4-m-long waves with a 0.56-Hz frequency and a 0.1-m amplitude were used in this experiment. Freshwater and saltwater experiments were completed to determine the magnetic difference generated by the difference in conductivity. Tests with an empty tank were conducted to identify the noise of the facility. When the magnetic signal was put through spectral analysis, it showed the primary peak at the wave frequency (0.56 Hz) and less pronounced higher-frequency harmonics, which are caused by the nonlinearity of shallow water surface waves. The magnetic noise induced by the wavemaker and related vibrations peaked around 0.3 Hz, which was removed using filtering techniques. These results indicate that the magnetic signature produced by surface waves was an order of magnitude larger than in traditional model predictions. The discrepancy may be due to the magnetic permeability difference between water and air that is not considered in the traditional model.