Magnetic Field Strength Fluctuations Research Articles

Mapping electro-vortex flow patterns from tornado to inverted tornado in a hemispherical container

This study aims to investigate the intricate interaction between fluid flow and magnetic fields, known as magnetohydrodynamic (MHD) phenomena, within a hemispherical container filled with conducting gallium–indium–tin (Ga-In-Sn) liquid. The primary objective is to explain the influence of the external magnetic field and electric current intensities on the flow structure. Novel insights into the emergence of Lorentz forces that drive the flow dynamics are pursued by varying these parameters. The motivation for this investigation is rooted in the desire to deepen our understanding and uncover new insights into magnetohydrodynamic (MHD) phenomena within a specific experimental setup. Specifically, we aim to understand how swirl velocity is generated and altered by fluctuations in magnetic field strength and electric current intensity within the system. Our investigation reveals a transformation in the flow pattern in a hemispherical pool as the magnetic field strength increases while maintaining a constant electric current intensity. Sequential transformations from a rope tornado to a tornado, cyclone, and finally an inverted tornado are observed, shedding light on the complex behavior of the system. On the other hand, under fixed external magnetic field conditions, it is observed that, as the electric current intensifies, the flow pattern evolves from a tornado to a rope tornado or from a cyclone to a tornado. Furthermore, once the electric current intensity exceeds a specific threshold, the flow pattern remains unchanged, providing valuable insights for process optimization and control. This study contributes to a deeper understanding of MHD phenomena and offers practical implications for optimizing processes such as electroslag remelting (ESR) and vacuum arc remelting (VAR) that involve a similar hemispherical pool of conductive liquid. The simulation results are validated against experimental measurements, ensuring the reliability and accuracy of our findings.

Probing 3D magnetic fields – I. Polarized dust emission

ABSTRACT Polarized dust emission is widely used to trace the plane-of-the-sky (POS) component of interstellar magnetic fields in two dimensions. Its potential to access 3D magnetic fields, including the inclination angle of the magnetic fields relative to the line of sight (LOS), is crucial for a variety of astrophysical problems. Based on the statistical features of observed polarization fraction and POS Alfvén Mach number $\overline{M_{\rm A}}_{,\bot }$ distribution, we present a new method for estimating the inclination angle. The magnetic field fluctuations raised by anisotropic magnetohydrodynamic (MHD) turbulence are taken into account in our method. By using synthetic dust emission generated from 3D compressible MHD turbulence simulations, we show that the fluctuations are preferentially perpendicular to the mean magnetic field. We find the inclination angle is the major agent for depolarization, while fluctuations of magnetic field strength and density have an insignificant contribution. We propose and demonstrate that the mean inclination angle over a region of interest can be calculated from the polarization fraction in a strongly magnetized reference position, where $\overline{M_{\rm A}}_{,\bot }^2\ll 1$. We test and show that the new method can trace the 3D magnetic fields in sub-Alfvénic, trans-Alfvénic, and moderately superAlfvénic conditions (0.4 ≲ MA ≲ 1.2). We numerically quantify that the difference of the estimated inclination angle and actual inclination angle ranges from 0° to 20° with a median value of ≤10°.

Comparing electromagnetic instabilities in global gyrokinetic simulations with local and MHD models

We perform a study of system-scale to gyro-radius scale electromagnetic modes in a pedestal-like equilibrium using a gyrokinetic code ORB5, along with a comparison to the results of wimulations in a local gyrokinetic code, GS2, and an MHD energy principle code, MISHKA. In the relevant large-system, short wavelength regime, good agreement between the gyrokinetic codes is found. For global-scale modes, reasonable agreement between MHD and the global gyrokinetic code is observed. There are various formulational and implementational issues with using standard gyrokinetic codes in this limit, so even this level of agreement is promising. In order to correctly model the physics it is important to keep the effect of magnetic field strength fluctuations (which are not directly included in ORB5) in this case, where the gradient of β is large. The pressure stability threshold does not change substantially between the MHD and global gyrokinetic simulations, for the conditions present in this paper. It is also noted that the main stabilising mechanism at short wavelength is the diamagnetic drift, for which a two-fluid (rather than gyrokinetic) formulation would be sufficient.

THE EFFICIENCY OF SECOND-ORDER FERMI ACCELERATION BY WEAKLY COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE

We investigate the effects of pitch-angle scattering on the efficiency of particle heating and acceleration by MHD turbulence using phenomenological estimates and simulations of non-relativistic test particles interacting with strong, subsonic MHD turbulence. We include an imposed pitch-angle scattering rate, which is meant to approximate the effects of high frequency plasma waves and/or velocity space instabilities. We focus on plasma parameters similar to those found in the near-Earth solar wind, though most of our results are more broadly applicable. An important control parameter is the size of the particle mean free path lambda_{mfp} relative to the scale of the turbulent fluctuations L. For small scattering rates, particles interact quasi-resonantly with turbulent fluctuations in magnetic field strength. Scattering increases the long-term efficiency of this resonant heating by factors of a few-10, but the distribution function does not develop a significant non-thermal power-law tail. For higher scattering rates, the interaction between particles and turbulent fluctuations becomes non-resonant, governed by particles heating and cooling adiabatically as they encounter turbulent density fluctuations. Rapid pitch-angle scattering can produce a power-law tail in the proton distribution function but this requires fine-tuning of parameters. Moreover, in the near-Earth solar wind, a significant power-law tail cannot develop by this mechanism because the particle acceleration timescales are longer than the adiabatic cooling timescale set by the expansion of the solar wind. Our results thus imply that MHD-scale turbulent fluctuations are unlikely to be the origin of the v^{-5} tail in the proton distribution function observed in the solar wind.

ESTIMATION OF MAGNETIC FIELD STRENGTH IN THE TURBULENT WARM IONIZED MEDIUM

We studied Faraday rotation measure (RM) in turbulent media with the rms Mach number of unity, using isothermal, magnetohydrodynamic turbulence simulations. Four cases with different values of initial plasma beta were considered. Our main findings are as follows. (1) There is no strong correlation between the fluctuations of magnetic field strength and gas density. So the magnetic field strength estimated with RM/DM (DM is the dispersion measure) correctly represents the true mean strength of the magnetic field along the line of sight. (2) The frequency distribution of RMs is well fitted to the Gaussian. In addition, there is a good relation between the width of the distribution of RM/$\bar{\rm RM}$ ($\bar{\rm RM}$ is the average value of RMs) and the strength of the regular field along the line of sight; the width is narrower, if the field strength is stronger. We discussed the implications of our findings in the warm ionized medium where the Mach number of turbulent motions is around unity.

Trains of magnetic holes and magnetic humps in the heliosheath

This paper discusses the existence of trains (sequences) of magnetic holes and magnetic humps in the heliosheath, based on Voyager 1 observations made in the intervals DOY 312.9707–317.0879, 2005 and DOY 185.2762–186.7957, 2005. These two trains represent a class of compressive fluctuations in the heliosheath. Varying from one region or time interval to another, this class of fluctuations probably depends on the varying conditions upstream of the Termination Shock and its nature. The trains of magnetic holes in the heliosheath resemble certain magnetic field strength fluctuations observed in planetary magnetosheaths.

Tsallis distributions of the large‐scale magnetic field strength fluctuations in the solar wind from 7 to 87 AU

The solar wind is a driven nonlinear, nonequilibrium system with large jumps and fluctuations in the temporal profiles of the magnetic field strength B. Relatively large clusters of strong fields (“merged interaction regions,” MIRs) form beyond 1 AU, grow out to ≈5–30 AU, and decay slowly between ≈30 AU and at least 90 AU. We analyze the probability distribution functions (PDFs) of fluctuations of B observed by Voyager 1 between 7 and 87 AU on scales from 1 to 128 days during each of four years (1980, 1991, 2001, and 2002). The 32 PDFs of the increments of B can be described by a single function, the q‐exponential distribution of the nonextensive Tsallis statistical mechanics. The tails of the PDFs are described by the entropic index q, which is scale dependent. The Tsallis distribution has a finite variance when q < 5/3 and a divergent moment when q ≥ 5/3. For the 1980 and 1991 data (near 8 and 45 AU, respectively), q ≥ 5/3 at all scales, owing to large tails of the PDFs caused by large fluctuations and jumps in B(t). For the 2001 and 2002 data (between 80 and 87 AU), q < 5/3, and q approaches 1 (the PDF tends to a Gaussian) at large scales. The standard deviation and kurtosis of the observed increments of B vary with the scale of the fluctuations. The transition from q > 5/3 at <45 AU to q < 5/3 at >80 AU suggests the possibility of a phase transition in the distant heliosphere.

The Pattern of Moving Magnetic Inhomogeneities in and Around Sunspots

High-resolution MDI magnetograms are used to study the pattern of moving magnetic inhomogeneities in sunspots. We examine the inward and outward moving features in sunspots. The velocity of these features is small in the umbra while it is about 0.5 km s−1 in the outer penumbra. The inward and outward moving features may be the possible origin for the long-term fluctuations of magnetic field strength in sunspots.

Multifractal structure of the large-scale heliospheric magnetic field strength fluctuations near 85AU

Abstract. During 2002, the Voyager 1 spacecraft was in the heliosphere between 83.4 and 85.9AU (1AU is the mean distance from the Sun to Earth) at 34° N heliographic latitude. The magnetic field strength profile observed in this region had a multifractal structure in the range of scales from 2 to 16 days. The multifractal spectrum observed near 85AU is similar to that observed near 40AU, indicating relatively little evolution of the multifractal structure of the magnetic field with increasing distance in the distant heliosphere in the epoch near solar maximum.

Evolution of Magnetic Fields in Corotating Interaction Regions from 1 to 95 AU: Order to Chaos

We discuss the large-scale heliospheric magnetic field strength fluctuations as a function of distance from the Sun during the declining phase of a solar cycle, based on a one-dimensional, MHD, three-fluid model with observations made at 1 AU during 1995 as input. We consider daily averages of the magnetic field strength, B, as a function of time for a ≈1 year interval. The model predicts that B(t) is quasi-periodic, and that the amplitudes of fluctuations in B relative to the yearly average of B (B) are relatively large between 5 and 20 AU corotating merged interaction region or CMIR The model predicts that the fluctuations are aperiodic and that their amplitudes are relatively small between 30 and 95 AU (the interaction region zone). It predicts a transition between these two zones at ≈25 AU. These results are consistent with a conceptual model proposed by Burlaga in 1983 for the declining phase of the solar cycle. In the CMIR zone, neighboring CMIRs merge in a sequence of events that defines a topological tree. The model predicts the following statistical properties of the fluctuations in B/B for the declining phase of a solar cycle in the CMIR zone: (1) the power spectrum of B/B has a prominent peak at 26 days and a secondary peak at 13 days; (2) the distribution of B/B has no simple form; and (3) the standard deviation (SD) of B/B is relatively large and has a maximum of 1.2 at 10 AU. In the wave interaction zone, (1) the spectrum has no significant peak, and the power level at 26 days is an order of magnitude smaller than in the CMIR zone; (2) the distribution of B/B is approximately lognormal; and (3) the SD(B/B) is nearly constant, ≈0.48. The SD(B/B) versus R shows that the transition between the CMIR and the wave interaction zones is at ≈25 ± 5 AU. The results of the model are consistent with the Voyager 1 (V1) observations near 15 and 55 AU during 1983 and 1994, respectively. During the declining phase of solar cycle 23, in ≈2003-2005, Voyager 2 (V2) will move from 69 to 76 AU while V1 moves from 87 to 95 AU. The model makes the following predictions for the properties of B between 65 and 95 AU: (1) B(t) will be aperiodic, with relatively low amplitude fluctuations similar to those observed at 55 AU; (2) the power spectra will resemble those observed near 55 AU, and there will be little radial variation in the power at the solar rotation period, 26 days; (3) the distribution of B will be approximately lognormal; (4) the SD(B) of the daily averages of B will be ≈0.48B; and (5) the tail of the distribution of B will be exponential.

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

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

Velocity and Magnetic Field Fluctuations in the Photosphere of a Sunspot

We use a data set of exceptionally high quality to measure oscillations of Doppler velocity, intensity, and the vector magnetic field at photospheric heights in a sunspot. Based on the full Stokes inversion of the line profiles of Fe I 630.15 and 630.25 nm, in the sunspot umbra we find upper limits of 4 G (root mean square [rms]) for the amplitude of 5 minute oscillations in magnetic field strength and 009 (rms) for the corresponding oscillations of the inclination of the magnetic field to the line of sight. Our measured magnitude of the oscillation in magnetic field strength is considerably lower than that found in 1997 by Horn, Staude, & Landgraf. Moreover, we find it likely that our measured magnetic field oscillation is at least partly due to instrumental and inversion cross talk between the velocity and magnetic signals, so that the actual magnetic field strength fluctuations are even weaker than 4 G. In support of this we show, on the basis of the eigenmodes of oscillation in a theoretical model of the sunspot umbra, that magnetic field variations of at most 0.5 G are all that is to be expected. The theoretical model also provides an explanation of the shift of power peaks in Doppler velocity to the 3 minute band in chromospheric umbral oscillations, as a natural consequence of the drastic change in character of the eigenmodes of oscillation between frequencies of about 4.5 and 5.0 mHz due to increased tunneling through the acoustic cutoff-frequency barrier. Using measurements of the phase of velocity oscillations above the acoustic cutoff frequency, we determine the relative velocity response height in the umbra of four different photospheric spectral lines from the phase differences between velocities in these lines, assuming that the oscillations propagate vertically at the local sound speed. In spacetime maps of fluctuations in continuum intensity, Doppler velocity, magnetic field strength, and field inclination, we see distinct features that migrate radially inward from the inner penumbra all the way to the center of the umbra, at speeds of a few tenths of a kilometer per second. These moving features are probably a signature of the convective interchange of magnetic flux tubes in the sunspot, although we failed to find any strong correlation among the features in the different quantities, indicating that these features have not been fully resolved.

Natural MHD oscillations of a neutron star

Natural, low-frequency, hydromagnetic oscillations of an isolated, nonrotating neutron star, which are localized in the peripheral crust, the structure of which is determined by the electron-nuclear plasma (the Ae phase), are studied. The plasma medium of the outer crust is treated as a homogeneous, infinitely conducting, incompressible continuum, the motions of which are determined by the equations of magnetohydrodynamics. In the approximation of a constant magnetic field inside the crust (the magnetic field outside the star is assumed to have a dipole structure), the spectrum of normal poloidal and toroidal hydromagnetic oscillations, due to presumed residual fluctuations of flow and their associated fluctuations in magnetic field strength, is calculated. Numerical estimates given for the periods of MHD oscillations fall in the range of periods of radio pulsar emission, indicating a close connection between the residual hydromagnetic oscillations and the electromagnetic activity of neutron stars.

Magnetic fields in the distant heliosphere approaching solar minimum: Voyager 1 and 2 observations during 1994

During 1994, Voyager 2 (V2) was at a heliocentric distance 〈R〉 = 43.4 AU and latitude 〈δs/c〉 = 11.9°S, while Voyager 1 (Vl) was at 〈R〉 = 56.3 AU and 〈δs/c〉 = 32.5°N. The mean magnetic field strength observed by Vl during 1994 was 0.05 nT, the weakest and most distant magnetic field ever measured in situ. A bimodal distribution of azimuthal magnetic field directions was observed by V2, and a single‐peaked distribution was observed by Vl. Thus V2 was in the “sector zone” (the range of latitudes that contains the heliospheric current sheet), and Vl was in the unipolar region above it, consistent with the latitudes of the heliospheric current sheet obtained from an extrapolation of the neutral line computed from solar magnetic field observations. A lognormal distribution of the magnetic field strength (hourly averages) was observed for 95% of the Vl data and most of the V2 data. An approximately lognormal distribution of B is a general property of the heliospheric magnetic field, observed out to 58.1 AU and up to 32.6°S latitude. During 1994 an exponential tail in the distribution of the magnetic field strength was observed by both Vl and V2 for fields stronger than average. An exponential tail in the magnetic field strength distribution was observed by Vl and V2 from 1983 to 1994 at latitudes from 11°S to 33°N and at distances from 13 to 58 AU. Thus an exponential tail of the distribution of magnetic field strengths is a basic property pf the heliosphere beyond 13 AU. There was no significant latitudinal gradient in the exponential tail observed by V2 in the sector zone and observed by Vl above the sector zone during 1994. Multifractal structure in the large‐scale fluctuations of the magnetic field strength was observed by Vl for periods from 8 hours to 256 hours equaling 10.7 days for the magnetic fields stronger than average. A multiffactal spectrum is a general property of the large‐scale magnetic field strength fluctuations, from 1983 through 1994 between 13 AU and 58 AU. There remains a need for a statistical theory of the solar wind that can account for these observations and for cosmic ray models that include the effect of multifractal magnetic field strength fluctuations.

Magnetic fields and cosmic rays in the distant heliosphere at solar maximum: Voyager 2 observations near 32 AU during 1990

The intensity of >70 MeV cosmic ray protons observed during solar cycle 22 by Voyager 2 (V2) in the distant heliosphere reached a minimum in 1990, corresponding to the maximum of solar activity in mid‐1989 (allowing for the propagation time of the solar wind from the sun to Voyager 2 near 32 AU). A step decrease in the cosmic ray intensity observed within the first ≈ 125 days of 1990 was caused by a global merged interaction region (GMIR), consisting of a cluster of large‐amplitude magnetic field strength fluctuations, in which the field was predominantly stronger than average. The step decrease consists of four events in each of which the decrease in cosmic ray intensity is relatively large, and the recovery is either brief or absent. The relation between the cosmic ray intensity and the magnetic field strength observed near 32 AU during this period at the maximum of solar activity in 1989/1990 is similar to that which Voyager 2 observed near 11 AU in 1982/1983 following the maximum of solar activity in the previous solar cycle in 1980. The local changes in the cosmic ray intensity profile are related to the magnetic field strength. Near solar maximum the emission rate of ejecta, which contain magnetic fields that deviate significantly from the spiral direction, is a maximum. Nevertheless, the distribution of elevation angles of the magnetic field observed by Voyager 2 during 1990 is essentially the same as that observed during earlier parts of the solar cycle from 1986 through 1989, including solar minimum in 1986 and 1987. During 1990, the width of the distribution of elevation angles at ≈ 2 AU was the same as that observed at 1 AU. Sectors were observed, but no sector structure was present during 1990, just as in 1988, 1989, and 1991. The distribution of daily averages of the magnetic field strength is lognormal for 0.05 nT < B < 0.25 nT. However, there are more strong magnetic fields than the lognormal distribution predicts for 0.25 nT < B < 0.4 nT, owing to the large MIRs. The large‐scale fluctuations of the magnetic field strength have a multifractal structure in the low‐frequency range from 2.7 days to at least 21.3 days that influences the cosmic ray intensity profile.

Multifractal structure of the magnetic field and plasma in recurrent streams at 1 AU

This paper demonstrates the existence of multifractal structure in the fluctuations of the magnetic field strength, temperature, and density in the recurrent flows at 1 AU, The multifractal scaling is observed over the range of periods from 2 hours to 32 hours for the magnetic field and density and from 2 hours to 16 hours for the temperature. The lower cutoff of 2 hours is related to the use of hour averages; it does not have physical significance. The upper cutoff of 32 hours (16 hours) represents the transition to the mesoscale regime in which the fluctuations are determined by the stream structure. Thus the multifractal structure represents fluctuations superimposed on the corotating stream profile and the heliospheric plasma sheet profile. One may think of the multifractal structure as a texture superimposed on the mesoscale profiles, the structure of the texture being related to the mesoscale structure itself. The multifractal structure of the magnetic field strength fluctuations might be produced by a multiplicative process involving the velocity fluctuations.

Large‐scale fluctuations in the interplanetary medium

Power spectra of measurements of the magnetic field strength in the heliosphere obtained by Voyager 1 between 1 AU and 9 AU have the form of a power law ƒ−a from periods of several hours to at least 6 days. The exponent was a = 2.0 ±0.05 for all of the spectra considered, which is the exponent for a series of steps and for Burgers' turbulence. Spectra of large‐scale speed fluctuations also have the form ƒ−b from a period of a few hours to periods greater than 13 days in the region from 1 AU to 8.9 AU. The exponent b is generally somewhat larger than b = 2, implying some “persistence” of the speed fluctuations. The low‐frequency cutoff (outer cutoff) of the power law increases from a period of 6.5 days at 1 AU to 26 days at (6.1–8.9) AU, which can be attributed to (1) the coalescence of interaction regions and (2) a transfer of energy from the spectrum of large‐scale speed fluctuations. The outer cutoff of the spectrum of speed fluctuations increases from a period of 13 days at 1 AU to 26 days between a few AU and 8.9 AU. Both the magnetic field strength fluctuations and the speed fluctuations have fractal behavior, suggesting that they are self affine rather than dominated by a few large discontinuities.

Electronic Components in Galactic Cosmic Rays

The intensity and the energy spectrum of cosmic electrons arising from the nuclear collisions of cosmic rays are calculated by reference to experimental data obtained with accelerators and cosmic rays. The electron spectrum thus obtained agrees reasonably well with recent observations of electrons with energies below 1 Bev. The Galactic radio spectrum expected from the electrons is calculated with particular attention to its low frequency part. The less steep spectrum recently obtained may suggest considerable fluctuations in magnetic field strength in the galaxy. The gamma -ray spectrum is also given of the same origin as the electrons. It is emphasized that the comparison of these three as well as the relative intensities of positons and negatons will be very important for the origin of cosmic rays and related astrophysical problems. (auth)