Instability Of Magnetic Field Research Articles

Spherical magnetic instabilities in the Earth’s core and equatorial symmetries

The Boussinesq rotating magnetohydrodynamic equations in a conducting fluid sphere, linearised about a steady basic state, are discretised using scalar and vector spherical harmonics. Vector spherical harmonic representations are used for the basic state vector fields as well as the interaction terms in the equations. The solenoidal property of the perturbation magnetic and velocity fields are imposed on the fields and equations using relations between vector spherical harmonics and toroidal–poloidal representations. The method has several distinct advantages over previous discretisation methods: it produces compact angular spectral equations which require only five core subroutines to generate all interactions and product terms, and only six core subroutines to radially discretise the equations using finite-differences; the core subroutines can be extensively tested using only simple models; and its generality permits very flexible code. We apply our approach to the magnetic instabilities of a steady axisymmetric azimuthal magnetic field. To isolate magnetic instabilities and suppress other instabilities the magnetostrophic approximation is made. The perturbation velocity and magnetic field satisfy the inviscid boundary and insulating exterior conditions, respectively. Results are presented for the simplest equatorially symmetric (quadrupole) and equatorially antisymmetric (dipole) magnetic field models which vanish on a single spherical surface. For each model the perturbation fields decouple into two subproblems, in which the perturbation magnetic field has the same or opposite symmetry to the basic state field. A strong preference is found for the equatorially symmetric perturbation magnetic field in the equatorially symmetric model. However, there is only a marginal preference for the equatorial antisymmetric perturbation magnetic field in the equatorially antisymmetric model. We also consider a class of equatorially unsymmetric basic state magnetic fields which are convex combinations of the first two models. Although the critical Elsasser number does not change appreciably, the most unstable mode changes totally from equatorially symmetric to equatorially antisymmetric. Finally, we consider the effect on the equatorially symmetric model of varying the spherical surface on which the field vanishes. The most unstable mode is always equatorially symmetric. When the dimensionless magnetic-zero radius is decreased below about 0.7 the most unstable mode switches from eastward to westward propagation. The magnetic field perturbation in the westward (eastward) case is strongly confined to the region outside (inside) the magnetic-zero radius.

Non-invasive MR thermography using the water proton chemical shift

Among various proton magnetic resonance (MR) parameters, such as longitudinal relaxation time, transverse relaxation time, diffusion coefficient and chemical shift, the chemical shift of water protons is recognized as the most reliable indicator of temperature. The chemical shift is the only frequency-based parameter and is independent of the other parameters, which are measured based on the intensity of the MR signal. In this paper, the basic principle and the recent progress in imaging temperature by spectroscopic techniques using the water proton chemical shift are discussed. The advantages of spectroscopic imaging over phase mapping for measuring temperature are that the former can distinguish water resonance from other resonances, and that another resonance can be used as an internal reference to reduce the effects of external magnetic field instability, tissue susceptibility and inter-scan tissue movement or deformation. Methods utilizing various magnetic resonance spectroscopy (MRS) techniques, such as single voxel spectroscopy, conventional magnetic resonance spectroscopic imaging (MRSI), echo planar spectroscopic imaging (EPSI) and line scan echo planar spectroscopic imaging (LSEPSI) are discussed.

Localized-magnon states in strongly frustrated quantum spin lattices

Recent developments concerning localized-magnon eigenstates in strongly frustrated spin lattices and their effect on the low-temperature physics of these systems in high magnetic fields are reviewed. After illustrating the construction and the properties of localized-magnon states we describe the plateau and the jump in the magnetization process caused by these states. Considering appropriate lattice deformations fitting to the localized magnons we discuss a spin-Peierls instability in high magnetic fields related to these states. Last but not least we consider the degeneracy of the localized-magnon eigenstates and the related thermodynamics in high magnetic fields. In particular, we discuss the low-temperature maximum in the isothermal entropy versus field curve and the resulting enhanced magnetocaloric effect, which allows efficient magnetic cooling from quite large temperatures down to very low ones.

A Two-Flux Radiation Model for Helical Instability of Arcs

A two-flux radiation model of the helical instability of arcs inaxial magnetic field is presented. The temperature (and electricalconductivity) is approximated in a more realistic way (parabolicinstead of flat profile) and a simplified term of radiation losses isincluded in the energy equation. The magnetohydrodynamic equations inan electrostatic approximation serve as the starting point of thetheory. Using a linear time-dependent perturbation theory, thecorresponding equations and an explicit analytic expression thatcorresponds to the term of radiation losses are derived in the presenceof the radiation transfer energy, from which the marginal Maeckernumber and the growth rate of the helical instability can be given. Itis found that, in comparison with the results without radiation, thearc stable area is reduced.

The Influence of Velocity Shear on Magnetic Buoyancy Instability in the Solar Tachocline

The Sun’s large-scale magnetic field is believed to be generated deep within the Sun, at the base of the convection zone, in a predominantly stably stratified region of strong radial shear, known as the tachocline. Observations indicate that, owing to magnetic buoyancy, this field rises to the surface to form active regions with systematic properties. Whereas previous investigations of magnetic buoyancy instability have generally assumed a static basic state, here we investigate the role of an aligned shear in modifying this instability. We adopt two complementary approaches. Using the energy principle, we derive sufficient conditions for the stability of a magnetic field in a stratified, compressible shear flow. To investigate the nature of the unstable modes, we have performed a series of numerical calculations; these suggest that the shear has an ‘‘axisymmetrizing’’ and stabilizing effect on the magnetic buoyancy instability. We discuss the implications for the instability of the solar magnetic field.

Instability of non-linear α 2-dynamos

Studies of the stability of prescribed magnetic fields in rapidly rotating systems have clearly demonstrated the relevance of the mechanism of magnetic field instability to the dynamics of planetary cores, see for example [Magnetic instabilities in rapidly rotating systems. In: Proctor, M.R.E., Matthews, P.C., Rucklidge, A.M. (Eds.), Solar and Planetary Dynamos. CUP, 1993, p. 59] The present study investigates the non-linear development of such instabilities and their feedback on the field generation process. The non-axisymmetric instability of a mean magnetic field B ̄ generated by a prescribed α-effect has been investigated in a rapidly rotating fluid spherical shell. The mean field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field at some finite amplitude. This amplitude increases with α 0, the strength of α. Above some critical value of α 0, the mean field becomes unstable to a non-axisymmetric instability. The present work is the continuation of preliminary work by [Phys. Earth Planet. Inter. 134 (2002) 213] to higher values of α 0, and to a different, more realistic, form of α. We are particularly interested in how the instability affects the mean field generated. We find that instability can dramatically reduce the strength of the mean field and significantly constrains the growth of B ̄ with α 0.

Backward wave oscillator regime of the whistler cyclotron instability in an inhomogeneous magnetic field

A linear theory for the backward wave oscillator generation regime of whistler waves in the Earth’s magnetosphere is presented. Using a parabolic profile of the magnetic field and a linear expression for the resonant current in the case of a zeroth order distribution function with a step discontinuity in the velocity component parallel to the magnetic field, the modes of the system are investigated by means of a search procedure. The existence of at least one mode exponentially growing in time is indicative of absolute instability, and such modes have been found. Therefore, an earlier prediction of such a regime, based on the homogeneous magnetic field model, is confirmed. The dependence of growth rates on the frequency mismatch and energetic electron density has been studied. These results yield the characteristic spatial profile and temporal growth rate of small-amplitude whistler-wave disturbances, which are likely to be the seeds for chorus emissions.

High-field proton MRS of human brain

Proton magnetic resonance spectroscopy ( 1H-MRS) of the brain reveals specific biochemical information about cerebral metabolites, which may support clinical diagnoses and enhance the understanding of neurological disorders. The advantages of performing 1H-MRS at higher field strengths include better signal to noise ratio (SNR) and increased spectral, spatial and temporal resolution, allowing the acquisition of high quality, easily quantifiable spectra in acceptable imaging times. In addition to improved measurement precision of N-acetylaspartate, choline, creatine and myo-inositol, high-field systems allow the high-resolution measurement of other metabolites, such as glutamate, glutamine, γ-aminobutyric acid, scyllo-inositol, aspartate, taurine, N-acetylaspartylglutamate, glucose and branched amino acids, thus extending the range of metabolic information. However, these advantages may be hampered by intrinsic field-dependent technical difficulties, such as decreased T2 signal, chemical shift dispersion errors, J-modulation anomalies, increased magnetic susceptibility, eddy current artifacts, limitations in the design of homogeneous and sensitive radiofrequency (RF) coils, magnetic field instability and safety issues. Several studies demonstrated that these limitations could be overcome, suggesting that the appropriate optimization of high-field 1H-MRS would expand the application in the fields of clinical research and diagnostic routine.

Relationship between decrease of net magnetic flux and solar major events

Using the full disk magnetograms taken by SOHO/MDI, we studied the evolution of magnetic fluxes in the line-of-sight for twelve solar active regions in the 23rd cycle, which produced strong solar activities. It is measured that the fluxes of these regions were appreciably imbalanced when they moved past the central meridian, where reliable measurements were obtained. In addition, it is found that, for seven regions for which the vector magnetic field was well observed at Huairou Solar Observing Station and thereby a vertical electric current can be derived, the vertical electric currents were out of balance. It has been found that the net fluxes of seven active regions which were associated with strong solar storms significantly decreased within 2 or 3 days prior to the major flares associated with the storms, and tended toward minimization before the onsets of the flares, suggesting a possible relationship between significant decrease of the flux imbalance of active regions and instability of large-scale magnetic fields.

Nonaxisymmetric Instabilities of a Toroidal Magnetic Field in a Rotating Sphere

It has been suggested that nonaxisymmetric instabilities of an axisymmetric toroidal magnetic field, independent of the existence of convective turbulence, provide an important dynamo effect for stars when the convective turbulence is largely suppressed by the magnetic field. We investigate analytically such three-dimensional magnetic instabilities arising from a purely toroidal magnetic field whose strength is proportional to distance from the rotation axis of a star. A three-dimensional perturbation approach is used in our stability analysis. The leading-order problem neglects dissipative effects and describes two- or three-dimensional hydromagnetic waves in spherical geometry. For the first time we are able to obtain general explicit solutions for the problem. Interesting properties of the hydromagnetic waves are revealed by the explicit solutions. We investigate the effect of ohmic dissipation on the stability of the toroidal magnetic field by first deriving the magnetic boundary layer solution and then matching it onto the interior leading-order solution. Furthermore, for the first time we are able to derive an explicit analytic expression for the growth rate of the magnetic instabilities. We find that the most unstable mode of the instabilities is always three-dimensional and characterized by small radial and latitudinal scales. Implications of these magnetic instabilities for the solar dynamo are discussed.

Unstable magnetic fluxes in heterotic string theory

We study exact string backgrounds representing a constant magnetic field background in heterotic string theory. These backgrounds are obtained by Kaluza-Klein reduction of a special class of plane wave solutions. For small values of the magnetic field they possess localized closed string tachyons analogous to the Nielsen-Olesen instability of a constant magnetic field in SO(3) Yang-Mills theory. When the magnetic field is embedded in the SO(32) gauge group of the heterotic string it is possible to study the lowest level tachyon in supergravity. We identify the closed string tachyons as fluctuations of the supergravity fields about the background. We argue that the tachyon signals the decay of the background to flat space. Our evidence rests on the study of the closed string tachyon potential, world sheet renormalization group equations in the supergravity approximation and the S-dual of this system in type I theory. In the S-dual description, the closed string tachyons in heterotic string theory correspond to open string tachyons in type I theory. Finally we analyze the non-perturbative stability of these models representing constant magnetic field backgrounds and show that it is stable to pair production of particles.

Secondary instabilities of large scale flow and magnetic field in the electromagnetic short wavelength drift-Alfvén wave turbulence

It is shown that the short wavelength (k⊥2ρi2>1, k⊥ is the characteristic wave vector, and ρi is the ion Larmor radius) electromagnetic drift wave turbulence in typical conditions is unstable with respect to the excitation of large scale perturbations of the plasma flow and magnetic field. It is found that the generation of zonal flow is reduced (compared to the long wavelength ion temperature gradient turbulence) due to the Boltzmann nature of the ion response. Magnetic fluctuations further reduce zonal flow drive due to competition of the Reynolds and Maxwell stresses. It is shown that secondary magnetic field structures may be generated in the electromagnetic drift wave turbulence thus leading to the increased levels of the electron energy transport.

Phase coherent averaging in magnetic resonance spectroscopy using interleaved navigator scans: compensation of motion artifacts and magnetic field instabilities.

The quality of spectra in (1)H magnetic resonance spectroscopy (MRS) is strongly affected by temporal signal instabilities during the acquisition. One reason for these instabilities are hardware imperfections, e.g., drifts of the main magnetic field in superconducting magnets. This is of special concern in high-field systems where the specification of the field stability is close to the spectral linewidth. A second major potential source of artifacts, particularly in clinical MRS, is patient motion. Using standard acquisition schemes of phase-cycled averaging of the individual acquisitions, long-term effects (field drifts) as well as changes on a shorter time scale (motion) can severely reduce spectral quality. The new technique for volume-selective MRS presented here is based on the additional interleaved acquisition of a navigator signal during the recovery time of the metabolite acquisition. It corrects for temporal signal instabilities by means of a deconvolution of the metabolite and the navigator signal. This leads to phase-corrected individual metabolite scans and upon summation to a phase-coherent averaging scheme. The interleaved navigator acquisition does not require any user interaction or supervision, while sequence efficiency is maintained.

Hall-drift induced magnetic field instability in neutron stars.

In the presence of a strong magnetic field and under conditions as realized in the crust and the superfluid core of neutron stars, the Hall drift dominates the field evolution. We show by a linear analysis that, for a sufficiently strong large-scale background field depending at least quadratically on position in a plane conducting slab, an instability occurs which rapidly generates small-scale fields. Their growth rates depend on the choice of the boundary conditions, increase with the background field strength, and may reach 10(3) times the Ohmic decay rate. The effect of that instability on the rotational and thermal evolution of neutron stars is discussed.

Screw instability in black hole magnetospheres and a stabilizing effect of field-line rotation

The screw instability of a magnetic field is a mechanism for prohibiting the generation of strongly twisted field lines on large scales. If it can work in black hole magnetospheres, the global axisymmetric structure and the main process of energy release will be significantly influenced. In this paper, we study the instability condition in the framework of the variational principle, paying special attention to the stabilizing effect due to field-line rotation against the screw-unstable modes satisfying the well-known Kruskal-Shafranov criterion. The basic formulation for the stability analysis of rotating force-free fields in Kerr geometry is provided. Then, for practical use of the analytical method, the stationary configuration is assumed to be cylindrical, and we treat the long-wave mode perturbations excited at large distances from the central black hole, where the strength of gravity becomes negligibly small. This allows us to derive clearly a new criterion dependent on the rotational angular velocity of the magnetic field lines, and the implications of the results obtained for magnetic activities of jets driven by a black hole are briefly discussed.

On the local magnetorotational instability of astrophysical jets

We present the local linear stability analysis of rotating jets confined by a toroidal magnetic field. Under the thin flux tube approximation, we derive the equation of motion for slender magnetic flux tubes. In addition to the terms responsible for the conventional instability of the toroidal magnetic field, a term related to the magnetic buoyancy and a term corresponding to the differential rotation become relevant for the stability properties. We find that the rigid rotation stabilizes while the differential rotational destabilizes the jet in a way similar to the Balbus–Hawley instability. Within the frame of our local analysis, we find that if the azimuthal velocity is of the order of or higher than the Alfven azimuthal speed, the rigidly rotating part of the jet interior can be completely stabilized, while the strong shearing instability operates in the transition layer between the rotating jet interior and the external medium. This can explain the limb-brightening effect observed in several jets. However, it is still possible to find jet equilibria that are stable all across the jet, even in the presence of differential rotation. We discuss observational consequences of these results.

Electromagnetic instabilities in unmagnetized plasmas

It is shown that local perturbations in nonuniform unmagnetized plasmas can give rise to linearly growing electromagnetic fields on both electron and ion time scales. The plasma vorticity and compressibility couple due to density inhomogeneity, giving rise to instabilities with partially transverse and partially longitudinal characteristics in electron plasmas for omega(pe)</=omega and in electron-ion plasmas for omega(pe)</=omega as well as omega<<omega(pe) (where omega(pe) is the electron plasma oscillation frequency). It is reconfirmed that the pure transverse modes due to the thermoelectric term do not appear in nonuniform unmagnetized electron plasmas. Furthermore, it has been found that the thermal fluctuations in a collisionless inhomogeneous electron plasma happen on a slower time scale of the order of 1/c(s)k (where c(s) is the ion sound speed). It seems that in the presence of a steep density gradient the ion acoustic wave becomes electromagnetic. Since the curl of electric field becomes nonvanishing in the presence of a density gradient, any nonuniform plasma can have magnetic field fluctuations in the limit omega<<omega(pe) as well. It is suggested that in the limit omega<<omega(pe) the ion dynamics becomes important and a pure electron plasma model to study magnetic field instability is not useful. The estimate for the magnitude of slowly and rapidly growing magnetic fields using the electron-ion plasma model in a special range of parameters turns out to be of the order of megagauss, in good agreement with the experimental observations.

Instability of the Stochastic Galactic Magnetic Field

We examine the effects of the stochastic galactic magnetic field on the dynamical instability of the interstellar gas and magnetic field. The large-scale random walk, or meandering, of the magnetic field exerts stresses across the average magnetic field direction, which suppress the growth of perturbations having a small wavelength normal to the field. The result is that, compared with a nonstochastic initial magnetic field, those perturbations, which grow, are significantly broadened in the direction normal to the field. Hence, the instability in a stochastic magnetic field, such as that observed in our Galaxy, should evolve into clouds that are more similar to those that are observed than are those found in the absence of the stochastic field.

A Picture of Solar Minimum and the Onset of Solar Cycle 23. I. Global Magnetic Field Evolution

NSO/Kitt Peak synoptic charts of magnetic flux in the period from 1996 to 1998 are analyzed together with time series for the 10.7 cm radio flux, sunspot number, and Mg II chromospheric index to determine the origin of the two times of minimum activity in 1996 and to study their relationships in the ascending phase of solar cycle 23. The solar activity minima in February-April and September-November of 1996 are found to correspond to periods of low magnetic activity in the southern and northern solar hemispheres, respectively. The new solar cycle becomes dominant in early 1997, but it is only in the summer of 1997 that a significant increase can be detected in the magnetic fields observations as well as in irradiance data, and by the end of 1998, the activity level has increased to a value comparable to the one observed in 1993. Using the magnetic synoptic charts, we determine the number of persistent longitude bands of active nests during this rising phase of solar cycle 23. We find an increase in the number of active nests from zero in 1996 to three by 1998. We speculate that these persistent bands of flux emergence correspond to a pattern of low-order modes of instability of the type found in the theoretical work of Gilman, Fox, and Dikpati on joint instability of latitudinal differential rotation and toroidal magnetic fields at the base of the convection zone. We argue that the observed increase in the number of active nests is consistent with the increase in the longitudinal wavenumber of magnetic instabilities in a concentrated toroidal field in the tachocline discussed in 1999 by Gilman and Dikpati.

Oscillatory instability of electromagnetically levitated solid bodies

This paper presents a linear-stability analysis of small-amplitude oscillations of a solid body suspended in an alternating magnetic field. An original theory is developed for an arbitrary configuration of the magnetic field. Stability of a solid sphere in an axisymmetric linear magnetic field is calculated analytically. Oscillations of the sphere are found to develop as the frequency of the held exceeds a certain critical threshold relative to the characteristic diffusion time of the magnetic field in the sphere. The critical frequency for the onset of oscillations in a linear magnetic field coincides with the critical frequency for the spin-up instability in a uniform magnetic field. The growth rate of oscillations attains a maximum at some frequency above the threshold and approaches zero at high frequencies.