Showing papers on "Magnetic field published in 1972"

Topological dissipation and the small-scale fields in turbulent gases.

Abstract: It is shown that a large-scale magnetic field possesses a hydrostatic equilibrium only if the pattern of small-scale variations is uniform along the large-scale field. Thus equilibrium obtains only if the variations in the field consist of simple twisting of the lines, with the twists extending uniformly the full length of the field. Any more complicated topology, such as two or more flux tubes wrapped around each other to form a rope, or braided or knotted flux tubes, is without equilibrium, no matter what fluid pressures are applied along the individual lines of force. The result is rapid dissipation and field-line merging, which quickly reduces the topology to the simple equilibrium form. The effect explains the absence of strong small-scale fields in the solar photosphere and in interstellar space in spite of the vigorous turbulence.

Polar-cap electric field distributions related to the interplanetary magnetic field direction

Abstract: The correlations between the azimuthal direction of the interplanetary magnetic field and the most simple polar cap signatures are discussed. Only the spatial distribution of the dawn-dusk polar cap field is considered. For each OGO 6 traverse across the northern or southern polar cap, the simultaneous values of the interplanetary magnetic field in solar-equatorial coordinates were recorded by the Explorer 33 magnetometer. Histograms of these values are presented and are discussed. The high degree of correlation with the longitudinal angle indicates that the relative geometry of the interplanetary magnetic field and magnetospheric magnetic fields must be fundamental to explaining the distribution of polar cap electric fields. The sign of the solar-equatorial component perpendicular to the sun-earth line appears to be a more critical parameter than the sign of the component toward the sun. The Svalgaard-Mansurov correlation and the correspondence between fast convection and parallel magnetospheric and interplanetary magnetic fields are described.

Origin of Magnetic Fields in Astrophysics (Turbulent "Dynamo" Mechanisms)

Abstract: We consider the generation of magnetic fields under astrophysical conditions. Principal attention is paid to "dynamo" mechanisms, i.e., mechanisms in which the energy of the magnetic field is drawn from the kinetic energy of plasma motion. The important role played by turbulent dynamo mechanisms is emphasized. The dynamo problem itself is divided into two: 1) generation of regular magnetic fields (i.e., the dynamo mechanism of fields having scales commensurate with the cosmic object itself by turbulent pulsations); 2) generation of random fields. A review is presented of the existing theories for the generation of regular fields (reference is made, in particular, to the work of Steenbeck and co-workers and of Parker), and a generalization of the existing results to include large magnetic Reynolds number Rem, characteristic of cosmic plasma, is indicated. Astrophysical examples are given. The existing theories in the dynamics of random fields are also reviewed. Results are presented on the turbulent dynamo in the presence of acoustic turbulence. Analogies with the question of excitation of vortices in a field of acoustic turbulence is indicated. The question of the turbulent dynamo in the field of "Kolmogorov" turbulence is discussed. Finally, an essential problem is that of the steady-state field produced by a nonlinear effect. It is shown that in the presence of a non-weak field there appears a gyrotropy acting in opposition to the action of the usual rotational gyrotropy. This observed gyrotropy is called magnetic and can cause nonlinear stabilization of the magnetic field.

On Practical Representation of Magnetic Field

Abstract: Various manners of determination of a magnetic field are reviewed briefly from the standpoint of practicality and uniqueness. Then a practical representation of magnetic fields in terms of a class of force-free magnetic field is described. The proposed scheme is based on the physical consideration that in the chromosphere and lower corona a quasistatic magnetic field must be nearly force-free and that for the class of force-free magnetic field, i.e., ∇×B=αB with α = constant, the magnetic field can be determined uniquely from the observed distribution of the vertical component of a magnetic field. The applicability of the representation is demonstrated by examples and the limitations are discussed.

Theory of Surface Magnetoplasmons in Semiconductors

Abstract: A theory of surface magnetoplasmons in semiconductors is developed with the inclusion of retardation for the geometry in which the magnetic field is parallel to the surface and the direction of propagation is perpendicular to the magnetic field. If the background dielectric constant ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$ lies in a suitable range for a given value of the magnetic field, gaps appear in the dispersion relation for the surface magnetoplasmons. The possible experimental observation of these gaps is discussed.

On the Filamentary Nature of Solar Magnetic Fields

Abstract: A method is presented for obtaining information about the unresolved filamentary structure of solar magnetic fields. A comparison is made of pairs of Mount Wilson magnetograph recordings made in the two spectral lines Fei 5250 A and Fei 5233 A obtained on 26 different days. Due to line weakenings and saturation in the magnetic filaments, the apparent field strengths measured in the 5250 A line are too low, while the 5233 A line is expected to give essentially correct results. From a comparison between the apparent field strengths and fluxes and their center to limb variations, we draw the following tentative conclusions: (a) More than 90 % of the total flux seen with a 17 by 17 arc sec magnetograph aperture is channeled through narrow filaments with very high field strengths in plages and at the boundaries of supergranular cells. (b) An upper limit for the interfilamentary field strength integrated over the same aperture seems to be about 3 G. (c) The field lines in a filament are confined in a very small region in the photosphere but spread out very rapidly higher up in the atmosphere. (d) All earlier Mount Wilson magnetograph data should be multiplied by a factor that is about 1.8 at the center of the disk and decreased toward the limb in order to give the correct value of the longitudinal magnetic field averaged over the scanning aperture.

Force-free magnetic-field structures and their role in solar activity.

Abstract: Magnetic-field structures in solar active regions are expected to be substantially force-free. A method is proposed for calculating such structures by numerical methods. The method is applied to the study of the magnetic-field pattern associated with a sunspot of one polarity surrounded by a magnetic region of opposite polarity when the sunspot rotates with respect to the surrounding region. Rotation introduces a toroidal component of magnetic field, and the associated pressure leads to inflation of the magnetic field pattern. If the differential rotation exceeds about 180 deg, the force-free magnetic field has energy greater than that of an open magnetic-field configuration with the same photospheric boundary conditions. It is concluded that, beyond this point, the force-free field structure is metastable and can be converted into an open field structure by an explosive MHD instability.

Theory and Computer Experiment on Self-Trapping Instability of Plasma Cyclotron Waves

Abstract: A theory explaining the self‐trapping instability (modulational instability) of plasma cyclotron waves is developed and the results are compared with computer experiments using a sheet current model. The observed growth rate at an initial phase of the instability is in rough agreement with that given by perturbation theory. However, as the level of the modulation increases, the rate of the growth of the modulation increases due to excitation of additional side bands, and finally, the carrier wave is found to collapse suddenly leading to rapid thermalization. The cause of the sudden collapse of the wave is attributed to the crossing of particles which are accelerated in the direction parallel to the ambient magnetic field by a large pressure gradient force, ∇(B⊥2/2μ0), developed by the instability, where B⊥ is the transverse magnetic field associated with the wave.

Theory of Spin Resonance in Dilute Magnetic Alloys

Abstract: The scheme of Kadanoff and Baym is shown to be useful for the rigorous derivation of Bloch or Boltzmann equations for spin systems. The scheme is applied to a system of conduction electrons in a metal interacting via an exchange interaction $J$ with a low density of local spins. The coupled Bloch equations appropriate to conduction-electron spin resonance are derived rigorously to second order in $J$. The prominent features of the derived equations are that (i) the disturbed magnetizations are shown to relax to the instantaneous local equilibrium magnetization with the result that correct static susceptibilities are obtained, (ii) the instantaneous magnetizations are not proportional to the effective magnetic fields causing the magnetizations to precess, and (iii) the equations are consistent with conservation of the total magnetization.

Suppression of the kink instability for magnetic flux ropes in the chromosphere

Abstract: Energy storage in chromospheric flux ropes is discussed, in the context of solar flares. The structure is represented by a cylindrically symmetric magnetic field of finite length. The field is assumed to be approximately force-free. The stability of the field to a kink perturbation is investigated. Flux ropes are rooted in dense photospheric material. So the ends of the field lines are taken to be fixed on rigid boundaries for all perturbations. An energy perturbation method is used and the boundary conditions give a stabilizing effect. It is shown that for a moderate degree of twisting the fields are stable to a kink perturbation. Thus energy can be stored in cylindrical fields prior to release in a solar flare.

Hydromagnetic convection in a rapidly rotating fluid layer

Abstract: The linear stability of a rotating, electrically conducting viscous layer, heated from below and cooled from above, and lying in a uniform magnetic field is examined, using the Boussinesq approximation. Several orientations of the magnetic field and rotation axes are considered under a variety of different surface conditions. The analysis is, however, limited to large Taylor numbers, T , and large Hartmann numbers, M . (These are non-dimensional measures of the rotation rate and magnetic field strength, respectively.) Except when field and rotation are both vertical, the most unstable mode at marginal stability has the form of a horizontal roll whose orientation depends in a complex way on the directions and strengths of the field and angular velocity. For example, when the field is horizontal and the rotation is vertical, the roll is directed parallel to the field, provided that the field is sufficiently weak. In this case, the Rayleigh number, R (the non-dimensional measure of the applied temperature contrast) must reach a critical value, R c , which is O ( T 2/5 ) before convection will occur. If, however, the field is sufficiently strong [ T = O ( M 4 )], the roll makes an acute angle with the direction of the field, and R c = O ( T 1/2 ), i.e. the critical Rayleigh number is much smaller than when the magnetic field is absent. Also, in this case the mean applied temperature gradient and the wavelength of the tesselated convection pattern are both independent of viscosity when the layer is marginally stable. Furthermore, the Taylor-Proudman theorem and its extension to the hydromagnetic case are no longer applicable even qualitatively. Over the interior of the layer, however, the Coriolis forces to which the convective motions are subjected are, to leading order, balanced by the Lorentz forces. The results obtained in this paper have a bearing on the possibility of a thermally driven steady hydromagnetic dynamo.

Interaction of Relativistic Particles and Free Electromagnetic Waves in the Presence of a Static Helical Magnet

Abstract: It is shown that a particle passing along the axis of a helical magnet (in which the field is perpendicular to the axis and rotating as a function of position along the magnet) can be continuously accelerated by its interaction with circularly polarized radiation passing in the same direction. An example is given in which an electron is accelerated to 10 GeV, using a laser of 1014 W. A second example shows how pions and kaons might be separated at momenta over 1000 GeV. It is further shown that bunched charged particles passing down the helical magnet will radiate coherent circularly polarized electromagnetic waves, and it is speculated that the required bunching may under some circumstances be self‐generating. An example is shown in which a 10‐A current of 15‐MeV electrons is used to generate a 75‐MW beam of 10‐μ radiation.

Alfven waves in inhomogeneous magnetic fields

Abstract: It has been found that the rigorous and general treatment of electrostatic oscillations in a cold plasma of nonuniform density given by Barston can be extended to the case of Alfven waves in an ideal fluid in the presence of a class of inhomogeneous magnetic fields.

Effect of the magnetic field ripple on diffusion in Tokamaks

Abstract: The magnetic field modulation due to the discrete nature of the field coils in a Tokamak leads to additional particle trapping. The resulting diffusion is evaluated and compared with the neoclassical diffusion. The two diffusion rates are found to be comparable in existing Tokamaks. The limit on the field ripple below which ripple diffusion should be negligible in the next generation of machines is evaluated.

Theory of modulation effects in resonant-nuclear-disorientation experiments. III

Abstract: Earlier calculations of the effects of a resonant, frequency-modulated, rf field and spin-lattice relaxation on the emission of radiations from thermally oriented radioactive nuclei are extended. A purely magnetic interaction is assumed for the nuclei. Simple formulas, applicable for any nuclear spin, are derived for the effects of fast modulation on the nuclear-orientation parameters ${B}_{\ensuremath{ u}}$. Also an analytic expression is derived for static nuclear orientation in a magnetic field at high temperatures.

Transverse Velocity Shear Instabilities within a Magnetically Confined Plasma

Abstract: Strong shear in the plasma rotation is produced in the interior of a magnetically confined Q‐machine plasma column by means of an externally controlled nonuniform radial electric field. Coherent low‐frequency oscillations are observed localized in the velocity shear layer, which contains up to seven ion gyroradii. The observed oscillations are shown to result from the transverse Kelvin‐Helmholtz instability by the good agreement with finite‐Larmor‐radius fluid theory for the mode frequencies, radial dependences of the potential and density fluctuations, and the mode structure at large magnetic field and small rotation. At large electric fields the low‐frequency Kelvin‐Helmholtz modes are completely suppressed. Simultaneously, there appear oscillations with ω>ωc, whose properties are described by the fluid equations when extended to arbitrary rotation and wave frequencies.

Ground and first excited states of excitons in a magnetic field

Abstract: An exact calculation of the ground state and of the first excited state withm = 0 and even parity of a hydrogenic system in a magnetic field is described, and results are given for the energy and the main features of the wave functions. Tor the excited state the shape of the nodal surface is given, and it is shown that in this case no contradiction exists between the noncrossing rule and the nodal-surface criterion for the connection of the levels in the low- and high-field regions.

The polarization of an e.m. wave propagating in a plasma with magnetic shear. The measurement of poloidal magnetic field in a Tokamak

Abstract: Studies the evolution of the polarization state of an electromagnetic wave propagating in a non-homogeneous plasma with a sheared magnetic field. A differential equation is given describing such evolution in the case of slowly varying plasma parameters. Assuming the model of a cold collisionless plasma one obtains an approximate solution giving the output polarization as a function of the input one and of the plasma parameters along the path. These results are applied to the case of a Tokamak; it is shown that in the some particular cases the output polarization is a relatively simple functional of the poloidal magnetic field. Therefore measurements of polarization can be used to determine the distribution of the poloidal field.

Electrical apparatus generating a low frequency, alternating magnetic field for promoting the growth of bone and other body tissues

Abstract: The growth or repair of fractured bones or the growth of other body tissues is promoted by means of a coil which is applied to produce a magnetic field at the site in which growth is to be encouraged. The coil is supplied with a low frequency alternating voltage below 50 Hz. A device is applied to the body or implanted in the body in order to concentrate the magnetic field produced by the coil.

Growth rates of instabilities of a diffuse linear pinch.

Abstract: In order to obtain growth rates of magnetohydrodynamic instabilities, the equation of motion of a diffuse linear pinch is solved analytically in the tokomak approximation and numerically without approximation. The growth rates of kinks are calculated for the Lundquist field. The constant‐pitch magnetic field is shown to be unstable to quasi‐kinks, quasi‐interchanges, and pure interchanges which dominate, respectively, at increasing values of the negative pressure gradient. Analytical expressions and numerical values for the growth rates of these modes are given. Interchanges in a sheared magnetic field are investigated numerically and checked by means of perturbation theory.

Radiative polarization of electrons in storage rings

Abstract: Polarization of electrons arising as the result of radiation during extended motion in a magnetic field is considered. A calculation is made with the quasiclassical operator method of the probability of a radiative transition in a magnetic field with spin flip, including the case of a nonuniform magnetic field. The kinetic equation is obtained for polarization of electrons in an external field with inclusion of radiation effects, and this is used to analyze the kinetics of radiative polarization. Effects are discussed which lead to depolarization of an electron beam in motion in a nonuniform magnetic field, and means of suppressing these effects and also of intentional depolarization of a beam are pointed out. Means are discussed for measurement of the transverse polarization of high energy electrons, and a description is given of an experiment in which the first indication of the existence of the radiative polarization effect has been obtained.

A Kinematic Theory of Large Magnetic Reynolds Number Dynamos

Abstract: An asymptotic analysis is made of the magnetic induction equation for certain flows characterized by a large magnetic Reynolds number R . A novel feature is the hybrid approach given to the problem. Advantage is taken of a combination of Eulerian and Lagrange coordinates. Under certain conditions the problem can be reduced to solving a pair of coupled partial differential equations dependent on only two space coordinates (cf. Braginskii 1964 a ). Two main cases are considered. First the case is examined, in which the production of azimuthal magnetic field from the meridional magnetic field by a shear in the aximuthal flow is negligible. It is shown that a term J (analogous to electric current) is related linearly to the vector B which determines the magnetic field. (Note that B is not the magnetic field vector: see (1.33) and (2.35 b ).) The current J is likely to sustain dynamo action. Secondly, the case is considered, in which shearing of meridional magnetic field is the principal mechanism for creating the azimuthal magnetic field and the effect described above is one mechanism for creating meridional magnetic field from the azimuthal magnetic field. It is shown that the term J is not only linearly related to B , but has an additional contribution P x (V x B ), where P is characterized by the flow (see (4.15)). Both these effects have been predicted previously in theories of dynamo action produced by turbulent motions. Under certain restrictive conditions the resulting equations in the second case reduce to Braginskil’s (1964 a , b ) formulation for nearly symmetric dynamos. The words azimuthal and meridional are not used here in the usual sense. The difference in terminology is a consequence of a coordinate transformation.

A two-fluid solar wind model with anisotropic proton temperature

Abstract: A two-fluid model of the solar wind with anisotropic proton temperature and allowing for extended coronal proton-heating is considered for the case of a purely radial and of a spiral magnetic field. Proton-proton Coulomb-collisions together with a spiral interplanetary magnetic field are found to be sufficient to reduce the thermal anisotropy in the proton gas to a value in agreement with observations. Reasonable values are obtained for the flow-velocity, number density and the protontemperature near the orbit of the Earth.

The electromagnetic fields of a subterranean cylindrical inhomogeneity excited by a line source

Abstract: The anomalous fields from a buried cylindrical inhomogeneity in an otherwise uniform half-space are analyzed. The problem is rendered two-dimensional by assuming that the uniform line source of current is parallel to the subsurface cylinder. The multipole scattered field coefficients are obtained from the numerical solution to the associated singular Fredholm integral equation of the second kind. The horizontal magnetic field amplitude, the vertical magnetic field phase, and the amplitude and phase of the ratio of horizontal to vertical magnetic fields are shown to be diagnostic of the location of the inhomogeneity. The results have possible applications to electromagnetic location in mine rescue operations and to geophysical prospecting.

Magnetoplasma Surface Waves in Metals

Abstract: The effect of a dc magnetic field of arbitrary magnitude and orienation on surface plasmons in a metal or degenerate semiconductor is studied in the "nonretarded" limit.