Showing papers on "Magnetic field published in 1970"

Calculation of hysteresis losses in hard superconductors carrying ac: isolated conductors and edges of thin sheets

Abstract: Two methods of calculating hysteresis losses in hard superconductors are described. The London model is assumed in which the critical current density is taken independent of magnetic field. Losses in isolated wires of different cross section are considered but it is found that losses for solid wires vary by at most a factor of 3 for different shaped wires of the same current-carrying capacity. The loss at saturation current is usually 0·4-0·6 Ic2μ0/π. Losses at the edges of thin sheets are also calculated and a fourth-power dependence on current (for low current) is found. Three systems are examined: a slit parallel to the current in a wide sheet (Lc similar, equals μ0j2g2π3 F4/24), one pair of the edges of two wide strips set back-to-back and carrying antiparallel currents (Lc similar, equals μ0πj2s2 F4/6) and a long thin wall parallel to the current flow on a wide sheet (Lc similar, equals μ0π3j2a2 F4/3). Lc is the loss per cycle per unit length, F is the current peak as a fraction of saturation current, g the width of the slit, s the spacing of strips, a the height of the asperity and j the critical current density per unit width. All in MKS units.

Characteristics of the Trochoidal Electron Monochromator

Abstract: An electron monochromator for use in an axial magnetic field is described. Electrons are injected parallel to the magnetic field and an electric field is applied in a perpendicular direction. The electrons thus describe trochoids and drift in a direction perpendicular to both the electric and magnetic fields and disperse according to their initial velocities. An electron energy width at half‐maximum of 0.020 eV can be obtained, with a transmitted current of about 10−9 A.

VLF electric field observations in the magnetosphere

Abstract: Magnetospheric VLF electric field emissions above electron cyclotron frequency from OGO 5 observation at magnetic equator

Nonlinear effects in quantum electrodynamics. photon propagation and photon splitting in an external field.

Abstract: The effective nonlinear Lagrangian derived by Heisenberg and Euler is used to describe the propagation of photons in slowly varying but otherwise arbitrary electromagnetic fields. The group and the phase velocities for both propagation modes are calculated, and it is shown that the propagation is always causal. The photon splitting processes are also studied, and it is shown that they do not play any significant role even in very strong magnetic fields surrounding neutron stars.

On the magnetic field generated outside an inhomogeneous volume conductor by internal current sources

Abstract: The magnetocardiogram results from the detection of magnetic fields generated outside the body by electric current sources in the heart. Let the source current dipole moment per unit volume be Ji, the conductivity g , the electric potential V , and the electric field intensity E . Then it may be shown that the magnetic field H is given by either H = (1/4\pi) \int J^{i} \times abla(1/r) dv + \sum_{i} \int (g' - g")(E \times dS_{i}/r) , or H = (1/4\pi) \int J^{i} \times abla(1/r) dv + \sum_{i} \int (g' - g")V abla(1/r) \times dS_{i} , where the surface integral is over all surfaces S i separating regions of different conductivity, i.e., g ' and g ", and r is the distance from the point of measurement to the element of volume or surface. The magnetic dipole moment m is given by m = \frac{1}{2} \int r_{1} \times J^{i}dv - \frac{1}{2} \sum_{i} \int (g'-g")Vr_{1} \times dS_{i} , where r 1 is a radius vector from an arbitrary origin.

Magnetic-field re-connexion in a highly conducting incompressible fluid

Abstract: A theoretical model is proposed for the process of re-connexion of frozen-in magnetic-field lines at an X-type null point in the field. The model involves a diffusion region, immediately adjacent to the null point and an outer wave- dominated region. For the latter an exact solution to the magneto-hydrodynamic equations is obtained; for the former an approximate relationship is derived between the field-re-connexion rate, measured by the Alfven number of the incident flow, and the magnetic Reynolds number, based on the width of the diffusion region. The maximum field-re-connexion rate is determined entirely by conditions near the null point and may under suitable conditions become large. A condition for maximum conversion of magnetic energy is derived.

Analogy between the Laser Threshold Region and a Second-Order Phase Transition

Abstract: An analogy between the laser threshold region and a second-order phase transition is presented. The electric field acts as the order parameter for the laser while the atomic-population inversion plays the role of a temperature. The quantum-statistical theory of a laser including a symmetry-breaking external signal is discussed in order to establish a correspondence with the problem of a ferromagnet (treated in the molecular-field approximation) situated in an externally applied magnetic field. It is demonstrated that the results of the laser analysis may be discussed in terms of an energy function which is similar to the free energy of a thermodynamic system.

Numerical simulation of the weibel instability in one and two dimensions.

Abstract: Particle‐in‐cell simulation methods for doing full electromagnetic simulations of collisionless plasma phenomena are described and applied to the Weibel instability in one and two dimensions. Magnetic particle trapping and subsequent mode coalescing are seen. Magnetic field energy is seen to reach 10% of the total particle energy. The different electromagnetic simulation methods are compared.

Application of RF discharges to sputtering

Abstract: The operation of rf discharges is described and the internal distribution of voltages is considered. The significance of this with respect to sputtering, particularly of insulators, is then discussed. An equivalent circuit for the discharge is presented and the influence of such parameters as pressure and magnetic field on the components of this circuit is described. Finally, energy distributions for positive ions, electrons, and negative ions incident at the substrate during deposition are given.

Infrared and microwave magnetoplasma effects in semiconductors

Abstract: The interaction of electromagnetic waves with free-carrier plasmas in semiconductors and semimetals is analysed, with particular emphasis on microwave and infrared effects arising in the presence of external magnetic fields. The general frequency- and field-dependent dielectric tensor is initially developed for a single isotropic band via the Boltzmann equation in the local approximation. Solution of the electromagnetic wave equation in the tensor medium yields two normal modes, whose complex propagation constants and polarizations are determined by the microscopic medium parameters as well as the angle θ between wave vector q and applied magnetic field B0. We first consider wave propagation in the lossless (collisionless) limit, and concentrate on the properties of normal modes in the Faraday (q parallel B0) and Voigt (q perpendicular B0) geometries. Essential features of the wave interaction with the medium are conveniently set forth in `contour maps' which display zeroes and infinities of the lossless dielectric constants, indicating resonances, dielectric anomalies and black-out regions for each mode of propagation over a wide range of frequencies and fields. Losses are then explicitly incorporated into the dielectric tensor, and their effect discussed in some detail. A number of experimental examples associated with the single band model are presented, including free-carrier absorption, cyclotron resonance, Faraday and Voigt effects, helicon waves, magnetoplasma reflection and small-particle effects. The presentation is subsequently generalized to more complicated systems. The dielectric tensor is developed for a multiple-carrier plasma and for anisotropic bands. A variety of new effects is seen to arise, including hybrid resonances, tilted-orbit resonances and Alfven wave propagation. `Contour maps' of appropriate lossless dielectric constants are again found convenient in discussing these new features. Effects of spatial dispersion (nonlocal phenomena) and of orbital quantization on the high-frequency response of a free-carrier system are then considered. The contribution of the polar lattice, which gives rise to a vast array of coupled magnetoplasma-phonon modes, is finally examined. A further elaboration of certain topics arising in this review is presented in an appendix, including a detailed discussion of electron dynamics, the `polariton' formalism, fundamentals of Kramers-Kronig analysis and magneto-optics of birefringent media.

Studies of chemical exchange by nuclear magnetic relaxation in the rotating frame

Abstract: The exchange of protons between sites with different chemical shift is studied by means of N.M.R. relaxation time measurements (T 1ρ ) in the presence of an r.f. magnetic field. The system studied is chair-to-chair isomerization in cyclohexane. The exchange rate and chemical shift are measured in the temperature range 215°k to 250°k. The method is compared with other N.M.R. techniques for studying chemical exchange and is found to have advantages particularly at high exchange rates.

Auroral arcs: Result of the interaction of a dynamic magnetosphere with the ionosphere

Abstract: A model of auroral arcs is presented. It is assumed that the magnetic field lines into the auroral oval are loaded with kev electrons, that precipitating auroral electrons locally constitute a net field-aligned current, and that currents close in the outer magnetosphere by polarization currents. The model predicts that a flux tube convecting through the oval will undergo a highly nonlinear oscillation that produces standing waves, the auroral arcs. The conditions to be satisfied are (1) Ohm's law in the ionosphere, (2) electron number conservation in the ionosphere, (3) electric current continuity, (4) the tendency for electric fields to map between ionosphere and magnetosphere. The physics of condition 4 is not understood, but it is probable that arc-like solutions exist for several models. A specific model, including perfect mapping of electric fields, is studied. The solutions to this model closely resemble the arcs. Predicted in agreement with observation are arc thickness, inter-arc spacing, and the electric field behavior. The thickness and the spacing are functions of both the amplitude of the oscillation and the physical properties of the system. However, thickness times spacing is a function of the physical properties only, and the thickness divided by the spacing is a function of amplitude only. Presumably these and other quantitative relationships can be checked by observations.

Propagation of High Current Relativistic Electron Beams

Abstract: Theoretical self‐consistent relativistic electron beam models are developed which allow the propagation of relativistic electron fluxes in excess of the Alfven–Lawson critical‐current limit for a fully neutralized beam. Development of a simple, fully relativistic, self‐consistent equilibrium is described which can carry arbitrarily large currents at or near complete electrostatic neutralization. A discussion of a model for magnetic neutralization is presented wherein it is shown that large numbers of electrons from a background plasma are counterstreaming slowly within the beam so that the net current density in the system, and therefore, the magnetic field, is nearly zero. A solution of an initial‐value problem for a beam–plasma system is given which indicates that magnetic neutralization can be expected to occur for plasma densities that are large compared with beam densities. It is found that the application of a strong axial magnetic field to a uniform beam allows propagation regardless of the magnitude of the beam current. Some comparisons are made with recent experimental data.

Magnetic Field Splitting of the Quasiparticle States in Superconducting Aluminum Films

Abstract: Magnetic field splitting of the quasiparticle energy states in superconducting aluminum films has been observed in a tunneling experiment. The magnitude of the splitting was found to be $2\ensuremath{\mu}H$, and is attributed to the magnetic moment of the quasiparticles. The observed tunneling conductance is in qualitative agreement with theory.

Microwave Behavior of Partially Magnetized Ferrites

Abstract: The high‐frequency permeability of partially magnetized ferrites is calculated for some simple domain configurations, comprising only ``up''‐ and ``down''‐domains. The method used is based upon the magnetostatic approximation and neglects exchange effects, but is otherwise substantially rigorous. The components of the effective permeability tensor (ratio of average induction to average magnetic field) in general depends upon details of the domain configuration in addition to the net dc magnetization. When the dc magnetization is cycled between the two states of complete magnetization the high frequency permeability, considered as a function of the dc magnetization, in general shows hysteresis. Detailed calculations of the high‐frequency permeability have been carried out for the case in which the domain configuration is cylindrically symmetric, i.e., invariant under rotation around the direction of magnetization. For any such domain configuration the two relevant components μeff and κeff of the effective ...

Refraction in Stratified, Anisotropic Media*

Abstract: The Abeles treatment of refraction in stratified isotropic media is extended to stratified anisotropic media. The present treatment is restricted to linear refraction problems with incident light assumed to be plane waves of infinite extent. A mathematical restriction excludes application to singular cases. Subject to these restrictions, the treatment is quite generally applicable. It is applied to the case of an isotropic semiconductor in an external magnetic field; results agreeing with published experimental data and with an alternative method of calculation for normal incidence are obtained.

Model study of plasmapause motion

Abstract: The ambient plasma in the equatorial plane is predominantly subject to the E×B drift. By approximating the earth's magnetic field by a dipole, characteristic steady state streamlines in the equatorial plane are determined, assuming the interaction between the solar wind and the magnetosphere is characterized by a constant electric field directed from dawn to dusk in the equatorial plane. The steady state plasmapause corresponds to the stagnation streamline in this flow. If the magnitude of the dawn-dusk field is suddenly increased, the plasmasphere bulge moves toward the sun. By suddenly decreasing the magnitude of this field, the bulge can be made to corotate with the earth. The model computations indicate that the spatial configuration of the plasmapause can be very complex, especially near the bulge, because its position depends upon the past history of the magnetosphere.

On the re-connexion of magnetic field lines in conducting fluids

Abstract: Magnetic field lines reconnection in steady incompressible hydromagnetic two dimensional flow, formulating governing equations with cylindrical polar coordinates

The theory of induced voltage electromagnetic flowmeters

Abstract: The performance of an electromagnetic flowmeter head is assessed in terms of a weight vector W such that the output voltage ∝ ∫ v. Wdτ, where v is the velocity and τ the flowmeter volume. The condition curl W = 0 with W → 0 at ∞ is shown to be necessary and sufficient for the velocity to depend only on the flow rate and not on the flow pattern. A class of such ‘ideal’ meters is described. It is shown that meters with point electrodes can never be ideal but may, with considerable complication of the magnetic field, be made immune to asymmetric velocity-profile variations if the flow is rectilinear.

Mössbauer study of the Ni–Zn ferrite system

Abstract: Mossbauer spectra of 57Fe in the nickel–zinc ferrite system (ZnO)x(NiO)1−xFe2O3 have been obtained, at room temperature and at 77 °K, in zero magnetic field and also in a longitudinal magnetic fiel...

Turbulent dynamo action at low magnetic Reynolds number

Abstract: The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

Dynamo action associated with random inertial waves in a rotating conducting fluid

Abstract: It is shown that a random superposition of inertial waves in a rotating conducting fluid can act as a dynamo, i.e. can systematically transfer energy to a magnetic field which has no source other than electric currents within the fluid. Dynamo action occurs provided the statistical properties of the velocity field lack reflexional symmetry, and this occurs when conditions are such that there is a net energy flux (positive or negative) in the direction of the rotation vector Ω.If the magnetic field grows from an infinitesimal level, then the mode of maximum growth rate dominates before the back-reaction associated with the Lorentz force becomes significant. This mode is first determined, and then the back-reaction associated with it alone is analysed. It is shown that the magnetic energy grows exponentially during the stage when the Lorentz forces are negligible, then reaches a maximum depending on the values of the parameters \[ R_m = u_0 l/\lambda,\quad Q = \Omega l^2/\lambda, \] (u0 = initial r.m.s. velocity, l = length scale characteristic of the velocity field, λ = magnetic diffusivity) and ultimately decays as t−1 (equation (5.15)). This decay is coupled with a decay of the velocity field due to ohmic dissipation, and it occurs because there is no external source of energy for the fluid motion.

Penetration of low‐energy protons deep into the magnetosphere

Abstract: By using a simple model with constant convection electric field and a dipole magnetic field, plasma flow patterns are calculated with the convection fields as scale factors. Unlike other particle trajectories, the flow patterns for protons with certain relative magnetic moments show double forbidden regions: one is composed of orbits that circle the earth; the other is composed of orbits that do not circle the earth. These protons can penetrate very close to the earth through the space between the two forbidden regions. The calculations based on the model of constant electric field with charge exchange as a loss mechanism indicate that protons of a few hundred electron volts convected in from the tail to L = 3–4 could be responsible for the storm-time ring currents.

Nonlinear Stabilization of High‐Frequency Instabilities in a Magnetic Field

Abstract: It is shown that the broadening of wave‐particle resonances by the random motion of particles in a turbulent electric field may determine the saturation level of a variety of high‐frequency instabilities. Secular changes of the guiding center positions, cyclotron radii, and phase angles give rise to resonance broadening and diffusion, similar to that produced by collisional scattering. The field dependent broadening is expressed in terms of resonance functions which replace the familiar resonant denominators of the linear theory. Resonance functions are derived in a simple manner from the solution of a Brownian motion problem, leading to an expression in terms of diffusion coefficients. The close resemblance of the theory to quasilinear theory and the linear theory including collisions allows one to start from a linear stability analysis and then assess the importance of nonlinear effects. This method is illustrated by the determination of the saturation level of cyclotron instabilities from the condition of vanishing nonlinear growth rate.