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Application of the sine-Poisson equation in solar magnetostatics
Solutions of the sine-Poisson equations are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model (j) is directed along the x-axis, where x is the horizontal ignorable coordinate; (j) varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. Solutions for the magnetostatic potential A corresponding to the one-soliton, two-soliton, and breather solutions of the sine-Gordon equation are studied. Depending on the values of the free parameters in the soliton solutions, horizontally periodic magnetostatic structures are obtained possessing either a single X-type neutral point, multiple neural X-points, or solutions without X-points.
An Analysis of Characteristics of Magnetostatic Waves Propagating in Nonhomogeneous Fields Across the Ferrospinel Film Thickness
The amplitude-frequency characteristics (AFCs) of magnetostatic waves in the films of magnesium-manganese ferrospinels with nanostructured inhomogeneities are discussed. A common effect, observed in the film AFCs under different process conditions, is the ‘oscillations of propagation’ of magnetostatic waves as a function of the frequency. The oscillation pattern is thought to depend on the inhomogeneous exchange parameters and the surface anisotropy constants. The wave instability is characterized by the resonant interaction of the dipole magnetostatic waves with the surface spin waves. It is shown that the ferrospinel films with periodic nanostructured inhomogeneities of 30–40 nm could be treated as magnon crystals. An inclusion of the inhomogeneity into consideration allows one to provide reasoning for the formation of the rejection bands within the range 9–12 GHz, whose frequencies correspond to Bragg frequencies.
Iterative spectral method for solving electrostatic or magnetostatic problems in complex and evolving heterostructures
Electrostatic or magnetostatic problems involving complex heterogeneity are nontrivial for modeling and simulation. Most existing numerical methods focus on sharp interface models and the computational cost increases with increasing complexity of the geometry. Here we develop an iterative spectral method, the bound charge successive approximation algorithm, to solve electrostatic or magnetostatic heterogeneity problems in the context of diffuse-interface modeling. As tests and verifications, this algorithm is applied to calculation of the depolarization factor of an ellipsoid, and simulation of random dielectric mixtures and the dielectophoretic motion of multiple particles. The algorithm shows excellent efficiency and the computational cost mainly depends on the permittivity or permeability contrast in the whole system, regardless of the complexity of the geometry. Specifically, for evolving heterostructures the solution of bound charge in one time step can be used as input for the next, which could further significantly shorten the iteration (approximation) process, making it practical to simulate the long-range electrostatic or magnetostatic interaction in complex and evolving heterostructures.
Quasistatic evolution of magnetostatic coronal structures
Four separate but related studies of coronal magnetostatic equilibria under a variety of boundary conditions and distributions of coronal current are reviewed. Physically, all four studies assume an axisymmetric corona whose radial magnetic field at the coronal base is dipolar. Electric currents in the model coronas are assumed to flow in the azimuthal direction, giving rise to Lorentz forces that must be balanced by pressure gradients and gravity. Mathematically, such coronas are described by the equation of magnetostatic force balance and Ampere's law. Although highly idealized, the axisymmetric magnetostatic models described provide insights into the behavior of a variety of coronal structures. The models show how more realistic current sheet boundary conditions and coronal density variations may be modeled.
On the magnetostatics of chains of magnetic nanoparticles.
A novel approach is presented for the computation of the magnetostatic energy of straight and bent chains of identical, uniformly magnetized particles of arbitrary shape. The formalism relies on the concept of the magnetometric tensor field, and allows for closed form expressions for the magnetostatic energy, demagnetization factor, Young's modulus, and bending modulus of chains in terms of the shape amplitude of the particles. Analytical solutions are presented for straight chains of spheres, cubes, and cylinders, and for bent chains of spheres. Numerical results include chains of octahedra, tetrahedra, cuboctahedra, and bi-cones. The axial demagnetization factor for the bi-cone shape is derived in analytical form. An approximate energy expression, using the full shape-dependent interaction formalism for short separation distances, and the standard dipolar interaction expression for larger distances, is introduced.
Effects of Magnetic Nanoparticles and External Magnetostatic Field on the Bulk Heterojunction Polymer Solar Cells
The price of energy to separate tightly bound electron-hole pair (or charge-transfer state) and extract freely movable charges from low-mobility materials represents fundamental losses for many low-cost photovoltaic devices. In bulk heterojunction (BHJ) polymer solar cells (PSCs), approximately 50% of the total efficiency lost among all energy loss pathways is due to the photogenerated charge carrier recombination within PSCs and low charge carrier mobility of disordered organic materials. To address these issues, we introduce magnetic nanoparticles (MNPs) and orientate these MNPS within BHJ composite by an external magnetostatic field. Over 50% enhanced efficiency was observed from BHJ PSCs incorporated with MNPs and an external magnetostatic field alignment when compared to the control BHJ PSCs. The optimization of BHJ thin film morphology, suppression of charge carrier recombination, and enhancement in charge carrier collection result in a greatly increased short-circuit current density and fill factor, as a result, enhanced power conversion efficiency.
Wave function for harmonically confined electrons in time-dependent electric and magnetostatic fields
We derive via the interaction “representation” the many-body wave function for harmonically confined electrons in the presence of a magnetostatic field and perturbed by a spatially homogeneous time-dependent electric field—the Generalized Kohn Theorem (GKT) wave function. In the absence of the harmonic confinement – the uniform electron gas – the GKT wave function reduces to the Kohn Theorem wave function. Without the magnetostatic field, the GKT wave function is the Harmonic Potential Theorem wave function. We further prove the validity of the connection between the GKT wave function derived and the system in an accelerated frame of reference. Finally, we provide examples of the application of the GKT wave function.
Magnetostatic effects on switching in small magnetic tunnel junctions
Perpendicular CoFeB/MgO/CoFeB magnetic tunnel junctions with diameters under 100 nm are investigated by conductive atomic force microscopy. Minor loops of the tunnel magnetoresistance as a function of applied magnetic field reveal the hysteresis of the soft layer and an offset due to the magnetostatic field of the hard layer. Within the hysteretic region, telegraph noise is observed in the tunnel current. Simulations show that in this range, the net magnetic field in the soft layer is spatially inhomogeneous, and that antiparallel to parallel switching tends to start near the edge, while parallel to antiparallel reversal favors nucleation in the interior of the soft layer. As the diameter of the tunnel junction is decreased, the average magnitude of the magnetostatic field increases, but the spatial inhomogeneity across the soft layer is reduced.
Diffusive cosmic-ray acceleration at relativistic shock waves with magnetostatic turbulence
The analytical theory of diffusive cosmic-ray acceleration at parallel stationary shock waves with magnetostatic turbulence is generalized to arbitrary shock speeds V{sub s}=β{sub 1}c, including, in particular, relativistic speeds. This is achieved by applying the diffusion approximation to the relevant Fokker–Planck particle transport equation formulated in the mixed comoving coordinate system. In this coordinate system, the particle's momentum coordinates p and μ=p{sub ∥}/p are taken in the rest frame of the streaming plasma, whereas the time and space coordinates are taken in the observer's system. For magnetostatic slab turbulence, the diffusion–convection transport equation for the isotropic (in the rest frame of the streaming plasma) part of the particle's phase space density is derived. For a step-wise shock velocity profile, the steady-state diffusion–convection transport equation is solved. For a symmetric pitch-angle scattering Fokker–Planck coefficient, D{sub μμ}(−μ)=D{sub μμ}(μ), the steady-state solution is independent of the microphysical scattering details. For nonrelativistic mono-momentum particle injection at the shock, the differential number density of accelerated particles is a Lorentzian-type distribution function, which at large momenta approaches a power-law distribution function N(p⩾p{sub c})∝p{sup −ξ} with the spectral index ξ(β{sub 1})=1+[3/(Γ{sub 1}√(r{sup 2}−β{sub 1}{sup 2})−1)(1+3β{sub 1}{sup 2})]. For nonrelativistic (β{sub 1}≪1) shock speeds, this spectral index agrees with the known result ξ(β{sub 1}≪1)≃(r+2)/(r−1), whereas for ultrarelativistic (Γ{sub 1}≫1) shock speeds the spectral index value is close to unity.
Critical role of isopotential surfaces for magnetostatic ponderomotive forces
By producing localized wave regions at the ends of an open-field-line magnetic confinement system, ponderomotive walls can be used to differentially confine different species in the plasma. Furthermore, if the plasma is rotating, this wall can be magnetostatic in the laboratory frame, resulting in simpler engineering and better power flow. However, recent work on such magnetostatic walls has shown qualitatively different potentials than those found in the earlier, nonrotating theory. Here, using a simple slab model of a ponderomotive wall, we resolve this discrepancy. We show that the form of the ponderomotive potential in the comoving plasma frame depends on the assumption made about the electrostatic potential in the laboratory frame. If the laboratory-frame potential is unperturbed by the magnetic oscillation, one finds a parallel-polarized wave in the comoving frame, while if each field line remains equipotential throughout the perturbation region, one finds a perpendicularly polarized wave. As a result, this in turn dramatically changes the averaged ponderomotive force experienced by a charged particle along the field line, not only its scaling, but also its direction.
Coupled Electronic–Nuclear Magnetostatic Oscillations in Magnetic Materials
Magnetization dynamics in spheroidal ferromagnetic samples is studied theoretically. It is shown that, in a magnetostatic approximation, electronic-nuclear magnetostatic modes with a discrete spectrum of eigen oscillations exist in such samples. The structure and the field dependence of the frequencies of these oscillations are substantially dependent on the parameter of the spheroid shape that is the ratio of it’s axes and also on the external magnetic field value. In a certain region of values of these parameters, the dependence of the eigenfrequencies of the system on them becomes nontrivial. The external field strength and the sample shape determine not only the eigenfrequencies in the system, but also the number of the eigenmodes. In addition, for each of the eigenmodes, there exists a “forbidden” region of magnetic fields and shape parameters in which this mode cannot be observed.
Diffusive cosmic ray acceleration at relativistic shock waves with magnetostatic turbulence. II. Influence of a finite downstream medium
The diffusive acceleration of relativistic cosmic rays at parallel shock waves with magnetostatic turbulence and a finite size of the downstream medium is investigated. For ultrarelativistic shock speeds with Lorentz factor Γ{sub 1}≫1, both the differential momentum spectrum at the shock and the volume-integrated momentum spectrum are power-law distribution functions with different spectral indices as compared to the case of an infinitely extended downstream medium. However, the spectral differences are only modest as compared to the case of nonrelativistic shocks. The behavior of the momentum spectrum of shock-accelerated particles depends sensitively on the relativistic shock wave Peclet number G(p)=τ{sub D}(p)/τ{sub C}, i.e., the ratio between the diffusion and convection timescales of cosmic rays to propagate from the shock position to the downstream boundary z {sub 0}. For large values of G(p)≫1 the free-escape boundary has no influence on the effectiveness of particle acceleration, still providing a flat momentum power-law spectrum of the accelerated particles. In the opposite case of small Peclet numbers G(p)≪1 at all momenta, the momentum spectrum at the shock steepens to the greater spectral index ξ{sub 0}=3−s+(3.18/Γ{sub 1}), whereas the volume-integrated momentum spectrum flattens by the same factor 2−s for its power-law spectral index, where s denotes the spectral index of the downstream power spectrum of magnetostatic turbulence. This effectiveness of relativistic shocks in generating flat power-law momentum spectra irrespective of the Peclet number G(p) differs completely from the behavior of nonrelativistic shocks.
Integrated optical signal processing with magnetostatic waves
Magneto-optical devices based on Bragg diffraction of light by magnetostatic waves (MSW's) offer the potential of large time-bandwidth optical signal processing at microwave frequencies of 1 to 20 GHz and higher. A thin-film integrated-optical configuration, with the interacting MSW and guided-optical wave both propagating in a common ferrite layer, is necessary to avoid shape-factor demagnetization effects. The underlying theory of the MSW-optical interaction is outlined, including the development of expressions for optical diffraction efficiency as a function of MSW power and other relevant parameters. Bradd diffraction of guided-optical waves by transversely-propagating magnetostatic waves and collinear TE/TM mode conversion included by MSW's have been demonstrated in yttrium iron garnet (YIG) thin films. Diffraction levels as large as 4% (7 mm interaction length) and a modulation dynamic range of approx 30 dB have been observed. Advantages of these MSW-based devices over the analogous acousto-optical devices include: much greater operating frequencies, tunability of the MSW dispersion relation by varying either the RF frequency or the applied bias magnetic field, simple broad-band MSW transducer structures (e.g., a single stripline), and the potential for very high diffraction efficiencies.
Three-dimensional magnetostatic models of the large-scale corona
A special class of magnetostatic equilibria is described, which are mathematically simple and yet sufficiently versatile so as to fit any arbitrary normal magnetic flux prescribed at the photosphere. With these solutions, the corona can be modeled with precisely the same mathematically simple procedure as has previously been done with potential fields. The magnetostatic model predicts, in addition to the coronal magnetic field, the three dimensional coronal density which can be compared with coronagraph observations.
Isothermal magnetostatic atmospheres. II - Similarity solutions with current proportional to the magnetic potential cubed
The paper presents a family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model J is directed along the x-axis, where x is the horizontal ignorable coordinate. The current J is taken to be proportional to the cube of the magnetostatic potential A and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. A range of similarity solution examples are displayed depending on the values of the similarity parameters. Each similarity parameter corresponds to a symmetry of the underlying nonlinear elliptic equation for A. The similarity parameters also determine the source currents for the potential field solution of the family. The solutions show the interplay between the gravitational force, the J & B force (B, magnetic field induction) and the gas pressure gradient.
Isothermal magnetostatic atmospheres. III - Similarity solutions with current proportional to the magnetic potential squared
A family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is considered. It is assumed that the current (J) is proportional to the square of the magnetostatic potential and falls off exponentially with distance. Results are presented for the contributions of the anisotropic J x B force (where B is the magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.
A magnetostatic-coupling based remote query sensor for environmental monitoring
A new type of in situ, remotely monitored magnetism-based sensor is presented that is comprised of an array of magnetically soft, magnetostatically-coupled ferromagnetic thin-film elements or particles combined with a chemically responsive material that swells or shrinks in response to the analyte of interest. As the chemically responsive material changes size the distance between the ferromagnetic elements changes, altering the inter-element magnetostatic coupling. This in turn changes the coercive force of the sensor, the amplitude of the voltage spikes detected in nearby pick-up coils upon magnetization reversal and the number of higher-order harmonics generated by the flux reversal. Since the sensor is monitored through changes in magnetic flux, no physical connections such as wires or cables are needed to obtain sensor information, nor is line of sight alignment required as with laser telemetry; the sensors can be detected from within sealed, opaque or thin metallic enclosures.